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Sphere Calculator: Radius, Surface Area and Volume

This free sphere calculator finds the radius, diameter, circumference, surface area and volume of a sphere from any one of them. It shows the formulas used.

By Debmedia Technologies LLP · Kolkata, India · Updated

What Is It and When Do You Need It?

A sphere is perfectly round in three dimensions. Its surface area and volume depend only on the radius, which makes every measurement easy to convert.

Choose what you know and type the value.

How to Use This Tool

  1. Enter the value or values asked for in the boxes.
  2. Choose the unit label if there is a choice.
  3. Press Calculate.
  4. Read every result in the table and copy what you need.

How the Calculation Works

The tool finds the radius first: r = d ÷ 2, r = √(S ÷ 4π) or r = ∛(3V ÷ 4π). Then surface area = 4πr², volume = ⁴⁄₃πr³ and the great-circle circumference = 2πr.

Worked Example

A sphere with radius 3 has a surface area and volume that are both 113.097 (a coincidence at this size), a diameter of 6 and a great-circle circumference of 18.85.

Common Uses

  • Balls and bubbles.
  • Tanks and domes.
  • Planets and astronomy homework.
  • Packaging and design.

Tips and Common Mistakes

  • Volume grows with the cube of the radius, so doubling it gives eight times the volume.
  • Use the same unit for all values.
  • Surface area is in squared units.
  • Measure carefully: a small error in a length is squared in an area and cubed in a volume, so a 5 percent error in a side can become a 10 percent error in the area or a 15 percent error in the volume.
  • Round only at the end. If you copy a result into another calculation, copy the full number from the tool rather than a rounded one, so small errors do not build up.

Next, you may need the circle calculator, cylinder calculator, cone calculator, arc length calculator.

Everything runs in your browser. Nothing you type is uploaded, stored or sent to any outside service.

Frequently Asked Questions

Surface area = 4πr² and volume = ⁴⁄₃πr³.
The distance around the sphere at its widest, which is 2πr.
r = ∛(3V ÷ 4π).
Balls, bubbles, planets and ball bearings are close to spheres.

Disclaimer: results are calculated in your browser from the numbers you enter. Check important results before you rely on them for money, health, safety or legal decisions.