Geometry and Measurement

Volume Calculator

Calculate the space occupied by one of four common solids, then express the answer in cubic units or capacity units.

Volume—

How to calculate volume for common shapes

  1. Choose Box, Cylinder, Sphere, or Cone. The visible dimension labels change to match the selected solid.
  2. Enter every visible dimension as a positive value in one shared input length unit. For round solids, the entered circular measure is radius, not diameter.
  3. Choose a volume unit. Changing the input unit converts stored dimensions to preserve the same solid; changing the output unit only changes the displayed result.

Volume formulas for a box, cylinder, sphere, and cone

A rectangular box or prism has volume V = length × width × height. A 2 m by 3 m by 4 m box encloses 24 m³. This assumes all three edges are perpendicular. Measure usable inside dimensions, rather than outside dimensions, when estimating container capacity.

A right circular cylinder has V = πr²h. At radius 2 m and height 3 m, V = 12π m³ ≈ 37.6991 m³. The radius is half the diameter. This is the ideal full cylinder, not the partially filled volume of a horizontal tank; the dedicated cylinder tool offers diameter entry.

A sphere has V = 4πr³/3. A sphere of radius 3 m has V = 36π m³ ≈ 113.0973 m³. A right circular cone has V = πr²h/3: radius 3 m and perpendicular height 4 m produce 12π m³ ≈ 37.6991 m³. The cone height is the straight perpendicular distance, not its sloping side.

All input lengths are converted to meters before cubing. One liter is exactly 0.001 m³ and one US liquid gallon is exactly 0.003785411784 m³. A US gallon is not an imperial gallon. A foot is exactly 0.3048 m, so one cubic foot equals 0.028316846592 m³. Changing length units by ten can change the numerical volume by a factor of one thousand.

Volume is a geometric estimate. Rounded corners, wall thickness, non-level fill, tapered walls, and manufacturing tolerances can change actual capacity. For purchasing or safety-critical planning, measure the real object, allow suitable margins, and verify the required convention for gallons.

Inputs, units, and results

ItemMeaningCheck
Solid shapeBox, right cylinder, sphere, or right coneOnly dimensions shown for the chosen shape are required.
DimensionsBox edges or circular radius and perpendicular heightAll visible inputs must be positive and finite.
Input length unitCommon unit for every entered dimensionA change converts stored numbers to preserve the solid.
Result volume unitCubic units, liters, or US liquid gallonsThe output unit does not change the physical volume.

Practical uses and limitations

Packaging

Compare simple rectangular package capacities from internal dimensions.

Round vessels

Estimate full ideal cylindrical or conical volume from radius and height.

Sphere models

Find a ball or spherical cavity volume from a measured radius.

Limits

These formulas describe ideal solids, not partial fills, irregular shapes, or wall thickness. Use the correct shape model before ordering material.

Frequently asked questions

Which shapes does this calculator support?

It supports a box, right circular cylinder, sphere, and right circular cone. Select the shape first so only relevant dimensions are required.

Can I enter diameter for a round solid?

This general tool accepts radius. Divide a measured diameter by two before entry, or use the dedicated cylinder calculator for diameter mode.

How do liters relate to cubic meters?

Exactly 1 m³ = 1,000 L. The numerical value depends on the volume unit even though the physical space does not change.

Is a US gallon the same as an imperial gallon?

No. This page uses US liquid gallons; one US liquid gallon is exactly 3.785411784 liters.

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Last reviewed: October 26, 2026. Calculations run in your browser. Confirm dimensions and units for consequential work.

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