Sphere Calculator
Calculate radius, diameter, volume, surface area and mass of a sphere from a single known value. Ideal for math, physics, 3D printing and tank design.
Calculator
kg/m³ – e.g. water 1000, steel ~7850
Results
All values below are derived from your single input.
Radius (m)
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Diameter (m)
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Volume (m³)
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Surface area (m²)
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Mass (kg)
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with density
Sphere formulas
| Parameter | Formula | Notes |
|---|---|---|
| Volume | V = 4/3 × π × r³ | r = radius |
| Surface area | A = 4 × π × r² | Always positive |
| Circumference (great circle) | C = 2 × π × r = π × d | Same as circle with same radius |
| Mass | m = ρ × V | ρ = density in kg/m³ |
How this sphere calculator works
Competitor tools usually ask only for radius or diameter. This one is more flexible: you can start from volume or surface area too, which is handy when you reverse-engineer a shape.
1. Normalize the input
The value you enter is converted to SI units (meters or m² or m³) depending on what you selected.
2. Reconstruct the sphere
We derive the radius first, because every other formula depends on it:
From diameter: \( r = \frac{d}{2} \)
From circumference: \( r = \frac{C}{2\pi} \)
From surface area: \( r = \sqrt{\frac{A}{4\pi}} \)
From volume: \( r = \sqrt[3]{\frac{3V}{4\pi}} \)
3. Compute everything else
With radius known, we compute volume, surface area, diameter, circumference and, if you entered density, mass.
FAQ
Can I enter diameter in inches?
Yes, select “Diameter” and “inches (in)” and the calculator will convert to meters.
How accurate is it?
It uses standard double-precision JavaScript math, which is more than enough for geometry and light engineering.
Formula (LaTeX) + variables + units
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From diameter: \( r = \frac{d}{2} \) From circumference: \( r = \frac{C}{2\pi} \) From surface area: \( r = \sqrt{\frac{A}{4\pi}} \) From volume: \( r = \sqrt[3]{\frac{3V}{4\pi}} \)
- No variables provided in audit spec.
- NIST — Weights and measures — nist.gov · Accessed 2026-01-19
https://www.nist.gov/pml/weights-and-measures - FTC — Consumer advice — consumer.ftc.gov · Accessed 2026-01-19
https://consumer.ftc.gov/
Last code update: 2026-01-19
- Initial audit spec draft generated from HTML extraction (review required).
- Verify formulas match the calculator engine and convert any text-only formulas to LaTeX.
- Confirm sources are authoritative and relevant to the calculator methodology.