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All Classical-physics Formulas List

Where,

m = Mass,
a = Acceleration

Where,

W =Work
F = Force
D = Distance

Total Work Done

Total Work:

where,
WT = Total Work,
m =Mass,
vi =Initial Velocity,
vf = Final Velocity.

where,
P = Power,
W = Work,
T = Time

Power with Displacement

Time:

where,
P = Power,
F = Force,
D = Displacement,
T = Time.

where,
P = Power,
F = Force,
V = Velocity

Kinetic Energy

Ek = 1/2 (mv2)

Mass:

m = Ek / 1/2 (v2)

Where,

m = Mass,
v = Velocity.

Potential Energy

PE = m x g x h

m = PE / (g x h)

g = PE / (m x h)

Height:

h = PE / (m x g)

Where,

m = Mass,
g = Acceleration of Gravity
h = Height
Gravitational Acceleration of the earth is 9.8 m/sec2.

where,
v =Velocity

Concave Mirror Magnification

Formula:

M = h i / h o

Where,

M = Magnification
hi = Image Height
ho = Object Height

F=mv2/r
r=mv2/F
v=√(Fr/m)
m=Fr/v2

Where,

F=Force
m= Mass
v= Velocity

where,
T =Time Period.

Velocity

Time:

where,
v = Velocity,
v0 = Initial Velocity
a = Acceleration,
t = Time.

Average Velocity

va = ½ (v0 + v)

v0 = 2xva - v

Velocity:

v = 2xva - v0

where,
v0 = Initial Velocity
v = Velocity.

Displacement or Distance

Average Velocity from Equation for Constant Acceleration:

Time:

where,
va = Average Velocity
t = Time.

Kinetic Friction

Normal Force:

where,
μk = Kinetic Friction Coefficient,
N = Normal Force.

Static Friction

Normal Force:

where,
μs = Static Friction Coefficient,
N = Normal Force.

Newton's Law of Gravitation

Distance Between the Objects:

Where,

G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2
m1 =Mass of Object 1
m2 =Mass of Object 2
r = Distance Between the Objects.

Kepler's Third Law

Planet Mass:

where,
G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2
r = Satellite Mean Orbital Radius
M =Planet Mass

Acceleration due to Gravity

Planet Mass:

where,
G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2
M = Planet Mass
r = Radius from Planet Center

Escape Velocity

Planet Mass:

where,
G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2
M = Planet Mass

Hooke's Law

Spring Equilibrium Position:

where,
Fx = Force,
k = Spring Force Constant,
x =Distance from Equilibrium,
x0 = Spring Equilibrium Position.

Elastic Potential Energy

Spring Stretch Length:

where,
U = Spring Potential Energy,
k = Spring Force Constant,
x = Spring Stretch Length.

Newton's Second Law of Motion

Acceleration:

where,
Fnet = Net Force
m = Mass
a = Acceleration.

Impulse with Velocity

Velocity Change:

where,
I = Impulse,
m = Mass,
Δv = Velocity Change.

Impulse with Time

Time Change:

where,
I = Impulse,
F = Force,
ΔT = Time Change.

Momentum with Velocity

Velocity Change:

where,
ΔM = Momentum Change,
m = Mass,
Δv = Velocity Change,

Momentum with Time

Time Change:

where,
ΔM = Momentum Change,
F = Force,
ΔT = Time Change.

Moment Force, Lever Arm Length

Lever Arm Length:

where,
M = Moment,
F = Force,
l = Lever Arm Length.

Simple Pendulum

Acceleration of Gravity:

Where,

T = Period
L = Length
g = Acceleration of Gravity

Physical Pendulum

Distance from Center of Mass to Pivot:

where,
T = Period,
I = Center of Mass or Moment of Inertia,
M = Mass,
g = Acceleration of Gravity,
D = Distance from Center of Mass to Pivot.

Torque

Distance or Length:

where,
T =Torque,
F =Force,
D =Distance or Length.

where,
d = Density,
m = Mass,
v = Volume

Einstein Mass Energy

Speed of Light in a Vacuum:

where,
E = Energy,
m = Mass,
c = Speed of Light in a Vacuum.

Where,

S = Stress
F = Force
A = Area

Strain

Length:

where,
S = Strain,
Lc = Change in Length,
L = Length

Youngs Modulus

Strain:

Where,

Y = Young's Modulus,
S = Stress,
St = Strain.

Ups Power Requirement

Formula Used :

Minimum UPS Capability = sysvoltage × ( addition of all device amps value ) + 1.4 × ( addition of all device watts value )

Where,

sysvoltage = System (AC) Voltage

Projectile Motion for Vertical Velocity

Time:

where,
Vy = Vertical Velocity at Time
Vy0 = Initial Vertical Velocity
g = Acceleration of Gravity
t = Time.

Projectile Motion for Vertical Displacement

Time:

where,
Δy = Vertical Displacement at Time
Vy0 = Initial Vertical Velocity
g = Acceleration of Gravity
t = Time.

Projectile Motion for Horizontal Displacement

Time:

where,
Δx = Horizontal Displacement at Time
Vx0 = Initial Horizontal Velocity
t = Time.

Projectile Motion for Range

Acceleration of Gravity:

where,
R = Range
V0 = Initial Velocity
g = Acceleration of Gravity.

Doppler Effect Wavelength Front

Source Frequency:

where, λf = Wavelength in Front of a Moving Source v = Wave Velocity us = Source Velocity f0 = Source Frequency.

Doppler Effect Wavelength Behind

Doppler Effect Wavelength Behind:

Wavelength in Behind of a Moving Source:
Wave Velocity:
Source Velocity:
Source Frequency:
where, λf = Wavelength in Behind of a Moving Source v = Wave Velocity us =Source Velocity f0 = Source Frequency.

Doppler Effect Approaching Source

Wavelength in Front of Source:

where, f =New Frequency of Approaching Source v =Wave Velocity λf = Wavelength in Front of Source.

Doppler Effect Receding Source

Wavelength Behind Source:

where, f' = New Frequency of Receding Source v = Wave Velocity λb = Wavelength Behind Source.

Wave Velocity:

where, f' = New Frequency of Approaching Receiver f0 = Source Frequency ur = Receiver Velocity v = Wave Velocity.

