A circle is fixed by a single number. Give the calculator the radius, the diameter, the circumference or the area – in any unit – and it works out the other three, showing each step. Add an angle and you also get the arc, the area of the slice (sector) and the straight line across it (chord).
Example: a round garden bed 3 m across. Radius 1.5 m, so the area is π × 1.5² = 7.07 m² and the edging around it is π × 3 = 9.42 m.
The formulas
| To find | From the radius r | From the diameter d | From the circumference C | From the area A |
|---|---|---|---|---|
| Radius | r | d ÷ 2 | C ÷ 2π | √(A ÷ π) |
| Diameter | 2r | d | C ÷ π | 2√(A ÷ π) |
| Circumference | 2πr | πd | C | 2√(πA) |
| Area | πr² | πd² ÷ 4 | C² ÷ 4π | A |
For a slice with angle θ: arc = r × θ (θ in radians, or 2πr × θ° ÷ 360), sector area = r² × θ ÷ 2 (or πr² × θ° ÷ 360), chord = 2r × sin(θ ÷ 2). A 60° slice of a circle of radius 5 has an arc of 5.24, an area of 13.09 and a chord of exactly 5 – the slice is an equilateral triangle with a rounded edge.
Circle table
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 3 | 6 | 18.8496 | 28.2743 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
| 15 | 30 | 94.2478 | 706.8583 |
| 20 | 40 | 125.6637 | 1,256.6371 |
| 50 | 100 | 314.1593 | 7,853.9816 |
At radius 2 the circumference and the area are the same number (12.566) – but one is a length and the other an area, so they are not really equal.
Pizza sizes, by area
| Pizza | Area (in²) | Area (cm²) |
|---|---|---|
| 8 in (20 cm) | 50.3 | 324 |
| 10 in (25 cm) | 78.5 | 507 |
| 12 in (30 cm) | 113.1 | 730 |
| 14 in (36 cm) | 153.9 | 993 |
| 16 in (41 cm) | 201.1 | 1,297 |
| 18 in (46 cm) | 254.5 | 1,642 |
A 16-inch pizza has four times the area of an 8-inch one. To compare prices, divide each by its area.
About π
π is the ratio of any circle’s circumference to its diameter: 3.14159 26535 89793… It never ends and never repeats. The calculator uses the full precision of your device (about 16 digits) and rounds the answers to 4 decimals; 3.14 is enough for most handwork, and 22/7 (3.142857) is a handy fraction that is off by 0.04%.
For right triangles, see the Pythagorean theorem calculator. Once zet4u is saved on your device, the calculator works offline, so it is there for homework or a workshop without Wi-Fi.
Frequently asked questions
What is the formula for the area of a circle?
A = π × r², where r is the radius (half the diameter). A circle with a radius of 5 cm has an area of π × 25 = 78.54 cm². From the diameter: A = π × d² ÷ 4.
How do I find the circumference?
C = 2 × π × r, or π × d. A circle 10 cm across has a circumference of 31.42 cm. Going back, r = C ÷ (2π): a tree trunk 1 m around has a diameter of about 31.8 cm.
How do I find the radius from the area?
r = √(A ÷ π). A round table top of 1 m² has a radius of √(1 ÷ 3.14159) = 0.564 m, so a diameter of 1.128 m. Choose "Area" in the calculator and it does this for you.
Is one 18-inch pizza bigger than two 12-inch pizzas?
Yes. An 18-inch pizza is 254.5 in²; two 12-inch pizzas are 2 × 113.1 = 226.2 in². Area grows with the square of the diameter, so 1.5 times the width gives 2.25 times the pizza.
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