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All calculatorsMethodology

Cone Volume Calculator

Calculate the volume of a cone or truncated cone (frustum) from radius or diameter and perpendicular height, with slant height and unit conversions.

Interactive calculator · Method CONE-VOLUME-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

Cone volume V = π r² h ÷ 3, where r is the base radius and h is the perpendicular height.

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Volume 37.6991 cubic units
Slant height 5 units
Lateral surface area 47.1239 sq units
Total surface area 75.3982 sq units
Volume if units are inches 0.6178 liters

V = π × r² × h ÷ 3 = π × 3² × 4 ÷ 3 = 37.6991 cubic units.

How to use the calculator

Choose cone or frustum, say whether you measured radius or diameter, then enter the base, the top (frustum only) and the perpendicular height in one unit.

What the result means

A cone with radius 3 and height 4 holds 12π ≈ 37.6991 cubic units, exactly one third of the cylinder with the same base and height.

Formula and units

Cone volume V = π r² h ÷ 3, where r is the base radius and h is the perpendicular height. Frustum volume V = π h (R² + R r + r²) ÷ 3 for base radius R and top radius r. A diameter entry is halved first. Slant height = √((R − r)² + h²); lateral area = π (R + r) × slant height; total area adds both circular ends. Displays round half-up to four decimals.

Worked examples

Cone with radius 3 and height 4: Base radius or diameter: 3 length unit; Top radius or diameter (frustum only): 1 length unit; Perpendicular height: 4 same length unit; Shape: cone; Entered measurement: radius.
Example result: Volume: 37.6991 cubic units; Slant height: 5 units; Lateral surface area: 47.1239 sq units; Total surface area: 75.3982 sq units; Volume if units are inches: 0.6178 liters.

Frustum 12 in to 8 in across and 10 in tall: Base radius or diameter: 12 length unit; Top radius or diameter (frustum only): 8 length unit; Perpendicular height: 10 same length unit; Shape: frustum; Entered measurement: diameter.
Example result: Volume: 795.8701 cubic units; Slant height: 10.198 units; Lateral surface area: 320.3808 sq units; Total surface area: 483.7437 sq units; Volume if units are inches: 13.042 liters.

Limitations and common mistakes

Use the perpendicular height, not the slant height. All lengths must use one unit; the answer is in that unit cubed. The liters line is only meaningful when lengths are inches. Real containers have wall thickness and rounded edges, so measure inside dimensions for capacity.

Entering the slant height as the height overstates the volume. Entering a diameter while “Radius” is selected quadruples the area term.

Sources and assumptions

Method CONE-VOLUME-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.