Wave Velocity:

where, f' = New Frequency of Receding Receiver f0 = Source Frequency ur = Receiver Velocity v = Wave Velocity.

Wood Density

Formula:

Density = Mass / Volume Wood varies considerably in weight per constant volume on a regional level and at the local level. Compare the densities of several wooden blocks.

Differential Pressure Measurement

Formula:

Differential Pressure = (1.59923 x P x d4 x ρ) / W2

Where,

P = Change in Pressure
d = Pipe Diameter
ρ = Fluid Density
W = Mass Flow Rate

Sound Pressure Level

Reference Pressure:

where,
SPL = Sound Pressure Level,
P = Sound Pressure,
Pref = Reference Pressure.

Sound Intensity Level

Reference Intensity:

where,
IL = Sound Intensity Level,
I = Sound Intensity,
I0 = Reference Intensity.

Sound Power Emitted

Radius or Distance from Point Source:

where,
PAV = Power Emitted,
I = Sound Wave Intensity,
r = Radius or Distance from Point Source.

Sound Wavelength

Wave Velocity:

where,
W = Wavelength,
F = Wave Frequency,
V = Wave Velocity.

Free Fall

Formula:

h = (1 / 2) * g * t 2
v = g * t

Related Calculator:

Where,

h = Free Fall Distance
g = Gravitational Force
t = Free Fall Time
v = Free Fall Velocity

Noise Pollution Level

Noise Pollution Level:

where,
NPL = Noise Pollution Level,
L10 = Level exceeded 10 Percent of Time,
L50 = Level exceeded 50 Percent of Time,
L90 = Level exceeded 90 Percent of Time.

Battery Storage Rating

Battery Storage Rating Calculation Formula:

BLT= Capacity of batery / Consumption of the device * 0.70

Celsius to Fahrenheit Conversion

Formula:

Tf = ( (Tc * 9) / 5 ) + 32

Where,

Tc = temperature in degrees Celsius,
Tf = temperature in degrees Fahrenheit

Fahrenheit to Celsius Conversion

Formula:

Tc = (Tf - 32) * (5 / 9)

Where,

Tc = temperature in degree Celsius,
Tf = temperature in degree Fahrenheit

True Porosity

Formula:

True porosity = ( 1 - ( Ga / Gt ) ) x 100 )

Where,

Ga - Apparent Solid Specific Gravity
Gt - True Specific Gravity

Souders Brown Equation

Souders Brown Equation:

V = ( K x √((PL - PV) / PV) )

Where,

V = Maximum Allowable Vapor Velocity
K = Vapor Velocity Factor
PL = Liquid Density
PV = Vapor Density

Concave Mirror Equation

Formula :

Where
,
f - Focal length,
di - Image distance,
d0 - Object distance.

Constant Q Transform

Formula :

δfk = (21 / n)k x δfmin

Where,

δfk - Frequency of k-th filter
n - Number of filters per octave
fmin - Centre frequency of the first bin

Horsepower (HP)

Formula:

Rotating Horsepower(HP) = T * (N / 5252) Watt

Where,

T - Torque
N - Speed

Moment of Inertia

Formula Used:

Moment of inertia = M * D2

Where,

M = Angular Mass of the Hollow material
D = Distance between axis and rotation

Transverse Strength of a Material

Formula Used:

Transverse strength of a Material = ( 8 * P * L) /( 3.14 * d3 )
where,
L - Average distance
D - Diameter

Standard Surface Factor

Formula:

Standard surface Factor(SSF) = [ (6 / s) * ( w1 / d1 + w2 / d2 + w3 / d3 + w4 / d4)]
where,
s - specific gravity of the material,
w - weight,
d - diameter.

Rectangular Tank Capacity

Formula Used:

Capacity (Cubic Inches) = Length x Width x Height
Capacity (Gallons) = capacity (cubic inches) / 231

Torsional Pendulum

Formula Used:

t = 2pi sqrt( l I0 / kt)
where,
pi = Constant(3.14)
t = Period [s]
l = Length of the spring[m]
I0 = Moment of Inertia of Bob [kgm2]
kt = Torsional Rigidity [Nm2]

Apparent Porosity

Formula:

E = [(S - W) / (S - I)] x 100

Where,

S = Weight of Piece Soaked
W = Weight of Dry Piece
I = Weight of the Piece Soaked and Immersed
E = Apparent porosity

Kinematic Viscosity

Formula Used:

v = m/p

Where,

v = Kinematic Viscosity [m2s-1]
m = Dynamic Viscosity [Nsm-2] ρ
= Density [kgm-3]

Speed of Sound

Formula Used:

c = sqrt [ γ * (p0/ ρ )]
where,
γ = Ratio of specific heats
P0 = Pressure [Pa]
ρ = Density [kgm-3]

Cylindrical Tank Capacity

Formula:

C (Cubic Inches) = ( ( Length × 3.1415 × Diameter2) / 4)
C(Gallons) = C (Cubic Inches) / 231

Where,

C = Capacity

Formula:

RMax = ( ( Pt *G* S * Ae ) / ( ( 4 * PI)2 * PMin))

Where,

Pt = Transmitted Pulse Peak Power
G = Maximum Power Gain of Antenna
Ae = Antenna Aperture
S = Radar Cross Section Area
PMin = Minimum Detectable Signal of Receiver

Lensmaker's Equation

Lensmaker's equation:

1/f = (n1/nm-1) * (1/r1-1/r2)

Where,

n1 -Refractive Index of Lens Material
nm -Refractive Index of Ambient Medium
r1 -Radius of Curvature of the First Surface
r2 - Radius of Curvature of the Second Surface

Podmore Factor

Formula Used:

Podmore Factor = ( ( Solubility * 100 ) / ( Specific Surface ) )

Leaf Spring Rate

Leaf Spring Formula:

k=8Enbt3/3l3
where,
E = Youngs modulus [Nm-2]
n = Number of leaves
b = Width of leaves [m]
t = Thickness of leaves [m]
L = Span [m]

Critical Frequency

Formula:

f c = [ sqrt(3)c2/pi*d ] * [ sqrt(ρ/Y) ]
where,
fc = Coincidence Frequency [Hz]
c = Speed of sound in air [ms-1]
d = Thickness of panel [m]
ρ = Density of panel [kgm-3]
Y = Youngs modulus of panel [Nm-2]

