Frustum Volume Calculator

Work out frustum volume instantly with clear inputs, formula shown and shareable results.

About Frustum Volume Calculator

A conical frustum is a cone with its tip sliced off parallel to the base. Its volume is ⅓πh(R² + Rr + r²), and the curved surface is π(R + r)l with slant height l = √((R − r)² + h²).

Formulas

Volume

V = ⅓πh(R² + Rr + r²)

Curved area

A = π(R + r)l, l = √((R − r)² + h²)

Worked example

With the default values below, Frustum Volume Calculator returns Volume of 527.7876. Change any input above and every figure here is recalculated in your browser.

Inputs used

Larger base radius Rminimum 0: 6
Smaller top radius rminimum 0: 3
Vertical heightminimum 0: 8

Results

Volume: 527.7876
Curved area: 241.5760
Total surface area: 382.9477
Slant height: 8.5440

Step by step

1Values used
2Volume
3Curved area
4Volume= 527.7876
5Curved area= 241.5760
6Total surface area= 382.9477
7Slant height= 8.5440

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What if r equals R?

The formula collapses to πR²h, the cylinder, which is the correct limiting case.

What if r is zero?

It becomes ⅓πR²h, the full cone. This calculator requires a positive top radius, so use the cone calculator for that case.