3D volume from radius, diameter, or surface area

Sphere Volume Calculator

Calculate the volume of a sphere — the total 3D space inside a perfectly round ball. Enter the radius, diameter, or surface area and get the volume in cubic units, plus the surface area, circumference, and cross-section area.

1. Select Input Type

r

Results

Volume(V)
(4/3)πr³
0.0000cm³
Surface Area(SA)
4πr²
0.0000cm²
Radius(r)
d/2
0.0000cm
Diameter(d)
2r
0.0000cm
Circumference(C)
2πr
0.0000cm
Cross-Section Area(A)
πr²
0.0000cm²
Computed radius: π = 3.1415926535…

Sphere Volume Calculator

A sphere is the three-dimensional analog of a circle. Every point on its surface is equidistant from the center. While a circle encloses a flat area (πr²), a sphere encloses a volume — the space inside a ball.

From 2D to 3D

A circle has radius and area (πr²). A sphere extends this into 3 dimensions — adding the third power (r³) and a scaling factor of 4/3. This jump from squared to cubed means volume grows much faster than area. Doubling the radius gives 4× the surface area but 8× the volume.

Where spheres appear

Spherical shapes are everywhere: ball bearings in engines, water droplets in mid-air, planets in orbit, pharmaceutical capsules, and pressure vessels in factories. Spheres minimize surface area for a given volume, which is why bubbles and planets tend toward this shape naturally.

Sphere Volume Formula

The volume formula uses three key components. Click each part to understand where it comes from.

Click each part to explore

V=
×
×

Alternative: V = πd³/6 from diameter, or V = SA^(3/2) / (6√π) from surface area.

How to Calculate Sphere Volume

Three steps from radius to volume. Enter a value to see each step with real numbers.

1

Measure the Radius

r = d/2

Find the radius of the sphere — the distance from its center to any point on the surface. If you know the diameter, divide by 2.

r = 6
2

Cube the Radius

r³ = r × r × r

Multiply the radius by itself three times (r × r × r). This converts the one-dimensional radius into a three-dimensional volume measure.

3

Multiply by (4/3)π

V = (4/3)πr³

Multiply the cubed radius by 4/3 × π (≈ 4.18879). This factor accounts for the sphere's curved shape.

Formula Variations

Three ways to compute sphere volume depending on your starting measurement.

FormulaV = (4/3)πr³

The standard sphere volume formula. Cube the radius to get a 3D measure, then scale by the sphere constant (4/3)π.

1Measure the radius (r)
2Cube it: r × r × r
3Multiply by (4/3)π ≈ 4.18879
V = (4/3)πr³

From radius

V = πd³/6

From diameter

V = SA^(3/2) / 6√π

From surface area

Example

Find the volume of a sphere step by step. Change the radius to try different sizes.

1Given
r = 6 cm

The sphere has a radius of 6 centimeters.

Frequently Asked Questions

Common questions about sphere volume, surface area, and 3D geometry.