What is the formula for the volume of a sphere?

V = (4/3) × π × r^3, where r is the radius.

Can I calculate volume from diameter or circumference?

Yes. Use r = d/2 for diameter and r = C/(2π) for circumference, then apply V = 4/3 π r^3.

Which units are supported?

Millimeters, centimeters, meters, inches, and feet. Results include derived cubic units, liters, ft³, in³, and US gallons.

How many decimal places can I set?

You can choose between 0 and 10 decimal places for displayed results.

Is the calculator accessible?

Yes. It follows WCAG 2.1 AA with keyboard navigation, visible focus, ARIA live regions, and accessible tooltips.

What sources back the formulas?

Formulas are based on Wolfram MathWorld's 'Sphere' entry and SI unit conversions per the BIPM SI Brochure.

Sphere Volume Calculator

Authoritative Data Source and Methodology

AuthoritativeDataSource: Weisstein, Eric W. “Sphere.” MathWorld—A Wolfram Web Resource (accessed 2025-09-14). Direct link. For SI units and conversions: Bureau International des Poids et Mesures (BIPM), The International System of Units (SI Brochure), 9th edition, 2019. Direct link.

Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte.

The Formula Explained

$$ V = \frac{4}{3}\,\pi r^3 $$

$$ r = \frac{d}{2}, \qquad r = \frac{C}{2\pi} $$

$$ A = 4\pi r^2 $$

The calculator derives the radius r from your chosen input (radius r, diameter d, or circumference C), then applies the exact formula for the volume V. Surface area A is also shown for convenience.

Glossary of Variables

Radius (r): Distance from the sphere’s center to its surface.
Diameter (d): Twice the radius; the longest distance through the center.
Circumference (C): Perimeter of a great circle: C = 2πr.
Surface area (A): Total area covering the sphere: A = 4πr².
Volume (V): Space enclosed: V = 4/3 π r³.
Units: Calculator accepts mm, cm, m, in, ft and outputs cubic/area conversions plus liters and US gallons.

How It Works: A Step-by-Step Example

Scenario: A spherical tank has a measured circumference of 75 cm. Find its volume.

Choose Circumference as input method, enter 75, and select cm.
Compute the radius: r = C / (2π) = 75 cm / (2π) ≈ 11.937 cm.
Apply the volume formula: V = (4/3) π r³ ≈ (4/3) × π × (11.937 cm)³ ≈ 7,119.5 cm³
Convert to liters: 1,000 cm³ = 1 L → 7,119.5 cm³ ≈ 7.12 L.

The calculator performs all steps automatically and shows equivalent units.

Frequently Asked Questions (FAQ)

Can I enter negative or zero values?

No. Radius, diameter, and circumference must be positive. The tool validates inputs and explains how to fix issues.

Why do I see scientific notation?

Very large or very small values are shown in scientific notation for readability and precision (e.g., 3.2e-7 m³).

Which π value is used?

The calculator uses JavaScript’s Math.PI (double-precision, approximately 3.141592653589793).

How accurate are the unit conversions?

Conversions use exact SI definitions: 1 in = 0.0254 m, 1 ft = 0.3048 m, 1 m³ = 1,000 L, 1 m³ ≈ 35.3146667 ft³, 1 m³ ≈ 61,023.7441 in³, 1 m³ ≈ 264.172052 US gal.

What if I only know the diameter?

Select “Diameter,” enter its value and unit. The tool converts to radius internally and computes the result.

Is this suitable for classroom and professional use?

Yes. The tool is designed for both, with accessible UX, transparent formulas, and authoritative sources.

Does the calculator support significant figures?

You can control display precision via “Decimal places.” For strict sig-fig workflows, adjust decimals to match your measurement certainty.

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