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All Areas Formulas List

Quadrangular Prism Area, Volume

Formula Used:

AL = PB x h
TA = AL + 2 x AB
V = AB x h

Where

AL = Lateral Area
PB = Perimeter of the base
h = Height
V = Volume
AB = Area of the base
TA = Total Area

Capsule Volume, Area, Circumference

Formula Used:

Volume(V) = π r2( ( 4 / 3 ) r + a )
Surface Area(S) = 2 π r ( 2 r + a )
Circumference(C) = 2 π r

Conical Frustum Volume, Surface Area and Height

Formula Used:

Volume V = ( 1 / 3 ) π h ( r12 + r22 + ( r1 * r2 ) )
Slant Height S = √( ( r1 - r2 )2 + h2 )
Lateral Surface Area L = π ( r1 + r2 ) s
Top Surface Area T = π r12
Base Surface Area B = π r22
Total Surface Area A = π (r12 + r22 + (r1 * r2) * s)

Cylindrical Pipe Volume

Formula:

Volume of Cylindrical pipe = (h * PI *( r02 - r12 ))

Where,

h = Height of the pipe,
r0,r1 = Radii of the pipe.

Aspect Ratio and Pixels

Formula to find Aspect Ratio:

Aspect ratio=a/b
Pixels=a*b

where,
a = Width of the image
b = Height of the image

Barell Volume

Formula:

Volume of Barrel = (h * PI * (2* r1 2 + r22) / 3 )

Where,

H = Height of the barrel
r2,r2 = Radii of the barrel

Rectangular to Polar Conversion

Formula Used:

R = sqrt(x * x + y * y) ,
angle=atan(y/x)

Where,

Rectangle coordinates:
x and y - horizontal and vertical distances from the origin.
Polar coordinates(r,q):
r - the distance from the origin to the point.
q - the angle measured from the positive x axis to the point.
t - angle (in degrees).

Volume of a Cylinder with Hemispherical Ends

Formula:

Volume of a Cylinder = (PI * r2 * h ) + ( ( 4 / 3 ) * PI * r3)

Where,

r = radius of the cylinder,
h = height of the cylinder.

Apothem of Regular Polygon

Formula:

r = a / [2 tan(π / n)]
[or]
r = R cos (π / n)

Apothem of Regular Polygon
π = 3.14159
a = Side length
n = Number of side

Octagonal Pyramid Volume

Formula:

Volume of Octagonal Pyramid = (B × h) / 3

Where

Base (B) = 2 × s² (1+√2)
s = Side Length
h = Height of Pyramid

Regular Polygon Cicumcircle

Formula:

Circumradius (r) = l / (2 x sin( π / n ))
Area of the polygon = ( n x l2 ) / ( 4 x tan( π / n ) )
Regular Polygon Circumcircle Area = 3.14 x r2

Where,

n = Number of sides of the polygon,
l = Length of the side of the polygon

Regular Polygon Incircle

Formula Used:

Inradius = l / 2 * tan(PI/n)
Area of the polygon = 0.5 * n * l * r
Area of the Incircle = PI * r2

Where,

n = Number of sides of the polygon,
l = Length of the side of the polygon

Regular Polygon

Formula Used:

Length of the side of the polygon = 2 * r * sin ( PI / n )
Area of the polygon = 0.5 * n * r2 * sin ( 2PI / n )
Area of the Circle = PI * r2

Where,
n = Number of sides of the polygon,
r = Circumradius of the polygon

Octogonal Prism Area, Volume, Surface Area

Formula :

A = 2 × a × d
V = A × l
SA = (2 × A) + (8 × a × l)

Where,

a = Side Length
l = Height
d = Distance

Area of Sector of Circle

Formula Used:

Area of Sector = 1/2 × Radius of Circle × Sector Angle

Trapezoid Area

Formula Used:

Area of Trapezoid = (b1 + b2) / 2 × h

Stadium Area and Perimeter

Formula Used:

Area (A) = π r2 + 2 r a
Perimeter (P) = 2 ( π r + a )

Hollow Cylinder Volume, Area, Surface Area, Circumference

Formula Used:

Circumference (C):
C1 = 2 π r1
C2 = 2 π r2

Lateral Surface Area (L):
L1 = 2 π r1 h
L2 = 2 π r2 h

Area (A):
A1 = π r12
A2 = π r22
A = A1 - A2

Volume (V):
V1 = π r12 h
V2 = π r22 h
V = V1 - V2

Thickness of the tube wall (t):
t = t1 - t2

Aquarium Fish Tank Volume

Formula:

Volume of Rectangle = l x b x h
where,
l = Length
b = width
h = height
Volume of Cylinder = π r2h
where,
h = height

Pipe Volume

Formula Used:

Pipe Volume = π r2 x Height

Circle Chord Length

Formula:

Chord length = 2r2 - d2
where,
r = radius of the circle
d = perpendicular distance from the chord to the circle center

Arc Length of Circle

Formula:

Arc Length of a Circle (S) = 2 x π x r (central angle/ 360)

Where,

r - Radius of arc

Rectangular Prism Surface Area, Volume

Formula:

Surface Area = 2 (wl + lh + hw)
Volume = w x l x h

Where,

w = width
l = length
h = height

Degree Measure of Sector

Formula

Angle of sector = (A x 360) / π r2

Where,

A = area of sector
r = radius of sector

Annulus Area

Formula:

A = π × (R2 - H2)

Where,

A = Area of Annulus (Annular)
R = Radius of the Outer Circle
H = Radius of the Inner Circle

LSA of a Square Pyramid

Formula:

L = a x √(4h2+a2)

Where,

L = Lateral Surface Area
h = Height of the Pyramid
a = Side of the Pyramid

Diagonal of a Rectangle

Formula:

d = √ (w2 + h2)

Where,

d = Diagonal of Rectangle
w = Width
h = Height

Total Surface Area of Rectangular Right Wedge

Formula:

SL=(1/2)*(a+c)*√((4*h)+b2)+(b*√(h2+(a-c)2))
SB=ab
S=SL+SB

Where,

a = Base side
b = Base width
c = Top edge
h = Height
SL = Lateral Surface Area
SB = Area of Base
S = Total Surface Area of Rectangular Right Wedge

Area of a Semicircle

Area of a Semi-Circle Formula:

A = (1/2) * π * r2

Where,

A = Area of Semicircle

Scalene Triangle Area and Perimeter

Formula:

Area = √(s(s-a)(s-b)(s-c))
s = (a+b+c)/2

Perimeter = a+b+c

where,
s is semiperimeter.

Area of a Regular Hexagon

Formula:

A = 3√3 ( a2) / 2

Where,

a = Side Length
A = Area

Central Angle of a Circle

Formula

Central angle = (Arc length x 180)/(3.142 x Radius)

Exterior Angles of a Convex Polygon

Formula:

N = 360 / (180-I)
Exterior Angle Degrees = 180 - I

Where,

N = Number of Sides of Convex Polygon
I = Interior Angle Degrees

Area of an Ellipse

Formula:

s=π(ab)

Where,

s=Area
a=Semimajor Axis (a)
b=Semiminor Axis (b)

Gradient of Line in a Plane

Formula:

k = (y2-y1) / (x2-x1)

Where,

k = Gardient of Line
x1, x2, y1, y2 = Point of Coordinates

Area of a Segment of a Circle

Formula:

S = r2 / 2 (α π / 180 - sin α)

Where,

s = Area of a Circle Segment
α = Central Angle in Degree
sin = Sine

Radius of an Inscribed Circle in an Octahedron

Formula:

r=a√6/6

Where,

r = Radius of Inscribed Circle
a = Edge

Radius of a Circumscribed Circle in an Octahedron

Formula:

R = A √2 / 2

Where,

R = Radius of Circumscribed Circle
A = Edge Length

S = 2a2√3

Where,

a = Edge
S = Surface Area

Volume of an Octahedron

Formula:

V = (A3 √2) / 3

Where,

V = Volume of an Octahedron
A = Edge

Radius of Inscribed Circle in an Dodecahedron

Formula:

r = a √(10(25+11√5)) / 2

Where,

r = Radius of Inscribed Circle
a = Edge

Area of a Segment of a Circle

Formula:

