Circle Calculator
Area, circumference, and diameter from radius.
What it does
Circles pack three linked measures around one radius: area grows with the square while circumference grows linearly, and diameter simply doubles. Pi binds them all as the circumference to diameter ratio.
The tool above takes the radius. It returns area, circumference, and diameter together.
Squaring punishes small errors twice: a five percent radius miss becomes ten percent on area. Measure diameters across centers and halve for the truest radius.
Pi never terminates, but 3.14159 carries everyday work far past tape measure precision. This page computes with full machine pi internally.
How to use
- Enter the radius, half the diameter.
- Read area for coverage and circumference for perimeters.
- Keep units consistent: radius in, area square.
- Double check diameter measurements across centers.
Formula
- π
- 3.14159265..., circumference over diameter.
- r²
- Radius squared driving area growth.
- 2r
- Diameter spanning the full circle.
Spheres and balls extend the pattern: surface 4πr² and volume 4/3πr³, outside this page scope.
Worked example
Example: radius 5
Circle radius 5 units.
- Area: π x 25 = 78.54.
- Circumference: 2 x π x 5 = 31.42.
- Diameter: 2 x 5 = 10.
- Check: circumference / diameter = 31.42 / 10 = 3.142, which is pi.
Reference table
| Radius | Area | Circumference |
|---|---|---|
| 1 | 3.14 | 6.28 |
| 5 | 78.54 | 31.42 |
| 10 | 314.16 | 62.83 |
| 24 | 1809.56 | 150.8 |
Limits
- Perfect circles assumed. Ovals need ellipse math.
- Radius precision doubles into area.
- Huge radii lose floating digits.
- Sectors and arcs need angle inputs.
Common mistakes
- Entering diameter as radius, quadrupling area.
- Using 3.14 then wondering at drift.
- Mixing radius and diameter mid problem.
- Forgetting area units square.
- Measuring off center diameters.
Try it yourself
Quick checks. Answers sit tucked under each question.
Radius 7. Area?
π x 49 = 153.94.
Circumference 50. Radius?
50 / (2π) = 7.96.
Questions
How do I find area of a circle?
Pi times radius squared. Radius 5 gives 78.54.
Diameter or radius: which to enter?
Radius. Halve any diameter first.
What is pi exactly?
Irrational near 3.14159265. It never repeats or ends.
How are area and circumference linked?
Area is circumference times radius over two.
What about semicircles?
Halve area and add the diameter to half circumference for perimeter.
Why does area grow faster?
Squaring: doubling radius quadruples area but only doubles circumference.