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# All Civil Engineering Formulas List

## Cantilever Beam Stiffness

#### Formula Used:

Stiffness (k) = (3 × E × I ) / l3

Where,

E - Young's Modulus
I - Area Moment of Inertia
l - Length

## Colebrook White Equation

#### Formula :

where,
S - hydraulic gradient,
v - kinematic viscosity of water,
D - Internal diameter,
Ks - Roughness coefficient,
g = 9.81 m/s2,
A - Area of section.

## Cantilever Beam Slope, Deflection With Couple Moment

#### Formula Used:

Slope at free end = ML / EI
Deflection at any section = Mx2 / 2EI

Where,
M is the couple moment at the free end,
E is the Elastic Modulus,
I is the Area moment of Inertia,
L is the Length of the beam and
x is the position of the load.

## Cantilever Beam Slope, Deflection with Uniformly Distributed Load

#### Formula Used:

Slope at free end = PL3 / 6EI
Deflection at any section = Px2( x3 + 6L2 - 4Lx ) / 24EI

Where,

P is the externally applied load,
E is the Elastic Modulus,
I is the Area moment of Inertia,
L is the Length of the beam and
x is the position of the load

## Cantilever Beam Slope, Deflection for Uniform Load

Formula Used:
Slope at free end = P0L3 / 6EI
Deflection at any section = P0x2 ( x3 + 6L2 - 4Lx ) / 24EI
P0 = PL / (L-x)

Where,
P0 is the Maximum intensity,
P is the Externally applied load,
E is the Elastic Modulus,
I is the Area moment of Inertia,
L is the Length of the beam and
x is the position of the load.

## Cantilever Beam Slope, Deflection for Load at Free End

#### Formula

Slope at free end = PL2 / 2EI
Deflection at any section = Px2(3L-x) / 6EI

Where,

P is the externally applied load,
E is the Elastic Modulus,
I is the Area moment of Inertia,
L is the Length of the beam and
x is the position of the load

## Cantilever Beam Slope, Deflection for Load at Any Point

#### Formula Used:

Slope at free end = Pa2 / 2EI
Deflection at any section = Px2(3a-x) / 6EI(for x less than a)
Deflection at any section = Pa2(3x-a) / 6EI(for a less than x)

Where,

P is the externally applied load,
E is the Elastic Modulus,
I is the Area moment of Inertia,
Lis the Length of the beam and
x is the position of the load
a is the distance of load from one end of the support

## Feet and Inches Arithmetic

#### Formula Used:

Multiplication = ( (Value1-ft X 12) + in) X ( (Value2-ft X 12) + in) Addition = ( (Value1-ft X 12) + in) + ( (Value2-ft X 12) + in) Subtraction = ( (Value1-ft X 12) + in) - ( (Value2-ft X 12) + in) Division = ( (Value1-ft X 12) + in) / ( (Value2-ft X 12) + in)

Where,

ft - Feet
in - Inches

## Flexible Pavement Structural Number

#### Formula:

L=a1ta + b1tb + c1tsb +d1tad

Where,

L=Structural Number of Flexible pavement,
a1=Layer coefficient for asphalt ,
ta=Asphalt layer thickness,
b1=Layer coefficient of base,
tb=Base layer thickness ,
c1=Layer coefficient of sub-base,
tsb=Sub-base layer thickness,
d1=Layer coefficient of additional layer,

## Vertical Curve Offset Distance

#### Formula Used:

E = [ L x (g2 - g1) ] / 8

Where,

E - Vertical Offset
g1 - Initial grade
g2 - Final grade
L - Length of the curve

## Vertical Curve Length

Formula Used:
Lm = [ S² × (g2 − g1) ] / 864 ∀ S<Lm
Lm = 2S - [ 864 / (g2 − g1) ] ∀ S>Lm

Where,
Lm - Minimum Curve length
g1 - Initial grade
g2 - Final grade
S - Passing Sight Distance

## Crest Vertical Curve Length

#### Formula Used:

Lm = ( A×S² ) / ( 200 × (√h1 + √h2)² ) ∀ S<Lm
Lm = 2S − { ( 200 × (√h1 + √h2)² ) / A } ∀ S>Lm

Where,

A - Absolute difference between g2 and g1
S - Sight Distance
Lm - Minimum Curve Length
h1 - Height of driver's eye above roadway surface
h2 - Height of object above roadway surface

## SAG Vertical Curve Length

Formula Used:
Lm = ( A×S² ) / ( 200 × (H + S ×tanβ) ) ∀ S<Lm
Lm = 2S − { ( 200 × (H + S ×tanβ) ) / A } ∀ S>Lm

If S > L, then the first formula is used, if L > S, then the second formula is used.

