Surface area and volume formulas are part of the math used in common science calculations. You may need to calculate surface area and volume to determine density, pressure and concentration, for example. While it's a good idea to memorize these formulas, here a list of surface area and volume formulas to use as a handy reference.
Prism
Todd Helmenstine
A prism can be described as a stack of shapes. The figure shows a prism of triangles stacked d thick, but any shape could be used.
Surface area = 2A + Pd
where
A = area of the base shape
P = perimeter of base shape
d = height of prism
Volume = Ad
Surface area = 2A + Pd
where
A = area of the base shape
P = perimeter of base shape
d = height of prism
Volume = Ad
Cylinder
Todd Helmenstine
A cylinder is a prism with a circular base.
Surface Area = 2πr2 + 2πrh
Volume = πr2h
Surface Area = 2πr2 + 2πrh
Volume = πr2h
Sphere
Todd Helmenstine
A sphere is a shape where the distance from the center to the edge is the same in all directions. This distance is called the radius ( r ).
Surface area = 4πr2
Volume = 4/3πr3
Surface area = 4πr2
Volume = 4/3πr3
Pyramid
Todd Helmenstine
A pyramid is a solid figure with a polygonal base and triangular faces that meet at a common point over the center of the base.
The height ( h ) is the distance from the base to the apex or top of the pyramid.
The side length ( s ) is the height of the face triangles.
The perimeter ( P ) and the area ( A ) of the base is calculated according to the shape of the base.
Surface Area = ( ½ x P x s ) + A
Volume = 1/3 Ah
The figure shows a pyramid with a square base ( a = b ) with equalateral triangles for faces.
The height ( h ) is the distance from the base to the apex or top of the pyramid.
The side length ( s ) is the height of the face triangles.
The perimeter ( P ) and the area ( A ) of the base is calculated according to the shape of the base.
Surface Area = ( ½ x P x s ) + A
Volume = 1/3 Ah
The figure shows a pyramid with a square base ( a = b ) with equalateral triangles for faces.
Surface area = a2 + √3( a2 )
Volume = √5(a3/6)
Cone
Todd Helmenstine
A cone is a pyramid with a circular base of radius ( r ) and the side length ( s ) is the length of the side.
s = √( r2 + h2 )
Surface Area = πr2 + π( r x s )
Volume = 1/3( πr2h )
s = √( r2 + h2 )
Surface Area = πr2 + π( r x s )
Volume = 1/3( πr2h )