Brinell Hardness Number (BHN)

Formula:

BHN = 2P / [ πD(D - √(D2-d2)) ]

Where,

D = Steel Ball Diameter
d = Depression Diameter

Voltage Divider Rule

Formula:

Vout = [ Rb / (Ra+Rb) ] x Vin

where,
Vin = Input Voltage
Vout = Output / Reference Voltage
Ra, Rb = Resistances

Electrodialysis (ED)

Formula:

I = ( F * N * Q * E1 ) / ( n * E2 )

Where,

F = Faraday's Constant = 96487 coulombs/g-equivalent
N = Normality of the solution
Q = Flow rate
E1 = Removal Efficiency
E2 = Current Efficiency
n = Number of cells
I = Current Passed through Ion exchange membrane

Amount of Substance

Formula Used:

Amount of substance (n)=Mass (m)/Molar mass (M)

Angular Acceleration

Formula:

α = T / I

Where,

α = Angular Acceleration
T = Total torque exerted on the body
I = Mass moment of inertia of the body

Battery Charging Time

Formula:

MTFC (10% Efficiency Loss) = ((BC / CRC) * 11) / 10
MTFC (20% Efficiency Loss) = ((BC / CRC) * 12)/10
MTFC (30% Efficiency Loss) = ((BC / CRC) * 13)/10
MTFC (40% Efficiency Loss) = ((BC / CRC) * 14)/10
MTFC (No Efficiency Loss) = ((BC / CRC) * 10)/10

Where,

MTFC - Maximum Time To Full Charge
BC - Battery Capacity
CRC - Charge Rate Current

Kva (Kilovolt-amps)

Formulas Used:

Three phase = I x V x 1.732 / 1000
One / single phase = I x V / 1000

Where,

I = Amps
V = Volts

Newton's Law of Cooling

Formulas Used:

T(t) = Ts + (To - Ts)*e^(-k*t)

Where,

T = Core temperature
t = time
Ts = Surrounding constant temperature
To = Initial temperature of the object
T(t) = Temperature of the object at time

Kilograms (kg) to Pounds (lbs) Conversion

Formulas Used:

pounds = kilograms x 2.2 and Kilograms = pounds/2.2

Potentiometer

Voltage Divider Formula:

VL=R2RL / ( ( R1RL+R2RL+R1R2)*Vs )

Infusion with Calibrated Tubing

Infusion with Calibrated Tubing Formula:

where,
VO = Ordered volume
CAL = IV calibration
RATE = IV Rate
CF = Conversion Factor = (UDO/USDA)
UDO = Units Dose Ordered
USDA = Units Standard Dose Available

RMS Noise Voltage

Formula for the RMS noise voltage:

Vn =sqrt( 4 * kB * T *If *R )
where,
Lu in dBu has the reference voltage V0 = 0.7746
and LV in dBV has the reference voltage V0 = 1 V
Boltzmann constant kB = 1.3806505*10-23 J/K (joule/kelvin); J=WÂ·s
Absolute temperature in kelvin T = 273.15
Bandwidth being considered .If = f2 - f1 = fmax - fmin in Hz; 20 kHz - 20 Hz = 19980 Hz
Resistance of the circuit element R.
R does not mean the universal gas constant!

Milling Speed, Feed Rate

Formula:

Mill spindle speed = CS*4/D

where
cs-cutting speed
D - diameter
n = number of flutes on the tool

Mass Flow Rate

Formula:

Mass Flow Rate(kg/hour) = (p × v × a)×3600

Where,

p = Density of the Flowing Liquid or Gas(kg/m3)
v = Flow Speed(m/s)
a = Flow Area(m2)

Drift Velocity

Drift velocity Formula :

V = I /(n*Q*A)

Where,

V = Drift velocity
I = Flow of current
n = Number of electrons
Q = Charge of electron
A = Cross section of area of wire

Gsm of Paper

Weight of Paper Calculation Formula:

Substance in gsm = (Weight of reel in kgs * 100000)/(Length of paper on meter * reel width in cms)

Helical Spring Rate

Formula:

K=(G*d)/(8*C3*N)

Where,

K = Spring Rate
d = Wire Diameter
N = Number Of Active Coils
G = Modulus of Rigidity
C =Spring Index

Helical Spring Axial Deflection

Formula:

D=((8*F*C3*N)/(G*d))*(1+(0.5/C2))

Where,

D = Spring Axial Deflection
F = Axial Force
d = Wire Diameter
N = Number Of Active Coils
G = Modulus of Rigidity
C = Spring Index

Helical Spring Index

Formula:

C = D/d

Where,

C = Spring Index
D = Spring Diameter
d = Wire Diameter

D Exponent

Formula

d = [ (log ( R / (60 × N) ) / log ( (12 × W) / (1000 × D) ) ] × ( Pn / Pm )c

Where,

d = d-exponent value
R = Penetration Rate
N = Rotary Speed
W = Weight on Bit
D = Drill Bit Diameter
Pn = Mud Weight Equivalent
Pm = Mud Weight Used
C = Shale Compactibility Coefficient

Gravitational Potential Energy

Formula:

Gravitational Potential = −(G×M(kg)) / x(m)

Where

G = 6.674 × 10-11 N(m/kg)²
M = Mass
x = Distance

Sound Decibel Distance

Formula Used:

Decible Distance (dB) = 20 × log(d1 ÷ d2)

Where,

d1 - Initial Distance from noise source
d2 - Target Distance from noise source

Offset Frequency Speed Error

Formula :

Vm = (fx × Vo) / fo
Verr = Vm - Vo

Where,

Vm = Measured Vehicle Speed
fx = Transmit Frequency
Vo = Traffic Speed
fo = Center Frequency
Verr = Vehicle Speed Error

Formula :

Shifted Frequency (Fr) = Ft × ( (1+(v/c)) / (1-(v/c)) )
Doppler Frequency (Fd) = Fr - Ft

Where,

Ft = Original Frequency
v = Target Velocity
c = Speed of Light

Motor Top Speed RPM

Formula :

Speed = Total RPM * Total Length
Total RPM (Revolutions per Minute) = RPM value * 60
Total Length = Circle * 0.00001578
Area of Circle = 2 * π * Radius

P=MV

Where,

P = Power
M = Mass
V = Velocity

Speedometer Calibration

Formula Used:

Motorcycle Speedometer Calibration (SC) = T *A/24.5*2+R.