S = (R2/2) × (X-sin X)

Where,

S = Area of Segment Circle
X =Central Angle

Lateral Area of an Oblique Prism

Formula:

s=p*l

Where,

s = Lateral Area of an Oblique Prism
p = Perimeter
l = Lateral Edge

Volume of a Oblique Prism

Formula:

v=bh

Where,

v = Volume of a Prism
b = Area of Base
h = Height

m=√(b2-(a2/4))

Where,

m = Slant Height
b = Lateral Edge
a = Side of Base

Lateral Surface Area of Regular Pyramid using Semi-perimeter

Formula:

SL = Semiperimeter x (√ (b2 - (a2 / 4)))

Where,

SL= Lateral Surface Area
b = Lateral Edge
a = Side of Base

Lateral Surface Area of Regular Pyramid using Base and Lateral Edge

Formula:

SL = 1/4 × n × a √ (4b2 - a2)

Where,

n = Number of Sides
a = Side of Base
b = Lateral Edge
SL = Lateral Surface Area

Regular Hexagon Area

Formula:

S = (L/2)*r

Where,

S = Area
L = Perimeter
r = Radius of Inscribed Circle

Height of a Regular Pyramid

Formula:

Height of Regular Pyramid = (√ (4b2 sin2 (π/n) - a2)) / 2 sin(π / n)

Where,

b = Lateral Edge
n = Number of Sides
a = Side of Base

Lateral Surface Area of Regular Pyramid

Formula:

SL = (1/2) (Perimeter x Slant Height)

Total Surface Area of Regular Pyramid

Formula:

SL = (1 / 4) x n x Base Length x √(4b2 - Base Length2)
SB = Semiperimeter x Radius
S = SL + SB

Where,

S = Total Surface Area (TSA)
SB = Area of Base
SL = Lateral Surface Area (LSA)
n = Number of Sides
b = Lateral Edge

Volume of Regular Pyramid based on Area of Base

Formula:

SB = Semiperimeter x Radius
V = (1/3) SB x Height

Where,

V = Volume of Regular Pyramid
SB = Area of Base

Radius of Inscribed Circle

Formula:

R = √((d12d22) - (a - b)2(a + b - p)2) / (2p)

Where,

r = Radius of Inscribed Circle
d1,d2 = Diagonals
a,b = Sides of Quadrilateral
p = Perimeter

Segment of a Circle Chord Length

Formula:

a = 2 √( 2hR - h2)

Where,

a = Chord
h = Height of the Segment
R = Radius of a Circle

Segment Height of Circle

Formula:

h = R-(1/2) √ (4R2 - a2)

Where,

h = Height of a Segment
R = Radius of a Circle
a = Chord

Segment of Circle Perimeter

Formula:

a = 2 √ (2hR - h2)
L = s + a

Where,

L = Perimeter
s = Arc Length
a = Chord
h = Height of Segment
R = Radius of Circle

Segment of Circle Area

Formula:

a = 2 √( 2hR - h2 )
S = (1/2) * [ sR - a(R - h) ]

Where,

S = Area
a = Chord
s = Arc Length
R = Radius of a Circle
h = Height of the Segment

Total Surface Area of an Oblique Prism

Formula:

s=pl+2b

Where,

s = Total Surface Area
p = Perimeter
l = Lateral Edge
b = Area of Base

Sagitta Arc Length

Formula:

Sagitta Length = Radius ± √(Radius2-Half Chord Length2)

Interior Angles of a Convex Polygon

Formula:

N = 360 / E

Interior Angle Degrees = 180 - E

Where,

N = Number of Sides of Convex Polygon
E = Exterior Angle Degrees

Slant Height of a Pyramid

Formula:

Slant Height = √(h2 + (b / 2)2)

Where,

h = Height of the Pyramid
b = Base of the Pyramid

Slant Height of Square Pyramid

Formula:

s2 = h2 + (1/4) a2

Where,

s = Slant Height of Square Pyramid
h = Height
a = Side Length

Scalene Triangle Height

Formula:

h = (2 * k) / Base

Where,

h = Scalene Triangle Height
k = Area
Base = Length of Base

Hip Roof Area

Formula:

