Volume Definition
Volume is the total amount of space enclosed or occupied in a solid. Volume generally has units of length and distance cubed (such as cm3, in3, m3 km3, etc.) In the case of a simple box calculating volume is V = L x W x H (Where V = volume, L = length, W = width, and H = height respectively). Volume can also be computed for irregularly shaped and curved solids such as cylinders or cones. The volume of a surface of revolution is particularly simple to compute due to its symmetry. For a more comprehensive breakdown of formulas for various figures see the table below.
Volume Formulas
Volume formulas for various figures including lateral surface area, area of base(s), and total surface area:
Figure |
Volume |
Lateral Surface Area |
Area of the Base(s) |
Total Surface Area |
Box (also called rectangular parallelepiped, right rectangular prism) |
lwh |
2lh + 2wh |
2lw |
2lw + 2lh + 2wh |
Prism |
Bh |
Ph |
2B |
Ph + 2B |
Pyramid |
1⁄3Bh |
- |
B |
- |
Right Pyramid |
1⁄3Bh |
1⁄2Ps |
B |
B + 1⁄2Ps |
Cylinder |
Bh |
- |
2B |
- |
Right Cylinder |
Bh |
Ph |
2B |
Ph + 2B |
Right Circular Cylinder |
πR2h |
2πRh |
2πR2 |
2πRh + 2πR2 |
Cone |
1⁄3Bh |
- |
B |
- |
Right Circular Cone |
1⁄3πR2h |
πRs |
πR2 |
πRs + πR2 |
Volume formulas for various figures including total surface area:
Figure |
Volume |
Total Surface Area |
Sphere |
4⁄3πr3 |
4πr2 |
Regular Tetrahedron |
√ 2 ⁄12a3 |
a2√ 3 |
Cube (regular hexahedron) |
a3 |
6a2 |
Regular Octahedron |
√ 2 ⁄3a3 |
2a2√ 3 |
Regular Dodecahedron |
15 + 7√ 5 ⁄4a3 |
3a2√ 25 + 10√ 5 |
Regular Icosahedron |
5(3 + √ 5 )⁄12a3 |
5a2√ 3 |
For the aforementioned tables:
h = height of solid |
s = slant height |
P = perimeter or circumference of the base |
l = length of solid |
B = area of the base |
r = radius or sphere |
w = width of solid |
R = radius of the base |
a = length of an edge |
Other Volume Unit Definitions
Acre Foot (ac∙ft)
Acre Foot US Survey (ac∙ft)
Acre Inch (ac∙in)
Attoliter (aL)
Barrel Beer US (bl)
Barrel Dry US (bl)
Barrel Liquid US (bl)
Barrel Petroleum US (bl)
Barrel UK (bl)
Barrel Wine UK (bl)
Billion Cubic Meter (billion m3)
Board Foot Measure (FBM)
Bucket UK (bkt)
Bucket US (bkt)
Bushel Dry US (bu)
Bushel UK (bu)
Centiliter (cL)
Cord Firewood (cd-ft)
Cord Foot Timber (cd-ft)
Cubic Angstrom (A3)
Cubic Centimeter (cm3)
Cubic Cubit Ancient Egypt (cubic dhirā)
Cubic Decimeter (dm3)
Cubic Dekameter (dam3)
Cubic Foot (ft3)
Cubic Hectometer (hm3)
Cubic Inch (in3)
Cubic Kilometer (km3)
Cubic Meter (m3)
Cubic Micrometer (μm3)
Cubic Mile (mi3)
Cubic Millimeter (mm3)
Cubic Nanometer (nm3)
Cubic Picometer (pm3)
Cubic Yard (yd3)
Cup Canada (c)
Cup Metric (c)
Cup US (c)
Decaliter (daL)
Deciliter (dL)
Dekaliter (daL)
Dessertspoon Metric (dsp)
Dram (dr)
Drum Petroleum Metric (drum)
Drum Petroleum US (drum)
Exaliter (EL)
Femtoliter (fL)
Fifth (fifth)
Gallon Dry US (gal)
Gallon Liquid US (gal)
Gallon UK (gal)
Gallon US (gal)
Gigaliter (GL)
Gill UK (gi)
Gill US (gi)
Gram Sugar (g)
Gram Water (g)
Half US Gallon (half-gallon-usa)
Hectare Meter (ha∙m)
Hectoliter (hL)
Hogshead UK (hhd)
Hogshead US (hhd)
Imperial Gallon (gil)
Jack Wine (jack)
Jigger (jigger)
Kiloliter (kL)
Kilolitro (kL)
Liter (L)
Litro (L)
Measure Ancient Hebrew (measure)
Megaliter (ML)
Microliter (μL)
Microlitro (μL)
Milliliter (mL)
Millilitro (mL)
Million Cubic Meter (million m3)
Minim UK (min)
Minim US (min)
Nanoliter (nL)
Ounce Liquid UK (oz)
Ounce Liquid US (oz)
Peck UK (pk)
Peck US (pk)
Petaliter (PL)
Picoliter (pL)
Pint Dry US (pt)
Pint Liquid US (pt)
Pint UK (pt)
Pipe UK (pipe)
Pipe US (pipe)
Pony (pony)
Pottle Liquid (pottle)
Quart Ancient Hebrew (qt)
Quart Dry US (qt)
Quart Germany (qt)
Quart Liquid US (qt)
Quart UK (qt)
Quarter Liquid UK (quarter)
Shot (shot)
Stere (stere)
Tablespoon Metric (tbsp)
Tablespoon UK (tbsp)
Tablespoon US (tbsp)
Teaspoon Metric (tsp)
Teaspoon UK (tsp)
Teaspoon US (tsp)
Teraliter (TL)
Thousand Cubic Meter (thousand m3)
Trillion Cubic Meter (trillion m3)
US Fluid Ounce (fl oz)
Yard (yd)
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Related Definitions
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Sources
“Volume.” From Wolfram MathWorld, mathworld.wolfram.com/Volume.html.