Where,

T = Width of the tire.
A = Ratio of height to its corresponding width.
R = Rim diameter.

Vehicles Angle, Angular Rate

Formula:

Vehicle Angle =tan(distance/range)*180/Math.PI

One Dimensional Motion with Constant Acceleration

Formula Used:

x(t) = 1/2(at2) + v0t + x0

Where
,
x(t) = Position at time t
a = 9.8 m/s2 (Gravity of Earth)
v0 = Velocity at time t=0
x0 = Position at time t=0
t = Time

Kirchhoff's Voltage Law (KVL) / Loop Rule

Formula Used:

VT = VR0 + VR1 + VR2 + ... + VRn

Where,

n = Number of Voltages
VT = Total Voltage

Helix Curve - Circumference, Length, Unit Rise, Handrail Radius

Formula:

Circumference = 2πr
h = (height of helix x 360) / angle
Length = √h2 + circumference2
Unit Rise = h / circumference
Handrail Radius = (4π2r2 + h2) / 4π2r

Where,

π = 3.1415926
h = Height required for Helix to complete one revolution

3 DB Bandwidth, Cutoff Frequency

Formula:

Where,

Q = Quality factor

Wien's Displacement Law

Formula:

λ = b / T

Where,

λ = Peak Wavelength
b = 0.028977 mK (Wien's constant)
T = Temperature

HP (Horsepower) to Amps Conversion

Formula:

1 Ph.Amps = ((( (746 x hp) / V ) / E.F ) / P.F )
1.FLA = ( (1 Ph.Ampere) x 1.25 )
3 Ph.Amps = (((( (746 x hp) / 1.732 ) / V ) / E.F ) / P.F )
3.FLA = ( (3 Ph.Ampere) x 1.25 )

Where,

V - Volts,
E.F - Efficiency,
P.F - Power factor,

Graham's Law of Effusion

Graham's law of effusion:

Rate1 / Rate2 =âMass2 / Mass1

Snell's Law Refraction

Formula:

n1 sinθ1 = n2 sinθ2

Where,

n1 = Refractive Index of first medium
n2 = Refractive Index of second medium
sinθ1 = Angle of Incidence
sinθ2 = Angle of Refraction

Vehicle Speed Error

Formula:

Speed Error =(100-Ms)/100*100
Ms=(100*T1)/(T1-Terr)

Or,
Ms=(D1-Derr)/(D1/Derr)

Where ,

Ms=Measured Traffic Speed
T1=Actual Time
Terr=Time Error
D1=Actual Distance
Derr=Distance Error

Root Mean Square Velocity Calculator

Formula :

μrms = (3RT/M)½

Where,

R = Ideal gas constant => 8.3145 (kg m2/sec2)/K mol
T = Absolute temperature in Kelvin
M = Molecular weight of the gas in kilograms

One Dimensional Motion Velocity

Formula:

v2 = u2 + 2as

Where,

v = Final Velocity
u = Initial Velocity
a = Acceleration
s = Distance

Acceleration Due to Gravity on Outside Earth

Formula:

g' = ( re2 / r2) * g

Where,

g - Earth Surface
r - Outside Radius of Earth
g' - Acceleration due to gravity

Boltzmann Gas Constant

Formula :

k = R / NA

Where,

k = Boltzmann constant
R = Gas constant
NA = Avagetro

De Broglie Wavelength

Formula :

λ = h / (m×v)

Where,

λ = Wave length
h = Plank's Constant (6.62607 x 10-34)
m = Mass
v = Frequency

Average Translational Kinetic Energy

Formula :

Average Translational KEmolecule = (3/2)kB × T

Where,

kB = Boltzmanns constant = 1.38 x 10-23 J/K

Energy of Photon

Formula:

Ephoton = hv

Where,

Ephoton = Energy of Photon,
v = Light Frequency,
h = Planck's constant = 6.63 × 10-34 m2 kg / s

Nature of Light

Formula :

ν = c/λ

Where,

ν = Frequency of Light,
c = Speed of Light = 29979245800,
λ = Wave Length

Ft = Fn - Ff

Where,

Ft = Ftidal
Fn = Fnear
Ff = Ffar

Angular Linear Velocity

Formula:

LV = x/t km/hr

Where,

ω=Angular velocity.
LV=Linear velocity.
θ=Angle the object traversed
x=Distance covered
t=Time taken

Planck's Constant

Formula:

Energy of Photon (E) =hc/λ or E =hv

Where,

h=planck's constant (6.6260695729x10-34)
c=velocity of light ( 2.99792458x108)
λ=Wavelength
v=Frequency

Vector Displacement

Formula:

Where,

(x1,y1) -> Co-ordinates of point P
(x2,y2) -> Co-ordinates of point Q
|r| = Displacement vector

Average Acceleration

Formula:

Average Acceleration = (Velocity Difference) / (Time Difference) = (vf - vi)/(tf - ti)

Where,

vi = Initial Velocity
vf = Final Velocity
ti = Initial Time
tf = Final Time

Kinematic Displacement By Velocity and Time

Kinematics Equation Formula:

d =(( v0+vf)/2)*t

Where,

d = displacement
v0 = inital velocity,
vf = final velocity,
t = time

Kinematic Distance

Kinematics Equation Formula:

d = (v * t ) + 1/2 (a * t2)

Where,

d = displacement,
v = velocity,
t = time,
a = acceleration

Kinematic Final Velocity

Kinematics Equation Formula:

vf= v0+a*t

Where,

vf = final velocity
v0 = initial velocity
a = acceleration
t = time

Kinematic Velocity

Kinematics Equation Formula:

vf =√( v0*v0)+(2*(a*d))

Where,

v0 = inital velocity
vf =final velocity
a = acceleration
d = displacement

Focal Length of Optical Convex

Formula:

f = (R1 × R2) / ((n-1) × (R2 - R1))

Where,

f = Focal Length

n = Index of Refraction

Magnitude of Vector

Formula:

Length of Vector = √X2 + Y2

Moment of Inertia of a Point Mass for Rod

Formula:

I = 1/2×(m×r2)

