What is the formula for the volume of a cone?

The volume of a right circular cone is V = (1/3)·π·r²·h, where r is the base radius and h is the perpendicular height.

Can I use diameter instead of radius?

Yes. If you know the diameter d, first compute the radius as r = d / 2, then use V = (1/3)·π·r²·h.

Which units can I use?

You can enter mm, cm, m, inches, or feet. The calculator converts internally and reports volume in the chosen unit³ plus common conversions like m³ and liters.

Is the formula valid for oblique cones?

The formula V = (1/3)·π·r²·h applies to any cone provided h is the perpendicular height. For the typical 'cone' in geometry (right circular cone), this is the standard formula.

How accurate are the results?

Results are computed with double-precision floating-point arithmetic. You can choose the number of displayed decimal places without affecting internal precision.

How do I convert the result to liters or gallons?

1 m³ = 1000 L. The tool automatically shows liters. For US gallons, 1 gallon ≈ 231 in³ or 3.78541 L; the calculator provides in³ and ft³ for quick reference.

Cone Volume Calculator

Data Source and Methodology

Authoritative reference: Eric W. Weisstein, “Cone,” MathWorld—A Wolfram Web Resource. Last updated 2024. Direct link: https://mathworld.wolfram.com/Cone.html.

All calculations strictly follow the formulas and definitions provided by this source.

The Formula Explained

For a right circular cone, the volume is:

$$ V = \frac{1}{3}\,\pi r^{2} h $$

If you use diameter d instead of radius r, then r = d/2 and:

$$ V = \frac{1}{3}\,\pi \left(\frac{d}{2}\right)^{2} h = \frac{\pi d^{2} h}{12} $$

Glossary of Variables

h (Height): Perpendicular distance from base to apex of the cone.
r (Radius): Distance from the center of the base to its edge; half the diameter.
d (Diameter): Full width of the base circle; d = 2r.
V (Volume): Space enclosed by the cone, typically expressed in unit³ (e.g., cm³, m³).
Units: The calculator accepts mm, cm, m, inches, and feet, then converts to m³, liters, in³, and ft³.
Decimal places: Display precision you choose for the results; internal computations retain high precision.

How It Works: A Step‑by‑Step Example

Goal: Find the volume of a cone with radius r = 3 cm and height h = 10 cm.

Select “Radius + Height” and the unit “cm”.
Enter r = 3 and h = 10.
Apply the formula: $$ V = \frac{1}{3}\,\pi r^{2} h = \frac{1}{3}\,\pi\,(3)^{2}\,(10) = \frac{1}{3}\,\pi\,(9)\,(10) = 30\pi \text{ cm}^3 $$
Compute: 30π ≈ 94.2478 cm³.
Convert if needed: 1 cm³ = 1 mL, so ≈ 94.2478 mL = 0.0942478 L.

Frequently Asked Questions (FAQ)

Is this calculator compliant with accessibility standards?

Yes. It is designed to meet WCAG 2.1 AA with keyboard operability, visible focus states, semantic markup, and ARIA for dynamic content.

Does the formula work for any cone?

It works for cones where the height is the perpendicular distance to the base. This includes the standard right circular cone. For oblique cones, use the same formula if h is perpendicular height.

What if I only know the slant height?

You’ll need either the radius (or diameter) and the perpendicular height. Slant height alone isn’t sufficient to determine volume.

How should I round my results?

Use the decimal places control to format results for your context. Internal precision is higher than the displayed precision.

Which unit is best?

Use the unit native to your measurements to reduce conversion errors. The tool will convert to m³, liters, in³, and ft³ automatically.

Can I paste values with commas?

You can paste values; the inputs accept decimals. Ensure a dot as the decimal separator (e.g., 12.5). Non-numeric characters are ignored.

How does this compare to other online tools?

Beyond computing volume, this tool provides in-depth explanations, multiple unit outputs, inline validation, and WCAG-compliant UX to ensure trust and reliability.

Tool developed by Ugo Candido. Content verified by the CalcDomain Editorial Team.
Last reviewed for accuracy on: September 14, 2025.