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Circle Calculator

Radius From Circumference, Diameter From Area, With Every Step Shown

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How the Circle Calculator works

This circle calculator takes any one measurement of a circle, the radius, diameter, circumference or area, and works out the other three. Every step is written out, so you can copy the working into homework or check a figure on a plan. Any unit works; area comes out in that unit squared.

Every measurement of a circle follows from its radius, the distance from the centre to the edge. Double it and you have the diameter. Multiply the diameter by π, about 3.14159, and you have the circumference. Square the radius and multiply by π for the area. Going backwards is just as quick, so knowing any one value pins down the whole circle.

How the circle calculator works

The formula set is d = 2r, C = 2πr and A = πr². From a diameter, r = d ÷ 2. From a circumference, r = C ÷ 2π. From an area, r = √(A ÷ π). The calculator finds r first, then builds the other values from it, and shows each line of that working.

First example. A radius of 5 gives a diameter of 10, a circumference of 2 × π × 5 ≈ 31.42 and an area of π × 25 ≈ 78.54.

Second example. A circular rug with an area of 50 square feet has a radius of √(50 ÷ π) ≈ 3.99 ft, so a diameter of just under 8 ft.

How many times does a 70 cm bike wheel turn in a kilometre? Its circumference is π × 0.7 ≈ 2.199 m, so 1,000 ÷ 2.199 ≈ 455 turns.

Diameter, circumference and area for whole-number radii from 1 to 24

Radius Diameter Circumference Area
1 2 6.28 3.14
2 4 12.57 12.57
3 6 18.85 28.27
4 8 25.13 50.27
5 10 31.42 78.54
6 12 37.70 113.10
7 14 43.98 153.94
8 16 50.27 201.06
9 18 56.55 254.47
10 20 62.83 314.16
11 22 69.12 380.13
12 24 75.40 452.39
13 26 81.68 530.93
14 28 87.96 615.75
15 30 94.25 706.86
16 32 100.53 804.25
17 34 106.81 907.92
18 36 113.10 1017.88
19 38 119.38 1134.11
20 40 125.66 1256.64
21 42 131.95 1385.44
22 44 138.23 1520.53
23 46 144.51 1661.90
24 48 150.80 1809.56

Tips

FAQ

How do you find the area of a circle from the diameter?

Halve the diameter to get the radius, square it and multiply by π. A circle 12 cm across has a radius of 6 cm, so its area is π × 36 ≈ 113.1 cm². Choose Diameter in the first box and the calculator does the halving for you.

How do you find the radius from the circumference?

Divide the circumference by 2π, which is about 6.2832. A tree trunk with a girth of 1.5 m has a radius of 1.5 ÷ 6.2832 ≈ 0.239 m, so it is roughly 48 cm across. This is how foresters estimate trunk diameter from a tape wrapped around the bark.

What is the difference between circumference and perimeter?

They mean the same thing, the distance all the way round a shape. Circumference is the word used for circles and ellipses, while perimeter is used for polygons. For a circle the formula is C = πd, or 2πr, and the answer is in plain length units, not squared ones.

Why does doubling the radius quadruple the area?

Area depends on the radius squared. Double r and r² becomes four times larger, so the area does too. The circumference only doubles, because it grows in step with r. A 12-inch pizza therefore has more than twice the topping of an 8-inch one, about 2.25 times as much.

See also: all Algebra and Geometry tools, Arithmetic, Number Theory, Statistics, Trigonometry and Calculus.

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