A frustum is the shape created when a cone is cut by a plane parallel to its base, removing the top. It has two circular faces of different radii connected by a slanted lateral surface.

What formula is used?

The volume is V = (π × h / 3) × (R² + R×r + r²), where R is the bottom radius, r is the top radius, and h is the perpendicular height between the two circular faces.

What units does this calculator support?

You can choose millimeters (mm), centimeters (cm), meters (m), inches (in), or feet (ft). The volume result is always in the corresponding cubic unit (mm³, cm³, m³, in³, ft³).

What happens if top and bottom radii are equal?

If both radii are equal, the shape becomes a cylinder, and the formula simplifies to V = π × r² × h — the standard cylinder volume formula.

What if the top radius is 0?

If the top radius (r) is 0, the frustum is a complete cone, and the formula gives V = (π × h × R²) / 3, which matches the standard cone volume formula.

Is this calculator accurate?

Yes. The calculation uses JavaScript's native Math.PI (IEEE 754 double precision) and applies the exact frustum formula. Results are rounded to 6 significant figures for display.

Volume of a Frustum Calculator

Name: Volume of a Frustum Calculator
Availability: InStock
Author: Nham Vu

Enter the top radius, bottom radius, and height of a frustum to instantly calculate its volume.

Frustum Dimensions

All values must be greater than zero.

Unit

Bottom Radius (R)

Top Radius (r)

Height (h)

Result

Enter dimensions on the left and click Calculate.

Volume

Parameter	Value
Bottom Radius (R)
Top Radius (r)
Height (h)
Formula	π·h/3·(R²+R·r+r²)
Volume (exact π)

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Summary

Enter the top radius, bottom radius, and height of a frustum to instantly calculate its volume.

How it works

Enter the bottom radius (R) of the frustum.
Enter the top radius (r) of the frustum.
Enter the height (h) of the frustum.
Choose your preferred unit (mm, cm, m, in, ft).
The volume is computed instantly using V = (π·h/3)·(R²+R·r+r²).
Copy the result or reset the form to calculate another frustum.

Use cases

Calculate the volume of a truncated traffic cone.
Estimate material needed for a tapered bucket or funnel.
Engineering and architecture calculations for frustum-shaped components.
Classroom and homework help for solid geometry problems.
Calculate the capacity of frustum-shaped containers or tanks.
3D modeling and printing volume estimation.
Verify manual calculations against a trusted online tool.
Compare frustum volumes across different dimensions.

Frequently Asked Questions

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Last updated: 2026-05-23 · Reviewed by Nham Vu