Circle Area Calculator
Calculate the area of a circle by entering its radius. Fast and precise result with A = pi x r^2.
Circle area, and the mistakes radius causes
The formula is one of the few most people remember from school. The errors are almost never in the formula - they are in using diameter where radius belongs, or in forgetting that area scales with the square of the radius rather than in proportion to it.
Formula
A = pi x r^2
If you have the diameter, halve it first. Using diameter directly gives an answer four times too large.
Area grows with the square, not the length
Double the radius and you quadruple the area. Triple it and the area is nine times larger. This is counter-intuitive enough that it drives real purchasing errors.
A 16-inch pizza is not slightly bigger than a 12-inch - it has 78% more surface. Two 12-inch pizzas give 226 square inches; one 16-inch gives 201. The single larger pizza looks like the better deal by diameter and is not.
The same relationship governs pipe flow, cable capacity, and lens light-gathering. A pipe with twice the bore carries roughly four times the volume at the same velocity, which is why small diameter increases produce large capacity gains.
Working from other measurements
You often have something other than the radius. Each has a direct route.
- From diameter d: A = pi x d^2 / 4. A 10 cm diameter gives 78.54 cm^2.
- From circumference C: A = C^2 / (4 x pi). A 31.42 cm circumference gives 78.54 cm^2.
- From a sector of angle theta degrees: A = (theta / 360) x pi x r^2.
- For an annulus (a ring) with outer R and inner r: A = pi x (R^2 - r^2).
- For a semicircle, halve the full area; for a quarter circle, quarter it.
How much precision pi actually needs
Pi is irrational, so any decimal value is an approximation. The practical question is how many digits matter.
Using 3.14 introduces an error of about 0.05%, which on a 5 m radius circle is around 0.04 m^2. Using 22/7 is slightly worse at 0.04% high. NASA uses 15 decimal places for interplanetary navigation, which is enough to compute the circumference of a 25 billion mile circle to within an inch.
For construction, materials, and everyday work, 3.1416 is more precision than the measurement of the radius will ever justify.
Worked example
A circular patio has a circumference of 18.85 m and you need to know how much paving to order.
Radius first: r = C / (2 x pi) = 18.85 / 6.2832 = 3.00 m. Then A = pi x 3^2 = 28.27 m^2.
Adding the standard 10% wastage allowance for cuts gives 31.1 m^2 to order. If you had mistakenly used 18.85 as the diameter, you would have calculated 279 m^2 and ordered nine times too much material.
Circle area at common radii
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.28 | 3.14 |
| 2 | 4 | 12.57 | 12.57 |
| 3 | 6 | 18.85 | 28.27 |
| 5 | 10 | 31.42 | 78.54 |
| 10 | 20 | 62.83 | 314.16 |
| 25 | 50 | 157.08 | 1,963.50 |
Units are consistent throughout: a radius in metres gives an area in square metres.
Frequently Asked Questions
Related calculators
References
- NASA JPL - how many decimals of pi do we really need
- NIST Special Publication 811 - Guide for the Use of the SI
Last reviewed: 2026-08-07. This page is informational. For legal, medical, tax, or financial decisions, confirm the result with a qualified professional.