Calculator Tools
Volume Calculator
Calculate the volume of a cube, box, sphere, cylinder, cone, pyramid, frustum, ellipsoid, or capsule. Step-by-step with surface area and unit conversions.
Volume calculator
A solid with six equal square faces. All edges have the same length s.
Volume formula
V = s³
Surface area formula
A = 6 s²
Volume
125 cm³
Volume of a cube with the values above.
Volume (cm³)
125 cm³
Same as the native unit; pick any unit above to convert.
In liters (L)
0.125 L
In milliliters (mL)
125 mL
In US gallons
0.033022 gal
In cubic meters
0.000125 m³
Surface area
Total outer surface for the shape, in the same length unit squared.
Surface area (cm²)
150 cm²
Volume to surface ratio
0.833333 cm
Average thickness if the volume were spread uniformly across the surface.
Step-by-step
Each line shows the substitution used to reach the next result.
- Plug s = 5 cm into V = s³.
- V = 5³ = 125 cm³.
- Surface area A = 6 s² = 6 × 5² = 150 cm².
Why these formulas
- V = l w h for a box is the product of the three perpendicular sides; the cube V = s³ is the special case where every side is the same.
- V = π r² h is the area of a circle (π r²) times the perpendicular height. The cone is one third of that because it tapers uniformly to a point.
- V = 4/3 π r³ for a sphere comes from integrating circular cross-sections across the diameter; an ellipsoid uses the same shape with a, b, and c standing in for r.
- The frustum formula is the cone formula evaluated at the bottom radius minus the cone formula evaluated at the (smaller) top, so it reduces to a clean expression in R, r, and the height of the slice.
Units and conversions
- Pick any length unit at the top. Volumes start in that unit cubed, then convert into liters, milliliters, US gallons, and the unit you select in the "Show volume in" field.
- 1 L equals exactly 1 000 cm³ (1 dm³). 1 m³ equals 1 000 L. 1 US gallon equals 231 in³ by definition.
- All math runs locally in your browser. Your inputs are not sent to a server.
How to use
- Pick a shape from the dropdown. The fields below update to the inputs that shape needs.
- Choose your length unit (mm, cm, m, in, ft, yd). All your inputs are interpreted in that unit.
- Enter a positive value for each field. Decimals and comma decimals both work; per-field errors call out missing or invalid entries.
- Read the headline Volume card for the result in the unit cubed, plus liters, milliliters, US gallons, and cubic meters.
- Use the Show volume in dropdown to convert the result into any other cubic unit on the fly.
- If the shape has a surface area formula, the Surface area panel reports the total outer surface and a volume-to-surface ratio.
- Read Step-by-step to see each substitution into the formula, then click Copy full report to drop the breakdown into a notes app or homework write-up.
- Switch shapes at any time. Click Load example to refill the default values, or Clear to empty the fields.
About this tool
Volume Calculator covers the twelve 3D shapes that come up most often in geometry homework, DIY projects, and engineering: cube, rectangular prism (box), sphere, hemisphere, cylinder, hollow cylinder (tube), cone, truncated cone (frustum), square pyramid, rectangular pyramid, ellipsoid, and capsule. Pick a shape, enter the side lengths or radii, and the tool returns the volume using the standard formula (for example V = 4/3 π r³ for a sphere, V = π r² h for a cylinder, V = 1/3 π r² h for a cone, V = 1/3 π h (R² + R r + r²) for a frustum). Where a clean closed-form expression exists, the surface area is shown alongside the volume, and the volume-to-surface ratio is reported as an average thickness check that is useful for material estimates. Volumes are reported in the unit cubed of your chosen length unit (millimeters, centimeters, meters, inches, feet, or yards), and converted into liters, milliliters, US gallons, and cubic meters at the same time. Each result includes a step-by-step derivation that plugs your numbers into the formula so you can see exactly how the value came out. Useful for figuring out fish tank capacity, paint and concrete quantities, packaging and storage volumes, balloon and ball volumes, container and tube capacities, and pyramid problems on geometry tests. Everything runs in your browser; the values you enter are never uploaded.
Free to use. Works in your browser. No signup, no login.
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