H = (B x tan α) / 2
Common Rafters = B / (2 x cos α)
Hip Rafters = √(H2 +(B2 / 2))
Hip Roof Area = 2 x Common Rafters x Roof Base Length

Where,

H = Roof Rise
B = Roof Base Width
α = Roof Pitch
tan = Tangent
cos = Cosine

Area of a Tube

Formula:

S = (2 * π *r2) + (2 * π * h * r)

Where,

S = Area of Tube
h = Height

Surface Area of Tube

Formula:

S = (2π * (R2 - r2)) + (2πh * (R + r))

Where,

S = Surface Area of Tube
R = Outer Radius
r = Inner Radius
h = Height

Lateral Surface Area of a Cylinder

Formula:

S = 2 x π x r x h

Where,

S = Lateral Surface Area of a Cylinder
h = Height

Circumference of Circle

Formula:

C = 2 * 3.14 * r

Where,

C = Circumference of Circle
r = Radius of Circle

Height of a Right Square Prism

Formula:

h = v / a2

Where,

h = Height / Altitude of a Right Square Prism
v = Volume
a = Area

Formula:

r = c / (2 * π)

Where,

r = Radius of Circle
π = 3.14
c = Circumference of Circle

Length of an Arc

Formula:

r = (h/2) + (w2/(8h))
C = 2 tan-1(w/(2×(r-h)))
if(C < 0)
C = 360 + C
l = C × 2 Π r / 360

Where,

r = Radius of Arc
h = Height of Arc
w = Width of Arc
C = Center Angle of Arc
l = Length of Arc

Circumference of Ellipse

Formula:

C = 2 * π * √((a2 + b2) / 2)

Where,

C = Circumference of Ellipse
a = Major Axis
b = Minor Axis

Perimeter of Right Triangle

Formula:

P = a + b + √(a2 + b2)

Where,

p = Perimeter of Right Angle Triangle
a = Height
b = Base

Area of Circle

Circle Formula:

Area of Circle = πr²
Diameter of Circle = 2r
Circumference of Circle = 2 πr = πd
Area of Sector = πr² (θ/360)

Where,

Volume Of Hypersphere Calculator

Formula:

V = (1/2) * π2 * r4

Where,

V = Volume of Hypersphere
r = Radius of Sphere

Curved Surface Area (CSA) of Cuboid

Formula:

A = 2h(l+b)

Where,

A = Curved Surface Area of Cuboid
h = Height
l = Length

CSA of Cylinder

Formula:

Curved Surface Area = 2 × π × r × h

Where,

h = Height

Dodecagon

Formula:

Area = 3 × S2 × (2 + √3)

Where,

s = Side Length

Slant Height of a Cone

Formula:

Slant Height = √((r2)+(h2))

Where,

h = Height

Surface Area of a Cone

Formula:

t = π × r × ( l + r )
l = √(r2 + h2)

Where,

t = Total Surface Area
h = Height
l = Slant Height

Curved Surface Area of Cone

Formula:

c = π × r × l
l = √(r2+h2)

Where,

c = Curved Surface Area
h = Height
l = Slant Height

Volume of a Cone

Formula:

Volume of Cone = 1/3 × π × (r2 × h)

Where,

h = Height

Diagonal of Rectangle Prism

Formula:

d = √l2 + w2 + h2

Where,

d = Diagonal of Rectangle Prism
l = Length of Rectangle Prism
w = Width of Rectangle Prism
h = Height of Rectangle Prism

Area of Circle Segment

Formula:

A = R² × (θ - sin(θ)) / 2

Where,

A = Area of Circle Segment
θ = Central Angle

Apothem of Pentagon

Formula:

Apothem of Pentagon = a / [2 tan(π / n)]

Where,

a = Side length
n = 5

Centroid of Parallelogram

Formula:

Xc = 0.5 x (B + C)
Yc = 0.5 x H

Where,

H = Height of Parallelogram
B = Width of Parallelogram
C = Length of Parallelogram