Geometry / Solids

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)

Diameter (m)

Volume (m³)

Surface area (m²)

Mass (kg)

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.