Shape Calculations

Note on Units: Remember to keep them constant, and don't mix different units in the formulas!
Area = Pi * Radius^{2}
Circumference = Pi * Diameter
Circumference = 2 * Pi * Radius
Divide the Area in Square Units by Pi
Take the Square Root of the Result. This is the radius.
Double that to get the diameter.
Area = Pi * (Axis_{Major} * Axis_{Minor}) / 4
or
Area = Pi * Axis_{Major} * Axis_{Minor}
Area = Length * Width
Perimeter = 2 * (Length + Width)
or
Perimeter = [2 * Length] + [2 * Width]
Area = Length * Width
Area = [ (Top_{Length} + Bottom_{Length}) * Height ] / 2
or
Area = 0.5 * (Top_{Length} + Bottom_{Length}) * Height
Area = Base * Height
Perimeter = [2 * Base] + [ 2 * Side]
or
Perimeter = Base + Base + Side + Side
Volume = Length^{3}
Surface Area = 6 * Length^{2}
Volume = Length * Width * Height
Surface Area = (2 * Width * Height) + (2 * Height * Length) + (2 * Width * Length)
or
Surface Area = 2 * ( [Width * Height] + [Length * Width] + [Length * Height] )
Notes: For this shape, the formula names are slightly different:
Base is the length/width of the base.
Side is the Length of the side (measured at an angle).
Volume = (1/3) * Base^{2} * Height
Surface Area = [ 2 * Base * Side ] + Base^{2}
Notes: For this shape, the formula names are slightly different:
Base is the width of the base.
Length: is the length of the prism.
Side is the length of the side angle (measured at an angle).
Volume = 0.5 * [ Base * Height ] * Length
Surface Area = [Base * Height] + [2 * Length * Side] + [Length * Base]
Volume = [ Pi * diameter^{3} ] / 6
Volume = (4/3) * Pi * Radius^{3}
Surface Area = 4 * Pi * Radius^{2}
This finds the cylinder with the smallest surface area for the largest volume enclosed:
Height = 2 * Radius
Volume = Pi * Radius^{2} * Height
Volume = (Pi * Diameter^{2} * Height) / 4
Height = Volume / (Pi * Radius^{2})
Radius = SQRT(Volume / (Pi * Height))
(Surface Area) Basic Formula
Surface Area = 2(Pi * Radius^{2}) + (2 * Pi * Radius) * Height
or
Surface Area = 2(Pi * Radius^{2}) + (2 * Pi * Radius * Height)
Surface Area = 2 * Pi * Radius * Height
Note: Both ends must be perfect halfspheres.
Volume = (Pi * Radius^{2} * Length) + (4 * Pi / 3 * Radius^{3})
or
Volume = Pi * Radius^{2} [ (4/3) * Radius + Length)
Example: 3m radius, 10m length = 395.841 m3.
Surface Area = 2 * Pi * Radius * Height + 2 * (2 * Pi * Radius^{2})
or
Surface Area = 2 * Pi * Radius * [ (2 * Radius) + Length ]
Example: 3m radius, 10m length = 301.593 m2.
Circumference = 2 * Pi * Radius
Example: 3m radius = 18.850 m2.
Notes: Will give a negative number if numbers are impossible to meet.
Length = [ Volume / (Pi * Radius^{2}) ] – [ (4 * Radius) / 3 ]
Example: 600 m3 volume and 5m radius = 0.973m length
Notes: Will give a negative number if numbers are impossible to meet.
Length = [Area_{Surface} / (2 * Pi * Radius) ] – 2 * Radius
Example: 500 m2 Surface Area and 5m radius = 5.915m length.
Volume = Pi * Axis_{Major} * Axis_{Minor} * Length / 4
Surface Area = [ 2 * Pi * (R^{2} – r^{2}) ] + [ 2 * Pi * Height (R + r)
Where:
R: Outer Radius
r: Inner Radius
Volume = (2/3) * Pi * Radius^{3}
Surface Area = 2 * Pi * Radius^{2}
Surface Area = (2 * Pi * Radius^{2}) + (Pi * Radius^{2})
or
Surface Area = 3 * Pi * Radius^{2}
Example: 10m radius = 942.478 m2
Circumference = 2 * Pi * Radius
Radius = (3 * Volume) / (2 * Pi)^{^(1/3)}
Radius = SQRT( Area / [2 * Pi] )
Volume = (Pi * Height / 12) * (Diameter_{Bottom}^{2} + Diameter_{Bottom} * Diameter_{Top} + Diameter_{Top}^{2})
Example: Height is 10m, top diameter is 5m, bottom diameter is 2.5m = 114.537 m3.
Volume = (1/3) * Pi * Height * (Radius_{Top}^{2} + Radius_{Bottom}^{2} + [ Radius_{Top} * Radius_{Bottom} ] )
Example: Height is 5m, top radius is 3m, bottom radius is 2m = 99.484 m3
Surface Area = Pi * (RadiusTop + RadiusBottom) * Slant
Example: Top Radius is 3m, bottom radius is 2m, slant is 5.09902m = 80.0952 m2
Slant = SQRT[ (Radius_{Top} – Radius_{Bottom})^{2} + Height^{2} ]
Example: Height is 5m, top radius is 3m, bottom radius is 2m = 5.09902m
Volume = [ Pi * Diameter^{2} * Height ] / 12
Volume = (1/3) * Pi * Radius^{2} * Height
(Smooth Curved Surface, Sharp Pointed Nose)
Volume = [ 2 * Pi * Diameter^{2} * Height ] / 15
(Smooth Curved Surface, Blunted Curved Nose)
Volume = [ Pi * Diameter^{2} * Height ] / 6