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# 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 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)

• 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)

For all other definitions & terms visit All Definitions

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Though every effort has been made to test this unit converter, we are not to be held liable for any special, incidental, indirect or consequential damages or monetary losses of any kind arising out of or in connection with the use of any of the converter tools and information sourced from this website. This unit converter is provided as a service to you, please use at your own risk. Do not use calculations for anything where loss of life, money, property, etc could result from inaccurate unit conversions.

### Sources

“Volume.” From Wolfram MathWorld, mathworld.wolfram.com/Volume.html.

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