How circle measurements are found
Every measurement of a circle follows from its radius and the constant π (the ratio of any circle's circumference to its diameter). Area grows with the square of the radius, while circumference and diameter grow in direct proportion to it.
- r — radius — center to edge
- π — ≈ 3.14159 (circumference ÷ diameter)
Common values
| Radius (r) | Area |
|---|---|
| 0.5 | 0.7854 |
| 1.3 | 5.3093 |
| 2.5 | 19.6350 |
| 5 | 78.5398 |
| 7.5 | 176.7146 |
| 10 | 314.1593 |
| 15 | 706.8583 |
| 25 | 1,963.4954 |
| 50 | 7,853.9816 |
More detail
Why area scales with r², not r
Doubling the radius doubles the diameter and circumference, but quadruples the area — because area depends on r². A pizza of twice the radius has four times the food. That squared relationship is why a small change in radius makes a large change in area.
Working backwards. If you know the diameter instead of the radius, just halve it (r = diameter ÷ 2) before entering it above. If you know the circumference, the radius is C ÷ (2π).
Frequently asked questions
What is the area of a circle with radius 5?
Area = π · r² = π · 5² = π · 25 ≈ 78.5398 square units. Enter r = 5 above to see the area, circumference, and diameter together.
What's the difference between circumference and diameter?
The diameter is the straight distance across the circle through its center (2·r); the circumference is the distance all the way around the edge (2·π·r). The circumference is always about 3.14159 times the diameter.
How do I find the radius from the area?
Rearrange Area = π·r² to r = √(Area ÷ π). For example an area of 78.54 gives r = √(78.54 ÷ π) ≈ 5. This calculator goes the other way — radius in, area out.
What value of π does this calculator use?
It uses the full double-precision value of π (≈ 3.14159265358979). Displayed results are rounded, so a hand calculation with π ≈ 3.14 may differ slightly in the last digits.
Why does the calculator show “—” for some radius values?
A radius of 0 or less doesn't describe a real circle, so area, circumference, and diameter all show "—" instead of a number.