📦 Volume Calculator

Calculate volume of cubes, cylinders, spheres, cones, and prisms from dimensions with formula steps.

3D Shape Volume — From Dimensions, Not Unit Conversion

BrainyCalculators editorial insight — unique to this tool

Cylinder V = πr²h for tank capacity; sphere V = 4/3 πr³. Concrete pour from slab dimensions differs from Volume Converter which swaps liters↔gallons. Excavation and pool fill use geometric volume then convert units separately.

When to use this calculator

Use when you have shape dimensions and need cubic measure. For liter↔gallon conversion, use Volume Converter.

Not what you need? Not for unit conversion between liters and gallons — use Volume Converter. For construction bag counts, use Concrete.

Converting liters, gallons, or cubic meters?

This page computes shape volume from dimensions. For unit conversion between capacity labels, use the Volume Converter →

Shape

Unit

Side length (s)

Example — Cylinder with r = 4, h = 10

Volume = π × r² × h = π × 16 × 10 ≈ 502.65 units³

Surface Area = 2π r(r + h) = 2π × 4 × 14 ≈ 351.86 units²

What is a Volume Calculator?

A geometry volume calculator applies 3D formulas to shapes: cube, rectangular prism, cylinder, sphere, cone, and pyramid from measured dimensions.

Use this page for math and construction geometry when you know shape type and sizes. For converting liters to gallons between unit labels, use the Volume Converter.

Perimeter and area are two-dimensional; volume is cubic measure of space enclosed.

How the Volume Calculator Works

Formula, assumptions, and calculation steps for this math tool.

Methodology

Math calculators apply the relevant arithmetic, algebraic, geometric, or numeric rule to the values entered and simplify the result where possible.

Calculation Steps

Read the values and operation selected.
Normalize signs, decimals, fractions, or units if needed.
Apply the mathematical rule or formula.
Format the answer and any intermediate values for checking.

Assumptions and Limits

Inputs must be within the supported domain of the operation.
Decimal answers may be rounded for readability.
Symbolic simplification is limited to the calculator scope.

Frequently Asked Questions

What is volume?

Volume is the amount of 3-dimensional space occupied by a solid shape. It is measured in cubic units (m³, cm³, ft³, etc.). Volume tells you how much a container can hold.

What is the difference between volume and capacity?

Volume is the space an object occupies. Capacity is how much a container can hold (usually for liquids). They are numerically equal for hollow containers — 1 cm³ = 1 mL.

How do I find the volume of a cylinder?

Volume of cylinder = π × r² × h, where r is the radius of the circular base and h is the height. For example, r = 3 cm and h = 5 cm gives V = π × 9 × 5 ≈ 141.37 cm³.

What is the difference between surface area and volume?

Surface area is the total area of all outer faces of a 3D shape (measured in square units). Volume is the space inside (measured in cubic units). A large volume does not always mean a large surface area.

What is the volume of a sphere?

V = (4/3) × π × r³. For a sphere of radius 5 cm: V = (4/3) × π × 125 ≈ 523.60 cm³. The surface area of the same sphere is 4 × π × 25 ≈ 314.16 cm².

Real-World Applications

🏗️

Construction & Civil Engineering

Calculate concrete volumes for slabs, columns, and footings; estimate excavation quantities and spoil removal costs.

🛢️

Storage Tanks & Vessels

Size cylindrical or rectangular tanks for water, fuel, or chemicals to meet capacity requirements without overflow risk.

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Manufacturing & Machining

Determine material usage for castings, mouldings, and CNC stock — reducing waste and improving cost estimates.

🚿

Plumbing & HVAC

Size hot-water cylinders, buffer vessels, and duct cross-sections for correct system performance.

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Laboratory & Science

Compute sample volumes for titrations, dilutions, and container selection in chemistry and biology experiments.

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Logistics & Packaging

Calculate parcel cubic volume for freight classification and determine how many units fit in a shipping container.

Common Mistakes

Confusing Volume with Surface Area

Volume measures the space inside (cubic units); surface area measures the outer faces (square units). Using the wrong formula leads to completely incorrect results.

Applying the Wrong Formula for the Shape

A sphere, cone, and cylinder all look rounded yet have different formulas. Always identify the shape precisely before calculating.

Mixing Units Within a Single Formula

Combining metres and centimetres in the same calculation produces nonsense. Convert all dimensions to one unit before substituting into the formula.

Forgetting the Cube in Cubic Units

Volume is always expressed in cubic units (cm³, m³, ft³). Reporting a result in cm² or m² is a dimensional error that flags a calculation mistake.

Partial-Fill Estimation Errors

A half-full sphere or cone is not simply half the total volume by height — the cross-sectional area changes with depth. Use segment or integration formulas for partial fills.

Volume Formulas by Shape

Shape	Formula	Variables
Rectangular Prism	V = l × w × h	l = length, w = width, h = height
Cylinder	V = π r² h	r = radius, h = height
Sphere	V = (4/3) π r³	r = radius
Cone	V = (1/3) π r² h	r = base radius, h = height
Pyramid	V = (1/3) × base area × h	h = perpendicular height

References

Coxeter, H.S.M. Introduction to Geometry. Wiley, 1969.
Euclid. Elements, Book XII. c. 300 BC — classical derivations of volume formulas.
NIST. Handbook of Mathematical Functions (DLMF). National Institute of Standards and Technology, 2010.
Weisstein, E.W. Volume. MathWorld — A Wolfram Web Resource.
ISO 80000-3:2019. Quantities and Units — Space and Time. International Organization for Standardization.