Circle Calculator

1. Choose what you know: radius, diameter, circumference or area.
2. Enter its value.
3. Read the area of the circle.
4. See the circumference, and the radius and diameter.

Here is what each result means:

A circle is the set of all points the same distance from a center. That distance is the radius, and twice the radius, straight across through the center, is the diameter. The distance all the way around is the circumference, and the space inside is the area.

Every one of these measurements is linked to the others through the constant pi, about 3.14159. Knowing any single one lets you find all the rest, which is exactly what this calculator does. Circles are everywhere, from wheels and pipes to plates and pizzas, so these formulas come up constantly.

Pi is the ratio of the circumference to the diameter, and it is the same for every circle, large or small. That single fact is what ties all the circle formulas together: once you know pi, a circle is fully described by just one measurement, and the others follow from simple multiplication or a square root.

It first finds the radius from whatever you entered, then computes the rest.

1. Convert your input into the radius.
2. Double it for the diameter.
3. Use pi to find the circumference and the area.

The area of a circle grows with the square of the radius, the same squared relationship used across many percentage and geometry problems.

Find the area and circumference of a circle with radius 5.

Calculation: the diameter is 10. The circumference is 2 pi (5) = 31.42, and the area is pi (5)^2 = 78.54. Doubling the radius to 10 would quadruple the area, since area depends on the radius squared.

If instead you started from the area of 78.54, you would divide by pi and take the square root to recover the radius of 5, then find everything else. That is how the calculator works backward from an area or a circumference to the radius before reporting all four measurements together.

Four measurements describe a circle, all tied together by pi.

Because they are all linked, knowing any one measurement is enough to find the other three.

These two are the most commonly confused.

The diameter is always twice the radius. Formulas usually use the radius, so halve a diameter before applying them.

The Radius

Area grows with the square of the radius, so a small increase in radius makes a larger jump in area.

Using Diameter by Mistake

Plugging the diameter into a radius formula overstates the area fourfold. Convert first.

The Value of Pi

Using a rounded pi like 3.14 gives a slightly different answer than full precision, which this tool uses. For everyday work the difference is tiny, but it can matter for large radii or exacting engineering, where a full-precision pi keeps the result accurate to many digits.

Geometry Homework

Find any circle measurement from another quickly.

DIY and Construction

Work out material for a round table, patio or pipe.

Design

Size a circular logo, plate or wheel from a known width or area.

1. Using Diameter as Radius

Halve the diameter first. Using it directly quadruples the area.

2. Forgetting to Square the Radius

Area is pi times the radius squared, not pi times the radius.

3. Mixing Up Area and Circumference

Circumference is the distance around; area is the space inside.

4. Rounding Pi Too Early

Round only the final answer, or small errors build up.

5. Unit Slips

Keep all measurements in the same unit, and remember area is in square units.

The formulas are exact; only the displayed decimals are rounded.

Multiply pi by the radius squared. For a radius of 5, the area is pi times 25, about 78.54. If you have the diameter, halve it to get the radius first.

Multiply pi by the diameter, or by twice the radius. For a radius of 5, the circumference is 2 times pi times 5, about 31.42.

The radius is the distance from the center to the edge, and the diameter is the full distance across through the center. The diameter is always twice the radius.

Yes. Divide the area by pi and take the square root. This tool does that when you choose area as the known value.

Pi is the constant ratio of a circle circumference to its diameter, about 3.14159. It appears in every circle formula and never ends or repeats.

Because area depends on the radius squared. Doubling the radius multiplies the area by two squared, which is four.

Most circle formulas use the radius. If you have the diameter, halve it first, or use the diameter form of the circumference, pi times the diameter.

The area is in square units of whatever length unit you used. If the radius is in centimeters, the area is in square centimeters.

No. The calculation runs in your browser and nothing you enter is stored or sent anywhere, unless you choose Save, which keeps the result only on this device.

• Circle (Wikipedia).
• Circle area and circumference (Maths Is Fun).
• Pi (Wikipedia).