What the circle calculator does
Give the calculator any one measurement of a circle — radius, diameter, circumference or area — and it returns the other three. That covers the everyday questions: how much fencing goes round a circular pond, how much area a round rug or patio covers, what diameter pipe has a given cross-section, or what size to cut a circle to get a certain circumference. It runs in your browser.
The formulas
Diameter d = 2r
Circumference C = 2πr = πd
Area A = πr²
From circumference: r = C ÷ 2π
From area: r = √(A ÷ π)
π ≈ 3.14159265π is the ratio of any circle's circumference to its diameter — the same for every circle, and irrational, so it never terminates. The calculator uses it to full floating-point precision; for hand calculation, 3.1416 is accurate to one part in 100,000 and 22/7 to one part in 2,500.
Worked examples
| Given | Radius | Diameter | Circumference | Area |
|---|---|---|---|---|
| Radius 5 | 5 | 10 | 31.42 | 78.54 |
| Diameter 12 | 6 | 12 | 37.70 | 113.10 |
| Circumference 100 | 15.92 | 31.83 | 100 | 795.77 |
| Area 50 | 3.99 | 7.98 | 25.07 | 50 |
Units carry through: a radius in metres gives circumference in metres and area in square metres. Doubling the radius doubles the circumference but quadruples the area — the reason a 12-inch pizza is not twice a 6-inch one but four times.
Practical uses
- Landscaping and building — edging, fencing or paving around a circular feature; concrete for a round footing (area × depth); turf or gravel for a circular bed.
- Pipes and tanks — cross-sectional area from a pipe diameter for flow calculations; volume of a cylindrical tank is area × height.
- Wheels and belts — one turn of a wheel moves the vehicle one circumference; belt length around two pulleys uses their circumferences.
- Cooking and crafts — cake tins, pizza sizes, round tablecloths (add the drop to the radius), knitting circular items.
- Science — orbital paths, lens and mirror apertures, the area a sprinkler covers.
Related shapes
| Shape | Formula |
|---|---|
| Sector (pie slice) area | (θ / 360°) × πr² |
| Arc length | (θ / 360°) × 2πr |
| Annulus (ring) area | π(R² − r²) |
| Cylinder volume | πr² × h |
| Sphere surface area | 4πr² |
| Sphere volume | (4/3)πr³ |
| Semicircle perimeter | πr + 2r |