Where,

A - Absolute difference between g2 and g1
S - Sight Distance
Lm - Minimum Curve Length
H - Height of headlight
β - Angle of Headlight Beam

## Rate of Change Vertical Curve

#### Formula Used:

r = (g2 − g1) / L

Where,

r - Rate of change of grade
L - Length of the curve

## Transportation Highways Horizontal Curve

##### Formula

R = 5729.58 / D
T = R * tan ( A/2 )
L = 100 * ( A/D )
LC = 2 * R *sin (A/2)
E = R ( (1/(cos (A/2) ) ) - 1 ) )
M = R ( 1 - cos (A/2) )
PC = PI - T
PT = PC + L

Where,

D = Degree of Curve, Arc Definition
1Â° = 1 Degree of Curve
2Â° = 2 Degrees of Curve
P.C. = Point of Curve
P.T. = Point of Tangent
P.I. = Point of Intersection
A = Intersection Angle, Angle between two tangents
L = Length of Curve, from P.C. to P.T.
T = Tangent Distance
E = External Distance
L.C. = Length of Long Chord
M = Length of Middle Ordinate
c = Length of Sub-Chord
k = Length of Arc for Sub-Chord
d = Angle of Sub-Chord

## Elevation Point of Vertical Curve

##### Formula Used:

y = epvc + g1x + [ (g2 − g1) ×x² / 2L ]

Where,
y - elevation of point of vertical tangency
epvc - Initial Elevation
g1 - Initial grade
g2 - Final grade
x/L - Length of the curve

## Vehicle Stopping Distance

#### Formula Used:

Stopping Distance =(v×t) + { v² / [2×g×(f±G)] }

Where,

g - gravity (9.8)
v - Vehicle Speed
t - perception Time
f+G - Grade of Uphill
f-G - Grade of Downhill

## Spiral Curve Tangent Distance

#### Formula Used:

Y = L − { L5 / ( 40×R²×Ls²) }

Where,
Y - Tangent distance to any point on the spiral
L - Length of spiral from tangent to any point
Ls - Length of spiral
R - Radius of Simple Curve

## Spiral Curve Deflection Angle

#### Formula Used:

i = L² / ( 6×R×Ls)

Where,
i - Tangent deflection angle to any point on the curve
L - Length of spiral from tangent to any point
Ls - Length of spiral
R - Radius of Simple Curve

## Earthwork Cross Sectional Area

Formula Used:

Where,
A - Area of cross section
Xi - Horizontal axis
Yi - Vertical axis
n - Number of points on cross section

## Earthwork Cross Section Volume

##### Formula Used:

V = ((A1 + A2) ×L) / 2

Where,

L - Length between two areas
A1 - Cross section area of first side
A2 - Cross section area of second side
V - Eathwork Volume

## Concrete Slab Maximum Length

#### Formula

L = ( 0.00047hr (fsS) ^2 ) ^ ( 1/3 )

Where,

L = Slab Length,
hr = Thickness of reinforced slab,
fs = Yield strength of steel reinforcement,
S = Steel reinforcing ratio

## Concrete Slab Volume

#### Formula Used:

Volume of concrete Slab = w × l × t

Where,

l - Length
w - Width
t - Thickness

## Concrete Slab Maximum Wall Load

##### Formula:

P = 9.93 ( fc^0.5 )( te^2 ) ( ( k / (19000 ( fc^0.5 )( te^3 ) ) ) ^ 0.25

Where,

fc = Concrete compressive strength,
k = Modulus of subgrade reaction,
te = Slab thickness.

## Maximum Floor Load Capacity

#### Formula:

w = 257.876s ( kh / E ) ^ 0.5

Where
,
w = Maximum Allowable Stationary Live Load,
k = Modulus of subgrade reaction,
h = Thickness of slab,
s = Allowable extreme fiber stress in tension,
E = Modulus of elasticity.