Where,

I = Moment of Inertia

m = Mass

r = Length of Rod

W = F cos(θ) d

Where,

W = Work

F = Force

d = Distance

θ = Angle

Sound Wave Velocity

Formula :

Wave Velocity Equation (v) = Frequency (f) * Wavelength (Î»)

Calculate Time Duration from Earth to Moon

Formula:

Time = (2 x d) / s
Where,

d = Light distance from earth to moon (approximately 384403 km)
s = Travelling speed of laser pulse

Ceramic Transverse Strength

Formula :

MT = (8PL) / (πd3)

Where,

MT = Transverse Strength
L = Average Distance
π = 3.1415
d = Diameter

Inelastic Collision

Formula:

m1v1 = (m1+m2)v2

Where

m1,m2 - Mass of Objects
v1,v2 - Velocity of Objects

Elastic Collision

Formula:

v1' = ((m1 - m2) / (m1 + m2)) v1
v2' = (2m1 / (m1 + m2)) v1

Where

m1,m2 - Mass of Moving Objects
v1 - Velocity of Moving Objects

Formula:

V' = a x T
a = v / t

Tangential acceleration = A x R
A = W / t
W = V'/ R

Where,

v = Final Velocity,
a = Final Acceleration
t = Final Velocity Time
W = Angular Frequency
A = Angular Acceleration
T = Acceleration at Time

Maximum Height of Projectile

Formula:

s = (vf2 - vi2) / 2a
where,
s = Distance travelled
vi = Initial velocity
vf = Final velocity
a = Acceleration

Tension of Wire Rope Holding a Load

Formula

Tension = ( Mass x Acceleration ) + ( Mass x Gravity )

Where,

Gravity = 9.8 m/s2 is Earth Gravity

Normal Force of an Object at Rest

Formula:

Normal Force of an Object at Rest = Mass (m) * Gravitational Force (F)

Normal Force of an Object on an Inclined Plane

Formula:

N = m * g * cos(x)

Where,

N = Normal Force of an Object on an Inclined Plane
m = Mass,
g = Gravitational Force,
x = Angle of Incline,

Normal Force of an Object with External Downward Force

Formula:

N = m * g + F[sin(x)]

Where,

N = Normal Force of an Object with External Downward Force
m = Mass,
g = Gravitational Force,
x = Angle of Incline,
F = Force,

Normal Force and Kinetic Friction

Formula :

N = f /μ

Where,

N = Normal Force
μ = Friction Coefficient,
f = Kinetic Friction

Refractive Index Formula

Formula

n = c / ν

Where,

n = Index of refraction
c =Velocity of light in vacuum
ν = Velocity of light in the medium

Hoop Stress

Formula:

σa =((pi x ri2 - po x ro2) / (ro2 - ri2)) - (ri2 x ro2(po - pi) / (r2 x (r02 - ri2))

Where,

σa = Hoop (Circumferential) Stress in Cylindrical Wall or Tube
pi = Internal Pressure in the Tube
po = External Pressure in the Tube
ri = Internal Radius in the Tube
ro = External Radius in the Tube
r = Radius to point in tube

Solid Shaft Maximum Torque

Formula:

Tm = (π/16) * τm * D3

Where,

π = 3.14
Tm = Maximum Twisting Moment or Torque
τm = Maximum Shear Stress
D = Solid Shaft Outside Diameter

Solid Shaft Diameter

Formula:

D = 1.72 * (Tmax / τmax)1/3

Where,

D = Diameter of Solid Shaft
Tmax = Maximum Twisting Moment
τmax = Maximum Shear Stress

Shear Stress in Shaft

Formula:

τ = (T * r) / J

Where,

τ = Shear Stress in Shaft
T = Twisting Moment
r = Distance from Center to Stressed Surface in the Given Position
J = Polar Moment of Inertia of an Area

Lowest Spring Resonant Frequency

Formula:

fres = (1/2) x √(K / M)

Where,

fres = Lowest Spring Resonant Frequency
M = Mass of Spring
K = Spring Constant

Hollow Shaft Maximum Torque

Formula:

Tmax = ( π / 16) x τmax x ((D4 - d4) / D)

Where,

Tmax= Maximum Torque (Twisting Moment) in Hollow Shaft
τmax = Maximum Shear Stress
D = Shaft Outside Diameter
d = Shaft Inside Diameter

Total Energy

Formula:

RE = m * c2
KE = (γ - 1) * (m * c2)
TE = RE - KE

Where,

RE = Rest Energy
TE = Total Energy
KE = Kinetic Energy
m = Mass
c = Speed
γ = Gamma Factor

Work Done by Frictional Force

Formula:

W(f) = F(f) * d

Where,

W(f) = Work Done by Frictional Force
F(f) = Frictional Force
d = Distance Moved

Tangential Velocity

Formula:

Vt = r ω

Where,

Vt = Tangential Velocity (meter per second)
ω = Angular Velocity ( 20 * π )

Peukerts Law

Formula:

Actual Battery Capacity = (C x I) / In
Peukert's Formula, T = C / In

Where,

C = Rated Battery Capacity
I = Rate of Discharge
n = Peukert's Number
T = Full Discharge Time

Stokes Law

Formula:

F=6π×a×n×v

Where,

v = Velocity
n = Shear Viscosity
F = Drag Force a Sphere

Newton's Third Law of Motion

Formula:

FAB = - FBA

Where,

FAB = Object A Exerts a Force
FBA = Object B Exerts a Force

Horizontal and Vertical Component

Formula:

H = cos(θ) * f
V = sin(θ) * f

Where,

H = Horizontal Component
V = Vertical Component
θ = Angle
f = Force

Convex Mirror Equation

Formula:

Convex Mirror Equation
1 / f = 1 / d0 + 1 / di

f = 1/ ((1/do) + (1/di))
do = 1/ ((1/f) - (1/di))
di = 1/ ((1/f) - (1/do))

Where,

f = Focal Length
do = Object Distance
di = Image Distance

Apparent Temperature

Formula:

AT = Ta+ 0.348 * e-0.70 * ws + (0.70* (Q * (ws+10)) - 4.25)
e = (rh)/100)*6.105*e((17.27 *Ta) / (237.7+Ta))

