Volume Calculation Formulas

Complete reference guide for all volume calculation formulas. Quick lookup with examples, variables explanation, and direct links to specialized calculators.

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Cube

Basic

Formula:

V = s³

Variables:

s = side length

Example:

V = 5³ = 125 cubic units

Applications:

PackagingStorage containersBuilding blocks

Use Cube Calculator

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Rectangular Prism

Basic

Formula:

V = l × w × h

Variables:

l = length, w = width, h = height

Example:

V = 8 × 6 × 4 = 192 cubic units

Applications:

BoxesRoomsContainers

Use Rectangular Prism Calculator

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Sphere

Intermediate

Formula:

V = (4/3)πr³

Variables:

r = radius

Example:

V = (4/3)π(3)³ = 113.1 cubic units

Applications:

BallsTanksBubbles

Use Sphere Calculator

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Cylinder

Intermediate

Formula:

V = πr²h

Variables:

r = radius, h = height

Example:

V = π(4)²(10) = 502.7 cubic units

Applications:

PipesCansPillars

Use Cylinder Calculator

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Cone

Intermediate

Formula:

V = (1/3)πr²h

Variables:

r = base radius, h = height

Example:

V = (1/3)π(3)²(8) = 75.4 cubic units

Applications:

FunnelsTraffic conesRoofing

Use Cone Calculator

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Square Pyramid

Intermediate

Formula:

V = (1/3)a²h

Variables:

a = base side length, h = height

Example:

V = (1/3)(6)²(9) = 108 cubic units

Applications:

PyramidsRoofingMonuments

Use Square Pyramid Calculator

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Triangular Prism

Intermediate

Formula:

V = (1/2)bhl

Variables:

b = base width, h = height, l = length

Example:

V = (1/2)(4)(6)(10) = 120 cubic units

Applications:

TrussesWedgesPrisms

Use Triangular Prism Calculator

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Pentagonal Prism

Advanced

Formula:

V = (1/4)√(25 + 10√5)a²h

Variables:

a = side length, h = height

Example:

V = (1/4)√(25 + 10√5)(2)²(8) = 27.5 cubic units

Applications:

ArchitectureCrystal structuresDesign elements

Use Pentagonal Prism Calculator

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Hexagonal Prism

Advanced

Formula:

V = (3√3/2)a²h

Variables:

a = side length, h = height

Example:

V = (3√3/2)(3)²(10) = 233.8 cubic units

Applications:

HoneycombNuts & boltsCrystals

Use Hexagonal Prism Calculator

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Ellipsoid

Advanced

Formula:

V = (4/3)πabc

Variables:

a, b, c = semi-axes lengths

Example:

V = (4/3)π(3)(2)(4) = 100.5 cubic units

Applications:

EggsPlanetsMedical implants

Use Ellipsoid Calculator

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Conical Frustum

Advanced

Formula:

V = (1/3)πh(R² + Rr + r²)

Variables:

h = height, R = large radius, r = small radius

Example:

V = (1/3)π(6)(5² + 5×3 + 3²) = 263.9 cubic units

Applications:

BucketsLamp shadesHoppers

Use Conical Frustum Calculator

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Capsule

Advanced

Formula:

V = πr²(4r/3 + a)

Variables:

r = radius, a = cylindrical height

Example:

V = π(2)²(4×2/3 + 8) = 133.9 cubic units

Applications:

PillsPressure vesselsTanks

Use Capsule Calculator

Additional Resources

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Formula Derivations

Learn how volume formulas are derived from first principles

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Unit Conversions

Master volume unit conversions with comprehensive guides

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Practice Problems

Test your knowledge with real-world calculation problems

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