## Concrete Footing Volume

#### Formula Used:

Volume of concrete Footer = [ (ow × ol) − (iw × il) ] × t

Where,

ol - Outside Length
ow - Outside Width
il - Inside Length
iw - Inside Width
t - Thickness

## Number of Cubic Yards Required for Concrete Column Fill

#### Formula:

Radius = diameter/24 cubic yards = (height*(radius)2*22/7)/27

## Concrete Footing

#### Formulas Used:

Footing Pours = ( Diameter * ( Width / 12 ) ) * ( Depth / 12 ) / 27 );

## Concrete Volume

#### Formula:

Concrete Volume = [( 22/7 )r2 * depth ) / 27 ] * Quantity

## Block Wall Cubic Yards

#### Formula:

For size = 8inch
Cubic Yards to be filled = (L * W * 0.32 / 27);
For size = 12inch
Cubic Yards to be filled = (L * W * 0.51 / 27);

## Cubic Yards of Circular Stepping Stones

#### Formula:

Single Stepping Stone = (Π X r2 X h) / 46656

Where,

h = Depth in inches
r = d / 2
d = Diameter in inches

## Cubic Yards of Rectangular Stepping Stones

#### Formula:

Single Stepping Stone = (l X b X h) / 324

Where,

l = Length in feet
b = Width in feet
h = Depth in inches

## Cubic Yards of Triangular Stepping Stones

#### Formula:

Single Stepping Stone = (l X b X h) / 648

Where,

l = Length in feet
b = Width in feet
h = Depth in inches

## Block

#### Formula:

Number Of Blocks = (Length × Width) / Block Size

## Concrete Mix Ratio

#### Formula:

Volume= Width × Height × Depth
Cement = Volume × 320
Sharp Sand= Volume × 600
Gravel = Volume× 1200
Water = Volume × 176

## Concrete Wall

#### Formula:

Concrete Wall (CW) = (Length × Thickness × Height) × 0.037037

## Concrete Driveways Cost

#### Formula:

Rectangle,
C = L × W × T × R
Circle,
C = π × (M/2)2 × T × R
Footing,
C = L × W × D × R
Circular column,
C = π × (M/2)2 × D × R

Where,

C = Total Cost Of Concrete Driveways
L = Length(yard)
W = Width(yard)
T = Thickness(yard)
R = Cost
D = Depth(yard)
M=Diameter(yard)

## Safe Speed For Horizontal Curve

#### Formula:

If Safe speed of Horizontal Curve greater than 50 mph
Safe Speed for Horizontal curve ( V > 50mph ) = ( ( ( -0.03 × r ) + ( √ (((.03 × r) × (.03 × r)) + ((4 × r) × ((15 × (e / 100)) + 3.6))))) / 2)

If Safe speed of horizontal curve less than 50 mph
Safe Speed for Horizontal curve ( V < 50mph ) = ((( -.015 × rhname ) + ( √ ((( .015 × rhname ) × ( .015 × rhname )) + ((4 × rhname) × (( 15 × ( ehname / 100 )) + 2.85 ))))) / 2);

Where,

r = Radius of Horizontal Curve(ft)
e = Superelevation

## Cornering Force

#### Formula:

t = u × m × g × sin(a)
f = ( u × m × g × sin(a) ) + ( m × g × cos(a) )
v = √ (((( u × m × g × sin(a) ) + ( m × g × cos(a) )) × r ) / m )

Where,

t = Static Friction
u = Static Friction's Coefficient
m = Mass of Vehicle (kg)
g = Gravity Accelaration
r = Radius (m)
f = Total Net Force
v = Maximum Speed
a = Slope of the Road

## Concrete Driveway

#### Formula:

A = l × b
P = 2 × (l+b)

Where,

A = Drive way Area
P = Drive way Perimeter
l = Length
b = width

## Roof Slope

#### Formula:

Run(inches)= ( 12 × Rise ) / Roof Pitch
Slope = ( Rise / Run ) × 100
Angle = tan-1( Rise / Run )

