Circle Calculator

What this calculator does

A circle has four measurements that everyone reaches for: the radius, the diameter, the circumference, and the area. The catch is that they are all tied together, so if you know any one of them, the other three are already decided.

This is the tool that fills them in. Tell it which measurement you have, type the number, and it works out the rest in one go.

Using the calculator

1. From the dropdown, choose which measurement you have: radius, diameter, circumference or area.
2. Type its value into the box.
3. Press Calculate.

You get all four back together. The value you enter has to be positive, since none of a circle's measurements can be zero or less.

How one value gives you the other three

Everything about a circle is set by a single number, the radius. The other three hang off it like this:

diameter = 2 × radius

circumference = 2 × π × radius

area = π × radius²

So whatever you hand the tool, the first thing it does is work back to the radius, then build the rest from there:

• Given the radius, it already has what it needs.
• Given the diameter, the radius is half of it: radius = diameter ÷ 2.
• Given the circumference, it undoes the 2π: radius = circumference ÷ (2 × π).
• Given the area, it undoes the square: radius = √(area ÷ π).

The constant doing the heavy lifting is π, the number that ties the straight measurements (radius and diameter) to the round ones (circumference and area).

Units and rounding

There are no unit menus here, so you can work in whatever unit suits you. The radius, diameter and circumference all come out in that same unit, and the area comes out in that unit squared, since area is a length times a length. Every value is rounded to two decimal places.

A worked example | starting from the diameter

Say all you know is the diameter, and it is 10.

1. Radius: 10 ÷ 2 = 5.
2. Circumference: 2 × π × 5 = 31.42.
3. Area: π × 5² = 78.54.

Start instead from the area or the circumference and the tool runs the same chain in reverse, taking a square root or dividing by 2π to recover the radius first, then filling in the rest.

The four measures for common radii

A few radii worked through. Diameter and circumference share the radius's unit, the area is in that unit squared.

Questions people ask

I only know the area. How do I get the radius?

Divide the area by π, then take the square root: radius = √(area ÷ π). The tool does this for you when you pick "area" from the dropdown.

How is this different from the area and circumference calculators?

Those each do one job from a radius. This one works in any direction, from any of the four measurements, and gives you all four at once. If you only need a single answer from a radius, the area of circle calculator or circumference of circle calculator is the quicker pick.

Do I need to enter units?

No. Work in whatever unit you like. The radius, diameter and circumference come back in that unit, and the area in that unit squared.

What is the link between radius and diameter?

The diameter is the full width across the centre, and the radius is half of it. So diameter = 2 × radius, and radius = diameter ÷ 2.

References

A note on where this comes from. The four measurements are tied together by π, the ratio of a circle's circumference to its diameter, whose value is tabulated by the US National Institute of Standards and Technology. That a circle's area is π × radius² was proved by Archimedes more than two thousand years ago in his Measurement of a Circle. For further reading, see Circle.

1. National Institute of Standards and Technology (NIST), Digital Library of Mathematical Functions, value and definition of π. https://dlmf.nist.gov/
2. Archimedes, Measurement of a Circle (c. 250 BCE), the proof that a circle's area equals π × radius².