Circle Calculator
Enter any one of radius, diameter, circumference or area and get the other three — with unit conversion and the π formulas worked step by step.
Circle Calculator: with the default inputs, area is 78.5398 m².
Used for radius, diameter or circumference, whichever you selected.
Used only when you selected Area.
- Radius
- 5 m
- Diameter
- 10 m
- Circumference
- 31.4159 m
Assumptions
- Worked steps are shown in meters and square meters (the internal base units); the results are converted to the units you choose.
- Only the input matching your selection is used.
| Radius(m) | Diameter(m) | Circumference(m) | Area(m²) | |
|---|---|---|---|---|
| 1.25 m | 2.5 m | 7.854 m | 4.9087 m² | 0.25× the radius, 0.06× the area |
| 2.5 m | 5 m | 15.708 m | 19.635 m² | 0.5× the radius, 0.25× the area |
| 3.75 m | 7.5 m | 23.5619 m | 44.1786 m² | 0.75× the radius, 0.56× the area |
| 5 m | 10 m | 31.4159 m | 78.5398 m² | ◀ your circle |
| 7.5 m | 15 m | 47.1239 m | 176.7146 m² | 1.5× the radius, 2.25× the area |
| 10 m | 20 m | 62.8319 m | 314.1593 m² | 2× the radius, 4× the area |
| 15 m | 30 m | 94.2478 m | 706.8583 m² | 3× the radius, 9× the area |
| 20 m | 40 m | 125.6637 m | 1,256.6371 m² | 4× the radius, 16× the area |
Area grows with the square of the radius: a pizza twice the width is four times the pizza.
How this is worked out
The formula
d = 2r C = 2πr = πd A = πr² = πd² ÷ 4 = C² ÷ 4π π ≈ 3.14159265…
Open How it’s calculated above to see this worked through with your own numbers.
What you enter
- I know the…
- Choose one of 4 options.Radius · Diameter · Circumference · Area
- Radius / diameter / circumference
- Used for radius, diameter or circumference, whichever you selected.in mm, cm, m, km, in, ft, yd, mi · 0 or more · defaults to 5
- Area
- Used only when you selected Area.in mm², cm², m², km², in², ft², yd², acre, mi² · 0 or more · defaults to 78.54
What you get back
- Areamain answer
- Radius
- Diameter
- Circumference
What this assumes
- Worked steps are shown in meters and square meters (the internal base units); the results are converted to the units you choose.
- Only the input matching your selection is used.
About this calculator
Every measurement of a circle follows from one number — its radius — and one constant, π. Give the calculator whichever measurement you have (radius, diameter, circumference or area) and it works back to the radius, then forward to everything else, converting units along the way.
How to use it
Pick what you know, type the value and choose its unit. Only the field matching your selection is used; the area field has its own unit menu because area is measured in square units. Outputs can each be shown in a different unit, so you can enter a diameter in inches and read the area in square feet.
Where the formulas come from
- Circumference, C = 2πr. π is defined as the ratio of any circle's circumference to its diameter, so C = πd, and d = 2r.
- Area, A = πr². Cut the circle into many thin wedges and lay them alternating point-up, point-down. They form a near-rectangle whose height is r and whose width is half the circumference, πr. Area = r × πr = πr². The more wedges, the more exact.
- Going backwards. From a circumference, r = C ÷ 2π. From an area, r = √(A ÷ π) — remember the square root; it's the step people skip.
Reading the results
Area grows with the square of the radius: double the radius and you get four times the pizza. Circumference only doubles. That's why a 16-inch pizza is not "twice" a 12-inch one but about 1.8 times as much (16²/12² = 1.78).
Common mistakes
- Using the diameter in πr² without halving it first — this quadruples the area.
- Mixing up 2πr (circumference) and πr² (area). The one with the square gives square units.
- Rounding π to 3 or 3.14 too early. The calculator uses full double precision; round only the final answer.
Frequently asked questions
▸How do I find the area of a circle from the diameter?
Halve the diameter to get the radius, then use A = πr². A 12-inch diameter gives r = 6, so A = π × 36 ≈ 113.1 in².
▸How do I find the radius from the circumference?
Divide the circumference by 2π. A 400 m track has r = 400 ÷ 6.283 ≈ 63.66 m.
▸How do I find the radius from the area?
Divide by π and take the square root: r = √(A ÷ π). For 78.54 m², r = √25 = 5 m.
▸What value of π does the calculator use?
The full double-precision value, 3.141592653589793. Using 3.14 by hand introduces about 0.05% error, which is fine for most purposes but not for checking answers to many decimals.
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