## Roof Angle

#### Formula:

Run(inches) = ( Rise / Slope ) × 100
Angle = tan-1( Rise /Run )
Roof Pitch = ( Rise /(Run/12) )

## Roof Pitch

#### Formula:

Pitch = S / ( N / 12 )
Slope = ( S / N ) × 100
Angle = tan-1 ( S / N )

Where,

S = Rise (inches)
N = Run (inches)

## Rise Run Slope

#### Formula:

Run(inches) = Rise / tan(angle)
Roof Pitch = Rise / ( Run/ 12 )
Slope = ( Rise / Run) × 100

## Curve Surveying

#### Formula:

l = π × r × i / 180
t = r × tan(i / 2)
e = ( r / cos(i / 2)) -r
c = 2 × r × sin(i / 2)
m = r - (r (cos(i / 2)))
d = 5729.58 / r

Where,

i = Deflection Angle
l = Length of Curve
t = Length of Tangent
e = External Distance
c = Length of Long Chord
m = Middle Ordinate
d = Degree of Curve Approximate

## lb/ft<sup>3</sup> to kN/m<sup>3</sup> Conversion

#### Formula:

T = S × (9.81 kN/m³ / 62.4 lb/ft³)

Where,

T = Total Unit Weight in kN/m³
S = Total Unit Weight in lb/ft³

## Insulation

#### Formula:

Approximate Sq.Ft Needed = Area Width × Area Height

## Trapezoidal Footing Volume

#### Formula:

V = h / 3(A1 + A2 + √(A1 * A2))

Where,

V = Volume of Trapezoid Footing
h = Height of Trapezoidal
A1 = Area of the Lower Shape
A2 = Area of the Upper Shape
A1 = m x n (Lower Height x Lower Breadth)
A2 = o x p (Upper Height x Upper Breadth)

## Concrete Yardage

#### Formula:

Concrete Yardage = L × W × H/12 × 0.037037

Where,

W = Width(ft)
L = Length(ft)
H =Thickness(inch)

## Curb and Gutter Barrier Concrete Yardage

#### Formula:

Concrete Yardage = (l×(f/12.0×(g/12.0+h/12.0))+l×(h/12.0×h/12.0)) × 0.037037

Where,

l = Length(ft)
f = Flag Thickness(inch)
g = Gutter Width(inch)
h = Curb Height(inch)

## Concrete Wall

#### Formula:

Concrete Yardage = Length × Height × (Thickness /12) × 0.037037

## Concrete Footing Yard

#### Formula:

Concrete Yardage = Length × Width(inch) /12 × Height(inch) /12 × 0.037037

## Concrete Yards

#### Formula:

c =((((n × t/12.0)×(n×r/12.0))/2)+((n×(t/12.0×r/12.0))/2))×w × 0.037037

Where,

c = Concrete Yardage
n = Number of stairs
r = Riser(inch)
w = Width(ft)

## Concrete Volume

#### Formula:

V = H x B x W
T = M + N + O
X = (M / T) x V
Y = (N / T) x V
Z = (O / T) x V

Where,

H = Height of Concrete
W = Width of Concrete
B = Breadth of Concrete
M = Cement Ratio
N = Sand Ratio
O = Coarse Ratio
V = Volume of Concrete
T = Total Ratio of ingredients
X = Cement Quantity
Y = Sand Quantity
Z = Coarse Quantity

## Plaster

#### Formula:

V = A x T
X = V x 1.54
C = X x (M / G)
S = X x (N / G)

Where,

T = Plastering Thickness
V = Volume of Cement Mortar
A = Area of Plastering
M = Ratio of Plastering Cement
N = Ratio of Plastering Sand
C = Cement Required (1 Part)
S = Sand Required (5 Part)
X = 35% Sand Bulkage
G = Total ratio (M+N )

## Floor Tile

#### Formula:

Perimeter of Room = (2 x ( Room length + Room breadth)) - Door width

Skirting Tiles Area = Perimeter of Room x Skirting Tiles Height

Area of Room = Room length x Room Breadth

Total Area to be Laid = Area of Room + Skirting Tiles Area

Area of Tiles = Tiles length + Tiles Breadth

Number of Tiles We Need = (Total Area to be Laid / Area of Tiles) x Tiles Wastage%