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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 & 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.

## SI Multiples

A table of various volume units derived from SI multiples:

 Submultiples Multiples Scientific Notation Value Prefix Name Scientific Notation Value Prefix Name 10-1 L 0.1 L Deci (d) Deciliter (dL) 101 L 10 L Deca (da) Decaliter (daL) 10-2 L 0.01 L Centi (c) Centiliter (cL) 102 L 100 L Hecto (h) Hectoliter (hL) 10-3 L 0.001 L Milli (m) Milliliter (mL) 103 L 1000 L Kilo (k) Kiloliter (kL) 10-6 L 0.000001 L Micro (µ) Microliter (µL) 106 L 1000000 L Mega (M) Megaliter (ML) 10-9 L 0.000000001 L Nano (n) Nanoliter (nL) 109 L 1000000000 L Giga (G) Gigaliter (GL) 10-12 L 0.000000000001 L Pico (p) Picoliter (pL) 1012 L 1000000000000 L Tera (T) Teraliter (TL) 10-15 L 0.000000000000001 L Femto (f) Femtoliter (fL) 1015 L 1000000000000000 L Peta (P) Petaliter (PL) 10-18 L 0.000000000000000001 L Atto (a) Attoliter (aL) 1018 L 1000000000000000000 L Exa (E) Exaliter (EL) 10-21 L 0.000000000000000000001 L Zepto (z) Zeptoliter (zL) 1021 L 1000000000000000000000 L Zetta (Z) Zettaliter (ZL) 10-24 L 0.000000000000000000000001 L Yocto (y) Yoctoliter (yL) 1024 L 1000000000000000000000000 L Yotta (Y) Yottaliter (YL) 10-27 L 0.000000000000000000000000001 L Ronto (r) Rontoliter (rL) 1027 L 1000000000000000000000000000 L Ronna (R) Ronnaliter (RL) 10-30 L 0.000000000000000000000000000001 L Quecto (q) Quectoliter (qL) 1030 L 1000000000000000000000000000000 L Quetta (Q) Quettaliter (QL)

## 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)

• Quectoliter (qL)
• Quettaliter (QL)
• Ronnaliter (RL)
• Rontoliter (rL)
• 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)

• Yoctoliter (yL)
• Yottaliter (YL)
• Zeptoliter (zL)
• Zettaliter (ZL)

## Convert to Another Volume Unit

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### Sources

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

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