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About the circle calculator
A circle has four numbers that belong together: the radius (r), the diameter (d), the circumference (C, the distance around) and the area (A, the space inside). If you know one of them, you can work out the other three.
Type the number you know into its box — any of the four. The other three boxes fill in at once. Under the form you see the formulas and the steps with your own numbers, and a drawing of the circle with the sizes on it.
Features
- Start from any value — radius, diameter, circumference or area
- Steps shown — each formula with your numbers filled in
- Exact π answers — r = 5 gives C = 10π and A = 25π as well as the decimals
- Half and quarter circle — the area of a semicircle and a quarter circle
- Any unit — mm, cm, m, km, in, ft, yd or mi; the area comes in square units
- A drawing — the circle with r, d, C and A written on it
- Saved on your device — your circle is still there next time
Circle formulas
| You know | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| radius r | r | 2 × r | 2 × π × r | π × r² |
| diameter d | d ÷ 2 | d | π × d | π × (d ÷ 2)² |
| circumference C | C ÷ (2π) | C ÷ π | C | C² ÷ (4π) |
| area A | √(A ÷ π) | 2 × √(A ÷ π) | 2 × √(π × A) | A |
π (pi) is about 3.14159. It is the circumference divided by the diameter — the same for every circle.
Worked examples
From the radius. r = 5 cm.
d = 2 × 5 = 10 cm. C = 2 × π × 5 = 10π ≈ 31.42 cm. A = π × 5² = 25π ≈ 78.54 cm².
From the circumference. A tree trunk is C = 100 cm around.
r = 100 ÷ (2π) ≈ 15.92 cm, d ≈ 31.83 cm, A ≈ 795.77 cm².
From the area. A round table top has A = 50 ft².
r = √(50 ÷ π) ≈ 3.99 ft, d ≈ 7.98 ft, C ≈ 25.07 ft.
Pizza sizes: a real-life example
Pizza sizes are the diameter. The area grows with the square of the size, so a slightly bigger pizza has a lot more pizza:
| Pizza (diameter) | Area |
|---|---|
| 8 in | 50.27 in² |
| 10 in | 78.54 in² |
| 12 in | 113.10 in² |
| 14 in | 153.94 in² |
| 16 in | 201.06 in² |
| 18 in | 254.47 in² |
A 16-inch pizza has (16 ÷ 12)² ≈ 1.78 times the area of a 12-inch pizza — not 1.33 times.
Frequently asked questions
What is the difference between radius and diameter?
The radius goes from the center to the edge. The diameter goes across the whole circle, through the center. The diameter is always two radii: d = 2 × r.
How do I find the radius from the area?
Divide the area by π, then take the square root: r = √(A ÷ π). For A = 50, r = √(50 ÷ 3.14159) ≈ 3.99.
How do I find the area from the circumference?
A = C² ÷ (4 × π). For C = 100, A = 10,000 ÷ 12.566 ≈ 795.77.
Why is the area in square units?
Area measures a surface, so it is in cm², m², in² or ft². The radius, diameter and circumference are lengths, so they stay in cm, m, in or ft.
What does 25π mean?
It is the exact answer with π left as a symbol. Many teachers ask for it. 25π ≈ 78.54.
Related tools
- Volume Calculator — cylinders, cones and spheres use the same r
- Pythagorean Theorem Calculator — the third side of a right triangle
- Square Footage Calculator — the area of rooms, with circles too
- Online Protractor — measure angles on your screen
- Scientific Calculator — π, powers and roots for your own sums
How to use it
- Type the value you know into its box: radius, diameter, circumference or area
- The other three boxes fill in at once
- Pick a unit if you want one (the area is in square units)
- Read the formulas and the steps under the form, and the drawing next to them
- Tap an example (r = 5, C = 100 …) to try it
