A circle is defined by a single measurement, and everything else follows from π. The diameter is twice the radius (d = 2r), the circumference is the distance around (C = 2πr), and the area is the space inside (A = πr²). Know any one of the four and you can find the rest — which is exactly what this calculator does, with the full working shown.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: standard circle mensuration formulas, recomputed in code.
The four circle formulas
The radius is the hub: from it, the diameter is a doubling, the circumference is 2π times it, and the area is π times its square. Each formula reverses cleanly, so you can start from any one quantity. The constant π (≈ 3.14159265) is irrational, so the answers are rounded for display — but the calculation keeps full precision.
Worked example — radius 5
Scenario: a circle with radius r = 5.
A radius of 5 gives a diameter of 10, a circumference of 31.4159, and an area of 78.5398. The relationships run both ways: starting instead from the area 78.5398, the radius is √(78.5398 ÷ π) = 5; starting from the circumference 31.4159, the radius is 31.4159 ÷ (2π) = 5. Because area depends on r², a radius of 10 would have an area of 314.159 — four times as much.
Frequently Asked Questions
A = πr². Radius 5 → π × 25 = 78.5398. Know the diameter? Halve it first. Know the circumference? r = C ÷ (2π).
C = 2πr = πd. Radius 5 → 2 × π × 5 = 31.4159. It's π times the diameter.
d = 2r and r = d ÷ 2. The diameter crosses through the centre; the radius runs centre to edge. r = 5 → d = 10.
Yes. r = √(A ÷ π) from area; r = C ÷ (2π) from circumference. Area 78.5398 → r = 5; circumference 31.4159 → r = 5.
Full-precision Math.PI ≈ 3.141592653589793. Results show six decimals but the maths keeps full precision.