Sphere calculator — volume and surface area from the radius

How to use the sphere calculator

1. Enter the Radius, the distance from the centre to the surface. It must be greater than zero.
2. Read Volume (4/3·πr³), the main result.
3. Below it, read Surface area (4πr²), Diameter and Great-circle circumference (2πr).

What it does and when to use it

Spheres appear in sports balls, ball bearings, water tanks, planets in a science project, and round sweets. You might want the volume to know how much air or liquid fits inside, or the surface area to know how much leather, paint or foil covers it. Students meet these two formulas in middle and high school and need to see how a change in radius affects each.

For other solids, the volume calculator and the surface area calculator let you choose from many shapes. The cylinder calculator is useful for comparing a ball with the can it fits in.

How it works

With radius r the tool computes:

• Volume: V = (4/3) × π × r³
• Surface area: SA = 4 × π × r²
• Diameter: d = 2r
• Great-circle circumference: C = 2 × π × r

A great circle is the largest circle you can draw on a sphere, like the equator on a globe.

Worked examples

A ball 7 cm across, step by step. The radius is 3.5 cm.

1. Cube the radius: 3.5³ = 42.875.
2. Multiply by π: 42.875 × 3.141592654 = 134.695785.
3. Multiply by 4/3: 134.695785 × 4 ÷ 3 = 179.59438.

The tool shows Volume (4/3·πr³): 179.59438, so the ball holds about 180 cm³. Its skin is Surface area (4πr²): 153.93804 cm², from 4 × π × 12.25.

Radius 10. The volume is 4,188.790205, the surface area 1,256.637061, and Great-circle circumference (2πr): 62.83185307.

Compare the two examples: the radius grew by a factor of 10 ÷ 3.5 ≈ 2.86. The surface area grew by that factor squared (about 8.2 times) and the volume by that factor cubed (about 23.3 times). This is why big tanks hold much more for the extra material they use.

Limits and tips

• The tool takes the radius only. Convert a diameter or circumference first, as in the FAQ.
• No unit menu: answers use your unit, squared for area and cubed for volume.
• Results show up to 10 significant figures; trailing zeros are dropped, so 179.5943800 shows as 179.59438.
• The calculation runs in your browser.