Circle Calculator

How to use the circle calculator

Select which measurement you know — radius, diameter, circumference or area — type in the value and, optionally, pick a unit. The calculator works out the other three straight away. When you start from the radius or diameter it also shows the exact answer in terms of π (for example, 25π), which is what many teachers ask for. The steps panel shows each formula with your numbers substituted, and the table adds handy extras such as the area of a semicircle, the largest square that fits inside the circle and the volume of a sphere with the same radius.

Circle formulas

• r — radius: the distance from the centre to the edge
• d — diameter: the distance straight across through the centre
• C — circumference: the distance around the circle (its perimeter)
• A — area: the space enclosed by the circle
• π (pi) ≈ 3.14159265 — the ratio of any circle's circumference to its diameter

Worked examples

From the radius

A circle has a radius of 5 cm. Its diameter is 2 × 5 = 10 cm. Its circumference is 2 × π × 5 = 10π ≈ 31.4159 cm. Its area is π × 5² = 25π ≈ 78.5398 cm².

From the circumference

You wrap a tape measure around a tree trunk and get 157 cm. The radius is 157 ÷ 2π ≈ 24.99 cm, so the trunk is about 50 cm across, and its cross-sectional area is about 1,962 cm². This is how foresters estimate a tree's diameter without cutting it.

From the area

A circular garden bed needs to cover 20 m². The radius is √(20 ÷ π) ≈ 2.523 m, so you need a diameter of about 5.05 m and roughly 15.85 m of edging around it.

Understanding π

Pi is the same for every circle, from a coin to a planet's orbit: circumference divided by diameter always equals about 3.14159. It is an irrational number, so its decimals never end or repeat. For everyday measurements, 3.14 is accurate to about 0.05%, and 22/7 to about 0.04%. This calculator uses the full double-precision value, accurate to about 15 significant figures.

Common mistakes

• Mixing up radius and diameter. If a problem gives the width across, halve it before using πr².
• Forgetting to square the units. If the radius is in metres, the area is in square metres (m²). Circumference stays in plain metres.
• Squaring π instead of r. πr² means π × (r × r), not (π × r)².

Where circle calculations are used

Circle formulas appear everywhere: sizing round tables, pools and patios; working out how much fencing surrounds a circular paddock; choosing pipe and duct sizes; calculating wheel travel per revolution (one turn moves a bike forward by one circumference); and estimating the coverage of a sprinkler or a Wi-Fi router. For part of a circle, such as a pie slice, use the sector option in the area calculator. For 3D shapes like cylinders and spheres, see the volume calculator and the surface area calculator. To work out how much flooring or paint a circular area needs, combine these results with the square footage calculator.