mathematics calculator
Cone Volume Calculator
Calculate a right circular cone's volume, base area, and matching cylinder volume from radius and perpendicular height.
Cone Volume Calculator
Cone volume
Enter the radius and perpendicular height of a right circular cone.
This tool models a right circular cone, not a frustum or oblique cone.
Formula version 1.0.0
How to use this calculator
- Enter positive base radius and perpendicular height in one unit.
- Select Calculate.
- Review circular base area and matching cylinder volume.
- Read cone volume as one third of that cylinder.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
r | Base radius | length |
h | Perpendicular height | length |
B | Base area πr² | square length |
V | Cone volume | cubic length |
Checked examples
Radius three, height four
Inputs: r=3, h=4
Calculation: V=⅓π×3²×4
Result: 12π cubic units
The matching cylinder volume is 36π.
Check: cone-volume-core.test.ts
Unit radius
Inputs: r=1, h=3
Calculation: V=⅓π×1²×3
Result: π cubic units
Height three cancels the one-third factor.
Check: cone-volume-core.test.ts
Assumptions, rounding, and limits
- The cone is right and circular.
- Radius and perpendicular height are positive and consistent.
- The result uses cubic input units.
- No wall thickness or fill allowance is modeled.
Frequently asked questions
Why divide cylinder volume by three?
A cone with the same base and height has one third of the matching cylinder's volume.
Can I enter slant height?
No. This formula requires perpendicular height.
How does scaling affect volume?
Scaling every dimension by k multiplies volume by k³.
Sources and review
- OpenStax: Geometric Formulas — Cone volume
- OpenStax: Solve a Formula for a Specific Variable — Cone-volume formula
- Formula version
- cone.volume@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Ideal right circular cone from radius and perpendicular height.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.