Where,

AT = Apparent Temperature
Ta = Dry Bulb Temperature
e = Water Vapour Pressure
ws = Wind Speed at an Elevation of 10 meters
Q = Net Radiation Absorbed per unit area of Body Surface
rh = Relative Humidity

Axial Stress of Cylinder Wall or Tube

Formula:

σa =(pi * ri2 - po * ro2) / (ro2 - ri2)

Where,

σa = Stress in Axial Direction of Cylinder Wall or Tube
pi = Internal Pressure in the Tube
po = External Pressure in the Tube
ri = Internal Radius in the Tube
ro = External Radius in the Tube

Distance from Center of Gravity to Triangle Base

Formula:

A = h / 3

Where,

A = Distance from Center of Gravity to Triangle Base
h = Height

Circle Center of Gravity

Formula:

d = (h x (b + c)) / (2 x (a + b + c))

Where,

d = Center of Gravity of Circle
h = Slant Height
a = Length of Side A
b = Length of Side B
c = Length of Side C

Friction Force

Formula:

F = μ * N
μ = F / N
N = F / μ

Where,

F = Frictional Force
μ = Friction Coefficient
N = Normal Force

i = 1 / r2

Where,

i = Intensity
r = Distance

Coefficient of Friction

Formula:

μ = Fmax / Fn

Where,

μ = Coefficient of Friction
Fmax = Frictional Force
Fn = Applied Normal Force

Center of Gravity of Multiple Objects or Bodies

Formula:

Where,

xcg = Center of Gravity
mi = Mass of (multiple) i number of objects
xi = Distance of i number of objects

Torsional Deflection of a Shaft

Formula:

θ = (L * T) / ( J * G)

Where,

θ = Torsional (Angular) Deflection of Shaft
L = length of shaft or cylinder
T = Twisting Moment
J = Polar Moment of Inertia of an Area
G = Modulus of Rigidity

Drag Force on Disk

Formula:

F=16*a*n*v

Where,

v = Velocity
n = Shear viscosity
F = Drag Force on a Disk Broadside to Flow

Wood Density

Formula:

ρmax = m / Vmin
ρmin = m / Vmax

Where,

ρmax = Maximum Density
ρmin = Minimum Density
m = Wood Mass
Vmax = Maximum Volume
Vmin = Minimum Volume

Hull Speed

Formula:

H = 1.34 × √(L)
M = H × 1.1508
N = H × 1.852

Where,

H = Hull Speed in Knots
M = Hull Speed in Miles/Hr
N = Hull Speed in Kilometers/Hr
L = Boat's Waterline Length

Vickers Hardness

Formula:

HV = 1.854 * (f / d2)

Where,

HV = Vickers Hardness
d = Arithmetic Mean

Soil Moisture / Water Content

Formula:

w = (Mw / Ms) * 100

Where,

w = Moisture Content
Mw = Mass of Water in Soil
Ms = Dry Mass of Soil

Muzzle Velocity

Formula:

V = √((e * 450240) / w)

Where,

V = Muzzle Velocity
e = Airgun Energy
w = Pellet Weight

Inverse Square Law

Formula:

I1 / I2 = (d2)2 / (d1)2

Where,

i = Intensity 1
x = Distance 1
y = Distance 2
z = Intensity 2

Lever Effort Force

Formula:

Fe = (Fl * dl) / de

Where,

Fe = Lever Effort Force
dl = Distance From Load Force to Fulcrum
de = Distance From Effort Force to Fulcrum

Aggregates Volume

Formula:

Metric
Volume = Depth * Width * Length
Amount = Depth * Width * Length * Density

Imperial
Volume = (Depth * 2.54 * Width * 2.54 * Length * 30.48 / 10000) / 100
Amount = Volume * Density

Ampere

Ampere Formula:

Using Horsepower,

A = ( h * 746 ) / ( v * e ) ( For, Direct Current )
A = ( h * 746 ) / ( v * e * p ) ( For, Single Phase AC )
A = ( h * 746 ) / ( v * e * p * 2 ) ( For, Two Phase AC )
A = ( h * 746 ) / ( v * e * p * 1.73 ) ( For, Three Phase AC )

Using Kilowatts,

A = ( kw * 1000 ) / ( v ) ( For, Direct Current )
A = ( kw * 1000 ) / ( v * p ) ( For, Single Phase AC )
A = ( kw * 1000 ) / ( v * p * 2 ) ( For, Two Phase AC )
A = ( kw * 1000 ) / ( v * p * 1.73 ) ( For, Three Phase AC )

Using Kilovolts Ampere,

A = ( kva * 1000 ) / ( v ) ( For, Single Phase AC )
A = ( kva * 1000 ) / ( v * 2 ) ( For, Two Phase AC )
A = ( kva * 1000 ) / ( v * 1.73 ) ( For, Three Phase AC )

Where,

A = Ampere
kva = Kilovolt-Amp
v = Voltage
p = Power Factor
e = Efficiency
h = Horsepower
kw = Kilowatts

Formula:

R = 3√((T2GM) / (4π2))

Where,

R = Satellite Mean Orbital Radius
T = Satellite Orbit Period
M = Planet Mass
G = Universal Gravitational Constant = 6.6726 x 10-11N-m2/kg2

Pulse Repetition Frequency

Formula:

Pulse Repetitive Frequency (PRF) = C / 2 * Runamb

Where,

C = 3*108 m/s
Runamb = Unambiguous Range

Density of Sand

Density of sand = Mass of sand / Volume of calibrating container

Change In Velocity

Formula:

Velocity Change = Impulse / Mass

Gravitational Potential Energy

Formula:

Gravitational Potential Energy = Mass (kg)x Gravitational Acceleration x Height(m)

Where,

Gravitational Acceleration = 9.8 m/s2

Resultant Force

Formula:

Resultant Force = √ ((F1 × cos(A) + F2 × cos(B))2 + (F1 × sin(A) + F2 × sin(B))2)
R = tan-1(F1×sin(A) + F2 × sin(B))) / ((F1 × cos(A)+ F2 × cos(B))

Where,

F1 = First Force
F2 = Second Force
A = Direction Angle of First force
B = Direction Angle of Second Force
R = Direction Angle of Resultant Force

Brewster Angle

Formula:

θpolarizing = arctan(nt/ni)

