Cone Volume Calculator
Cone Calculator works out Volume and Slant height from Shape, Measurement supplied and Base radius or diameter. The default figures on this page give volume of 37.699112; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
6 steps
- Radius r = 3 cm, height h = 4 cm
- Slant height l = sqrt(r^2 + h^2) = sqrt(9 + 16) = 5 cm
- Volume V = pi r^2 h / 3 = pi x 9 x 4 / 3 = 37.699112 cm^3
- Curved surface = pi (R + r) l = 47.12389 cm^2
- Total surface = curved + base = 75.398224 cm^2
- Taper half angle = atan((R - r)/h) = 36.869898 deg
Its 4 worked examples are re-run on every release, last on 15 September 2026. What changed
What the Cone Calculator calculates
Solves a right circular cone or truncated cone for volume, slant height, lateral and total surface area, taper angle and capacity.
How to use this Cone Calculator
Enter Shape, Measurement supplied, Base radius or diameter and Top radius or diameter (frustum only). Volume updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Volume, Slant height and Perpendicular height.
The method follows Weisstein, Eric W. "Cone." MathWorld — A Wolfram Web Resource, Weisstein, Eric W. "Conical Frustum." MathWorld — A Wolfram Web Resource and NIST Special Publication 811 (unit factors used for capacity and mass output).
3-4-5 cone (r = 3, h = 4) example
With Shape: cone, Measurement supplied: radius, Base radius or diameter: 3, Perpendicular height: 4, the calculator returns Slant height: 5, Volume: 37.6991118, Total surface area: 75.3982237. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Volume, Slant height and Perpendicular height. The inputs you can vary are Shape, Measurement supplied, Base radius or diameter, Top radius or diameter (frustum only), Perpendicular height and Slant height.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How do you find the volume of a cone?
Solves a right circular cone or truncated cone for volume, slant height, lateral and total surface area, taper angle and capacity. Open “How this is worked out” beside the result to see each step for your own figures.
Why is 1/3 in the volume of a cone?
Solves a right circular cone or truncated cone for volume, slant height, lateral and total surface area, taper angle and capacity. On the figures this page opens with — base radius or diameter 3 and perpendicular height 4 — the volume is 37.699112. Put your own figures in their place and the working updates beside the result.
How do you calculate the volume of this cone?
It needs Shape, Measurement supplied, Base radius or diameter, Top radius or diameter (frustum only), Perpendicular height and Slant height. Nothing else is required, and the figures stay in your browser.
How to calculate the total surface area of a cone?
The result gives Volume, Slant height, Perpendicular height, Base radius, Top radius and Base area, each labelled with its unit so the figure can be read on its own.
What information do I need for the Cone Calculator?
You need Shape, Measurement supplied, Base radius or diameter, Top radius or diameter (frustum only), Perpendicular height, Slant height, Length unit and Density (optional). The page opens with default figures that give volume of 37.699112, so you can see the scale before entering your own.
What does this Cone Calculator show?
It shows Volume, Slant height, Perpendicular height, Base radius, Top radius, Base area, Top area and Lateral (curved) surface area, with the working and any warnings for your entries.