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# Surface Area & Volume Formulas

## Calculate Surface Area and Volume

Surface area and volume formulas are occasionally needed in many 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.

### Triangle

Todd Helmenstine
A triangle is a three sided closed figure.
The perpendicular distance from the base to the opposite highest point is called the height ( h ).

Perimeter = a + b + c
Area = ½bh

### Parallelogram

Todd Helmenstine
A parallelogram is a quadrangle where opposite sides are parallel to each other.
The perimeter ( P ) is the distance around the outside of the parallelogram.

P = 2a + 2b

The height ( h ) is the perpendicular distance from one parallel side to it's opposite side.

Area = b x h

It is important to measure the correct side in this calculation. In the figure, the height is measured from side b to the opposite side b, so the Area is calculated as b x h, not a x h. If the height was measured from a to a, then the Area would be a x h. Convention considers the side the height is perpendicular to is called the 'base' and usually denoted with a b.

### Rectangle

Todd Helmenstine
A rectangle is a special type of quadrangle where all the interior angles are equal to 90° and all opposite sides are the same length.
The perimeter ( P ) is the distance around the outside of the rectangle.

P = 2h + 2w
Area = h x w

### Square

Todd Helmenstine
A square is a rectangle where all four sides are of equal length.

Perimeter = 4s
Area = s2

### Trapezoid

Todd Helmenstine
A trapezoid is another special quadrangle where only two sides are parallel to each other.
The perpendicular distance between the two parallel sides is called the height ( h ).

Perimeter = a + b1 + b2 + c
Area = ½( b1 + b2 ) x h

### Circle

Todd Helmenstine
A circle is an ellipse where the distance from the center to the edge is constant.
Circumference ( c ) is the distance around the outside of the circle.
Diameter ( d ) is the distance of the line through the center of the circle from edge to edge.
Radius ( r ) is the distance from the center of the circle to the edge.
The ratio between the circumference and the diameter is equal to the number π.

d = 2r
c = πd = 2πr
Area = πr2

### Ellipse

Todd Helmenstine
An ellipse or oval is a figure that is traced out where the sum of the distances between two fixed points is a constant.
The shortest distance between the center of an ellipse to the edge is called the semiminor axis ( r1 )
The longest distance between the center of an ellipse to the edge is called the semimajor axis ( r2 )

Area = πr1r2

### Hexagon

Todd Helmenstine
A regular hexagon is a six sided polygon where each side is of equal length. This length is also equal to the radius ( r ) of the hexagon.

Perimeter = 6r
Area = (3√3/2 )r2

### Octagon

Todd Helmenstine
A regular octagon is a eight sided polygon where each side is of equal length.

Perimeter = 8a
Area = ( 2 + 2√2 )a2

### Rectangular Solid

Todd Helmenstine
Surface Area = 2(lh) + 2(lw) + 2(wh)
Volume = l x h x w

where
l = length
h = height
w = width

Anne Marie Helmenstine, Ph.D.