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Circle calculator — radius, diameter, circumference and area
A circle has only one independent measurement, so any one of these four numbers fixes the other three. Type whichever you actually have — including a circumference you measured with a tape — and the drawing highlights the one you are entering.
How to use it
- Choose your unit first. Every box is read and written in it, and the area is shown in that unit squared.
- Type into whichever box you already know. The other three update on every keystroke, and the drawing highlights the measurement you are editing.
- Measured around a pipe, a tree or a barrel with a tape? That is the circumference — put it in the third box and read the diameter off the second.
- The working lines under the boxes show the arithmetic with your own numbers substituted, so you can check it by hand or copy it into homework.
Why any one of the four is enough
A circle has a single degree of freedom: fix its size once and every other measurement follows. The diameter is twice the radius, the circumference is π times the diameter, and the area is π times the radius squared. Run those backwards and you get the forms that matter in practice — the radius is the circumference divided by 2π, and it is also the square root of the area divided by π.
Most circle calculators accept only the radius, which is the one measurement you can rarely take. You cannot get a tape to the centre of a tree, a pipe or a column; you can only get it around the outside. This page takes whichever of the four you actually have, and the working lines underneath show the substitution it made, so no step of the answer is hidden from you.
Area grows with the square of the radius, and that surprises people
Doubling the radius does not double the area — it quadruples it, because the radius appears squared. The cheapest place to see this is a pizza menu. A 30 cm pizza covers about 707 cm²; a 20 cm one covers about 314 cm². The larger is not 50% more food, it is 125% more, and two of the smaller ones come to 628 cm² — still less than one large.
The same arithmetic runs the other way when you are buying material. Cutting a circle 10% smaller across removes 19% of its area, not 10%. If you are pricing a round tabletop, a pond liner or a cake board by area, the diameter you quote and the cost you pay do not move in step, and the gap widens the bigger the circle gets.
What the drawing does and does not tell you
The diagram is schematic, not to scale: the circle stays the same size on screen whatever you type. That is deliberate rather than lazy. Because a single number defines a circle completely, a drawing scaled to your input would carry no information at all — it would be the same picture at a different size, every time.
What the drawing is for is telling the four quantities apart, which is where people actually go wrong. So it highlights whichever one you are editing: the radius as a line from the centre outwards, the diameter as the full width across, the circumference as the outline itself, and the area as the filled interior.
Questions
Is it the area of a circle, or the area of a disk?
Strictly, a circle is the curve itself and the region it encloses is a disk — so the curve has a length and the disk has an area. Everyday English, and most school textbooks, say "the area of a circle" and nobody is confused by it. If a marker has pulled you up on the wording, that distinction is why. Several other languages give the two things separate words outright, which is why this trips up more people than it should.
Are circumference and perimeter the same thing?
Yes. "Perimeter" is the general word for the distance around any shape, and "circumference" is the specific word for a circle. The word that genuinely gets confused with it is arc: an arc is only part of the way around, and calculating one needs the angle as well as the radius, so it is not what the circumference box here gives you.
Is π equal to 22/7?
No. 22/7 is 3.142857…, π is 3.141592…, and they part company at the third decimal place. It is a fine approximation for mental arithmetic and a poor one for cutting material: on a circle one metre across, 22/7 overstates the circumference by about 1.3 mm. This page uses your browser's own value of π, which carries roughly sixteen significant digits.
I measured around a pipe with a tape. How do I get the diameter?
Divide what you measured by π. That is the whole trick, and it is why circumference is an input on this page rather than only a result: type your tape measurement into the third box and the diameter appears in the second. This is the normal situation for pipes, trees, barrels and columns, where the centre is not reachable at all.
What is the difference between a circle and a sphere?
A circle is flat; a sphere is not. The area here is πr², while the surface area of a sphere of the same radius is 4πr² — exactly four times as much — and a solid ball has a volume of (4/3)πr³, which this page does not calculate. If you are working with a ball, a tank or a dome, the circle formulas will hand you an answer that looks perfectly reasonable and is wrong.
Updated 2026-08-10. Runs fully in your browser — nothing is uploaded.