Circle Calculator
Enter any one measurement (radius, diameter, circumference, or area) and get the other three with the formulas shown.
Details
Area
9π
≈ 28.274334 – in square units
This works out every measurement of a circle from any one of them. Enter the radius, diameter, circumference or area and it returns the other three.
That means you never have to rearrange a formula yourself, whichever measurement you happen to have.
The parts of a circle
A circle is described by four linked numbers, and knowing any one gives you the rest. The radius is centre to edge, the diameter is all the way across, the circumference is the distance around, and the area is the space inside.
The diameter is simply twice the radius. That one relationship causes more errors than anything else in geometry, because it is easy to measure across a circular object and hard to find its exact centre.
Tying it all together is π, roughly 3.14159. It is what you get when you divide any circle's circumference by its diameter, and it comes out the same for every circle that has ever existed.
Circumference uses the radius once; area uses it twice, because it is squared. That is why doubling a circle's size doubles its edge but quadruples its area.
What to enter
- What do you know?
- Choose whether you are entering the radius, diameter, circumference or area. Everything else is worked out from it.
- Value
- Your measurement. Be certain whether you measured to the centre or all the way across.
The four relationships
- Diameter
- d = 2r. Twice the radius, straight through the centre.
- Circumference
- C = 2πr, or πd. The distance all the way around.
- Area
- A = πr². The radius is squared, which is why area grows so fast.
- From circumference back
- r = C ÷ 2π. Useful when you can wrap a tape around something but cannot find its centre.
- π
- About 3.14159. The ratio of any circle's circumference to its diameter, identical for all circles.
What this assumes
The shape is a true circle. An oval needs different formulas entirely.
π is used to full precision, so answers may differ slightly from a hand calculation using 3.14.
How to calculate a circle's measurements
Get to the radius first. Every other formula follows from it easily.
- r
- The radius: centre to edge
- π
- About 3.14159
Find the radius. If you measured across, halve it. From a circumference, divide by 2π. From an area, divide by π and take the square root.
For the distance around, multiply. C = 2 × π × r. For a radius of 5 that is 31.42.
For the space inside, square first. A = π × r². Square the radius before multiplying by π, not after.
Sanity check the size. The area in square units should be noticeably larger than the circumference for any circle bigger than radius 2.
See a worked example: working backwards from a tape measure
- Measured around a tree
- 31.42 inches
You cannot reach the centre, but you can wrap a tape around it.
Radius: 31.42 ÷ (2 × π) = 31.42 ÷ 6.2832 = 5 inches.
Diameter: 10 inches.
Area of the trunk's cross-section: π × 5² = 78.54 square inches.
Radius 5 in, diameter 10 in, area 78.54 sq in
Frequently asked questions
The radius goes from the centre to the edge. The diameter goes all the way across, through the centre, so it is exactly twice the radius.
Getting them mixed up is the most common circle error by a wide margin, and because the radius is squared in the area formula, using a diameter by mistake makes the area four times too big.
Divide the circumference by 2π, which is about 6.2832. A tape reading 31.42 inches gives a radius of 5.
This is genuinely useful in practice: measuring around a tree, a pipe or a tank is easy, while locating the exact centre is not.
Because area depends on the radius squared. A 16-inch pizza has an area of about 201 square inches against 113 for a 12-inch, so it is roughly 78% more pizza, not 33% more.
This is why two 12-inch pizzas give you less than one 16-inch, which surprises almost everyone.
The ratio of a circle's circumference to its diameter. Divide the distance around by the distance across, for any circle at all, and you get about 3.14159.
It is irrational, meaning its decimals never end or repeat. Using 3.14 is fine for most jobs, and 3.14159 is more than enough for anything practical.
A semicircle is half a circle: work out πr² and halve it. Do not forget the straight edge if you also need the perimeter.
For a sector, take the fraction of the full turn. A 90° sector is a quarter of the circle, so it is πr² ÷ 4.
Problems people actually run into
Measuring across and using it as the radius
Measuring a circular table at 60 inches across and putting 60 into the area formula gives 11,310 square inches instead of 2,827. That is four times too much.
The habit worth building: whenever you measure across a circle, halve it immediately and write down the radius, before touching any formula.
Squaring after multiplying by π
The area formula is π × r², which means squaring the radius first. Working out πr and then squaring that gives (πr)², a completely different and much larger number.
For r = 5: the correct answer is π × 25 = 78.54, while squaring afterwards gives 246.7.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026