Where,

θpolarizing = Brewster Angle / Polarization Angle
ni = Light from a Medium of Index
nt = Light Incident upon a Medium of Index

Barlow's Formula

Formula:

Pressure = (2 x S x T) / D

Where,

S = Allowable Stress
T = Wall Thickness
D = Outside Diameter

NPSHA

Formula:

NPSHa = (Pa-Pv+Pn)/ρ

Where,

NPSHa = NPSH Available
Pa = Atmospheric Pressure
Pv = Vapor Pressure
Pn = Gage Pressure at the Pump Suction
ρ = Density

Simple Harmonic Motion Calculator

Formula:

ω = 2πf
v = Aω cos (ωt)
a= - d ω2 sin (ωt)

Where,

ω = Angular Frequency
f = Frequency
v = Velocity
A = Ampltude
t = Time
d = Displacement
a = Acceleration

Horizontal Velocity

Formula:

Horizontal Velocity (V) = Distance Travelled / Time Taken

Miles Equation

Formula:

Xgrms = √[(Π / 2) F x Q x P]
Xpeak = 3 Xgrms

Where,

F = Frequency
P = Acceleration
Q = Quality Factor

Planck's Equation

Formula:

e = h × v

Where,

e = Energy of Photon
h = Planck's Constant(6.63 × 10-34 J / s)
v = Light Frequency

Period Of Oscillation

Formula:

Period of Oscillation = 2 π √(L / g)

Where,

T = Period
L = Length
g = Acceleration of Gravity

Frequency Wavelength

Formula:

Frequency (F) = C / W

Where,

C = Speed Of Light(3×108)
W = Wavelength

Wavelength Frequency

Formula:

Wavelength (λ) = C / F

Where,

C = Speed Of Light(3 × 108)
F = Frequency

Frequency to Energy

Formula:

Energy of Light (E) = 6.626 × 10 - 34 × Frequency

Wavelength to Energy

Formula:

Energy of Light = (6.626 × 10-31 × c) / w(m)

Where,

e = Energy
c = Speed Of Light(300000000 m/s)
w = Wavelength

Doppler Effect Blue Shift Frequency

Formula:

Observed Blue-Shift Frequency = F × (1+(V/C))

Where,

F = Emitted Frequency
V = Velocity Towards You
C = Speed of Light from Source

Doppler Effect Blue Shift Wavelength

Formula:

L = (E × C) / (C + V)

Where,

L = Observed Blue-Shift Wavelength
E = Emitted Wavelength
C = Speed of Light from Source
V = Velocity Towards You

Doppler Effect Blue Shift Velocity

Formula:

V = C × ((E / b)-1)

Where,

V = Blue-Shift Velocity
C = Speed of Light from Source
E = Emitted Wavelength
B = Blue-Shift Wavelength

Doppler Effect Red Shift Frequency

Formula:

Observed Red-Shift Frequency = F × (1-(V/C))

Where,

F = Emitted Frequency
V = Velocity Away from You
C = Speed of Light from Source

Doppler Effect Red Shift Velocity

Formula:

V = C × (1 - E / R)

Where,

V = Red-Shift Velocity
C = Speed of Light from Source
E = Emitted Wavelength
R = Red-Shift Wavelength

Doppler Effect Red Shift Wavelength

Formula:

L = (E × C) / (C - V)

Where,

L = Observed Red-Shift Wavelength
E = Emitted Wavelength
C = Speed of Light From Source
V = Velocity Away from You

Velocity

Velocity Time Distance Formula:

Velocity = Distance / Time
Time = Distance / Velocity
Distance = Velocity * Time

Magnitude of the Total Initial Momentum of the Two Block System

Formula:

Total Initial Momentum = M1 × V1 + M2 × V2

Where,

V1 = Velocity of Block1
V2 = Velocity of Block2
M1 = Mass of Block1(kg)
M2 = Mass of Block2(kg)

Speed of Falling Object

Formula:

s = g×t

Where,

s = Speed
g = Gravitational constant
t = Time

Gas Pressure kPa

Formula:

P = nRt / V

Where,

P = Pressure
V = Volume
n = Moles of gas
t = Temperature
R = Gas Constant (8.314 J K-1 mol-1)

t = d / s

Where,

t = Time
d = Distance
s = Speed

Hooke's Law Spring Constant

Formula:

k = F / (X - X0)

Where,

k = Spring Constant
F = Force
X = Distance from Equilibrium
X0 = Spring Equilibrium Position

Angular Momentum

Formula:

Moment of Inertia = Mass x Radius2 / 2
Angular Momentum = Moment of Inertia x Angular Speed

Work Power and Force | Power

Formula:

Force = (Time × Power) / Distance
Power = (Force × Distance) / Time
Work = Force × Distance

t = f × d / p
f = t × p / d
d = t × p / f
p = f × d / t

Where,

f = Force
d = Distance
p = Power
t = Time

Free Fall

Formula:

V = G × T

Where,

V = Downward Velocity
G = Gravitational Acceleration
T = Time of Downward Fall

Mayer's Relation

Formula:

R = Cp - Cv

Where,

R = Universal Gas Constant
Cp = Specific Heat at Constant Pressure
Cv = Specific Heat at Constant Volume

Second Moment of Area

Area Moment of Inertia Formula:

Rectangle
Ix = w × h3 / 12
Iy = h × w3 / 12

Triangle
Ix = w × h3 / 36

SemiCircle
Ix, Iy = π × r4 / 8

Circle
Ix, Iy = π × r4 / 4

Where,

Ix, Iy = Area Moment Of Inertia
w = Width
h = Height

Gauge Pressure

Formula:

Gauge Pressure = Absolute Pressure - Atmospheric Pressure

Online Total Energy

Formula:

TE = U + (mc2) / 2 + mgz

Where,

m = Mass of System
z = Height Relative Reference Frame
c = Velocity of System
U = Internal Energy
TE = Total Energy
g = Gravity (9.8 m/s)

Deceleration Distance

Formula:

Deceleration = v2 - u2 / 2s

Where,

v = The Final Velocity
u = The Initial Velocity
s = Distance

Heat Capacity at Constant Volume

Formula:

Q = n × Cv × Δ T

Where,

Q= Heat Capacity
n = Number of Moles
Cv= Specific Heat at Constant Volume
ΔT= Temperature Change

