Circle Calculator: Radius, Area and Circumference Made Simple

Everything about a circle follows from a single number. Once you have the radius, the other three measurements are two multiplications away, which is why the calculator only ever asks for one input.

The two formulas and what they do

Area is π times the radius squared. Circumference is 2π times the radius. The diameter is simply twice the radius, so a 4 metre radius gives an 8 metre diameter, an area of π x 16 = 50.27 m², and a circumference of 2 x π x 4 = 25.13 m. Change the radius and all three move together.

Working backwards is just as easy. If you know the circumference, divide by 2π to get the radius. If you know the area, divide by π and take the square root. The calculator does whichever direction you need, but knowing the route helps you spot a wrong answer.

Why area grows faster than you expect

Radius gets squared, so widths and areas move at completely different speeds. A 12 inch pizza has an area of 113.10 square inches. A 16 inch pizza has 201.06. That is 78% more food, not the 33% the diameters suggest. The same effect shows up in round tables, paddling pools and grain bins, and it is the reason the bigger option is usually better value than it looks.

Using the circle calculator

Pick the measurement you actually have and leave the rest blank. Radius is the distance from the centre to the edge. Diameter is the widest straight line across, and on a physical object it is the largest number you can get with a tape held flat against it. Circumference is the distance right around the outside. Set your units before you type, because the calculator will happily report an area in square centimetres when you meant square metres.

Measuring a diameter you cannot reach across

For a tree, a tank or anything you cannot lay a tape over, measure around it instead. A trunk with a 141 cm circumference has a diameter of 141 / π = 44.88 cm, and a radius of 22.44 cm. Going around beats guessing where the widest line falls, which is hard to judge on anything that is not perfectly round. One caveat: a tape pulled over bark follows every ridge, so it reads a little high, and the diameter you get from it comes out high with it.

Circles in real jobs

A round patio 12 feet across has a radius of 6 feet, so its area is π x 36 = 113.10 square feet. Pour it 4 inches deep and you need 113.10 x 0.333 = 37.7 cubic feet, which is 37.7 / 27 = 1.40 cubic yards. Order 1.5 or 1.6 to allow for spillage and an uneven base. Our guide to calculating square footage covers the same conversion for rectangular pours.

Flooring, turf and paint all work the same way: get the area, then multiply by depth, coverage rate or price per unit. For shapes that are a circle plus something else, such as a rounded-end lawn, split the shape, calculate each piece, and add. That approach is set out in our notes on area formulas across different shapes and units.

Common questions

What is the difference between radius and diameter? The diameter runs all the way across through the centre. The radius is half of it, from the centre to the edge. Mixing them up is the single most common circle mistake, and it makes your area four times too big or four times too small.

How do I find the area if I only know the circumference? Divide the circumference by 2π to get the radius, then square it and multiply by π. A circumference of 25.13 m gives a radius of 4 m and an area of about 50.3 m². There is a shortcut too: area = C² / 4π.

Is perimeter the same as circumference? Yes. Circumference is just the word used for a circle's perimeter. Some calculators label the field either way.

How many digits of pi do I need? For anything you build, 3.1416 is more than enough. Across a 12 foot patio, using 3.14 instead of the full value changes the concrete order by less than a tenth of a cubic foot.