Circle Calculator
Enter any one circle property — radius, diameter, circumference, or area — and instantly get all the others.
Radius (r): half the diameter. Circumference = 2πr = πd. Area = πr². From area: r = √(A/π). From circumference: r = C/(2π). π = 3.14159265...
Key formulas:
r = d/2 = C/(2π) = √(A/π)
C = 2πr = πd
A = πr² = π(d/2)²
How π is Used in Education by Country
| Country | Primary school | Secondary school | Answer format |
|---|---|---|---|
| 🇺🇸 USA | π ≈ 3.14 | Full decimal / exact π | Decimal or exact |
| 🇬🇧 UK | π ≈ 3.14 | Exact π preferred | Leave as 6π cm² |
| 🇯🇵 Japan | 円周率 = 3.14 | π symbol | Decimal (3 s.f.) |
| 🇮🇳 India (CBSE) | 22/7 or 3.14 | 22/7 or 3.14 | Decimal or fraction |
| 🇩🇪 Germany | π ≈ 3,14* | Exact π | Exact or decimal |
| 🇫🇷 France | π ≈ 3,14* | Exact π | Exact preferred |
| 🇰🇷 Korea | 원주율 ≈ 3.14 | π symbol | Decimal |
* German/French use comma as decimal separator (3,14 not 3.14)
Frequently Asked Questions
How do you find the area of a circle from circumference?
From circumference C: first find r = C/(2π), then A = πr². Or directly: A = C² / (4π). Example: C = 20 cm → r = 20/(2π) ≈ 3.183 cm → A ≈ 31.83 cm².
What is the difference between radius and diameter?
Diameter = 2 × radius. The radius is the distance from the centre to the edge. The diameter is the distance across the circle through its centre. Formula connection: C = πd = 2πr.
Why is π irrational?
π cannot be expressed as a fraction of two integers. This was proven by Johann Heinrich Lambert in 1761. It also cannot be expressed as the root of any polynomial (it is transcendental, proven by Lindemann in 1882).
What precision should I use for π?
For most practical calculations: 3.14159 is sufficient. Engineering typically uses 3.14159265. Space navigation (NASA) uses 15 decimal places. The built-in Math.PI in JavaScript equals 3.141592653589793.