Net Force

Formula:

if the object is at rest
n = a + g

if object is not at rest
n = Sum of All Force Values of the Object

Where,

n = Net Force
a = Applied Force
g = Gravitational Force

Dc Motor Speed

Formula:

Torque = Prot / ω

Where,

Prot = Rotational Mechanical Power
ω = Angular Velocity

Total Acceleration of Disc at Moment of Release

Formula:

a = t / r

Where,

a = Total Acceleration of Disc
t = Net Tangential Acceleration

Spring Stiffness

Formula:

s=(64 × n × (m/2)3 × f)/(d4 × g × 103)

Where,

s = Spring Stiffness
n = Number of Coils
g = Shear modulus
d = Diameter of spring (metre)
m = Mean coil diameter (metre)
f = Spring Force

Von Mises Stress

Formula:

v) = √(σx2 - (σx x σy) + σy2 + (3 ×τxy2))

Where,

σv = Von Mises Stress
σx, σy = Normal Stress
τxy = Shear Stress

Maximum Shear Stress

Formula:

Maximum Shear Stress (σmax ) = √(((σx - σy)/2)2xy2)

Where,

σx, σy = Normal Stress
τxy = Shear Stress

Momentum

Formula:

Momentum = Mass x Velocity

Specific Gravity and Water Absorption Test

Formula:

Water Absorption = (S - W / W) x 100

Where,

S = Weight of Dry Piece Soaked in Fluid
W = Weight of Dry Piece in Fluid

Apparent Solid Specific Gravity

Formula:

Ga = (W x D) / (W - I)

Where,

Ga = Apparent Solid Specific Gravity
W = Weight of Dry Piece in Fluid
D = Density of Fluid
I = Weight of Dry Piece Soaked & Immersed in Fluid

Bulk Specific Gravity

Formula:

Gb = (W x D) / (S - I)

Where,

Gb = Bulk Specific Gravity
W = Weight of Dry Piece in Fluid
D = Density of Fluid
S = Weight of Dry Piece Soaked in Fluid
I = Weight of Dry Piece Soaked & Immersed in Fluid

True Specific Gravity

Formula:

Gt = (W2 - W1) / (W3 - W1) - (W4 - W2)

Where,

Gt= True Specific Gravity
W1 = Weight of S.G Bottle
W2 = Weight of S.G Bottle + Powdered Sample
W3 = Weight of S.G Bottle + Water
W4 = Weight of S.G Bottle + Water + Powdered Sample

Bagnold Number

Formula:

Bagnold Number (Ba) = (ρ × d2 × λ1/2 × γ) / μ

Where,

ρ = Particle Density
d = Grain Diameter
λ = Linear Concentration
γ = Shear Rate
μ = Dynamic Viscosity of the Interstitial Fluid

Lame's First Parameter in Three Dimensional

Formula:

λ = K - (2 / 3) x μ

Where,

K = Bulk Modulus
μ = Shear modulus
λ = Lame's First Parameter

Time of Flight

Formula:

Time of flight = (2 v0Sin(θ)) / g

Where,

T = Time of Flight (s)
v0 = Initial Velocity (m/s)
g = Acceleration Due to Gravity (9.80 m/s2)
θ = Angle of the Initial Velocity from the Horizontal Plane (radians or degrees)

Maximum Height Projectile

Formula:

Maximum height reached = V0² sin² θ / 2g

Where,

V0 = Initial Velocity
θ (sin θ) = Component Along y-axis
g = Acceleration of Gravity

Momentum with Time

Formula:

ΔT = ΔM / F

Where,

ΔM = Momentum Change
F = Force
ΔT = Time Change

Hollow Shaft Diameter

Formula:

Diameter Ratio = Inner Diameter / Outside Diameter
Inner Diameter = Diameter Ratio × Outside Diameter
Outside Diameter = Inner Diameter / Diameter Ratio

Log Volume | Doyle Log Scale

Formula:

l = (d - 4) × (d - 4) × (h / 16)
s = (0.79 × d × d - 2 × d - 4) × (h / 16)
i = (0.796 × d × d - 1.375 × d - 1.23) × (h / 16)

Where,

l = Doyle Scale
s = Scribner Scale
i = International Scale
d = Log diameter (inches)
h = Log length(feet)

Upstream Downstream

Formula:

Speed in upstream (km/hr) = a + b
Speed in downstream (km/hr) = a - b

Where,

a = Speed of a boat in still water (km/hr)
b = Speed of the stream (km/hr)

Speed of Man in Stream

Formula:

Speed of Man (km/hr)= a x ((n + 1) / (n - 1))

Where,

a = Speed of stream (km/hr)
n = Number of times to row upstream to row downstream the river

Distance Between Two Places in Water

Formula:

Distance between two places (km) = ((a2 - b2)t) / 2a

Where,

a = Speed in still water (km/hr)
b = Speed of stream (km/hr)
t = Time taken to reach place A than place B (hours)

Distance Covered by a Person in Upstream Downstream

Formula:

Distance covered by person in journey (km) = ((a2 - b2)t) / 2b

Where,

a = Speed in still water (km/hr)
b = Speed of stream (km/hr)
t = Time taken in upstream than downstream (hours)

Speed of Man in Still Water

Formula:

Speed of man in still water (km/hr)= ((b + a) / (b - a)) x c

Where,

a = Time taken to cover distance at downstream (hours)
b = Time taken to cover distance at upstream (hours)
c = Speed of stream (km/hr)

Average speed of Boat in Upstream and Downstream

Formula:

Average Speed of a Boat (km/hr) = ((a + b) x (a - b)) / a
Speed in Downstream (km/hr) = a + b
Speed in Upstream (km/hr) = a - b

Where,

a = Speed in Still Water (km/hr)
b = Speed of Stream (km/hr)

Speed of Boat in Still Water

Formula:

Speed in still water (km/hr)= (1 / 2) (a + b)
Rate of stream (km/hr)= (1 / 2) (a - b)

Where,

a = Downstream (km/hr)
b = Upstream speed (km/hr)

Relation Between Momentum and Kinetic Energy

Formula:

K = P2/ 2 m

Where,

P = Momentum
m = Mass of the Particle
K = Kinetic Energy

P = G2* u *V

Where,