Circle Calculator
Find a circle's radius, diameter, circumference and area — given any one of them.
Pick what you know — the rest will be derived
Half the diameter
Circle from radius = 5
radius = 5
Radius
5
r
Diameter
10
2r
Circumference
31.4159
2πr
Area
78.5398
πr²
The formulas
d = 2r
C = 2πr
A = πr²
With r = 5, π ≈ 3.141593
Every circle is fully described by any one of its four measurements — give one, get the other three. For just the area of common shapes, use the Area Calculator; for the distance around (perimeter / circumference of other shapes), the Perimeter Calculator.
How to use this calculator
- Pick which measurement you know — radius, diameter, circumference or area.
- Enter the value.
- Read all four measurements in the result grid.
How it works
A circle is fully described by any single one of its four measurements — give one and the other three are determined. The calculator first solves for the radius:
- From radius — already known.
- From diameter —
r = d / 2 - From circumference —
r = C / (2π) - From area —
r = √(A / π)
Then it derives the other three from the standard formulas:
d = 2rC = 2πrA = πr²
For arc length and sector area (a portion of the circle defined by an angle), switch to the Arc & Sector tab at the top of the calculator.
Frequently Asked Questions
What's the difference between radius, diameter, circumference and area? ▾
Radius is the distance from the centre to the edge. Diameter is twice the radius — the distance across through the centre. Circumference is the distance around the outside (perimeter for a circle). Area is the surface inside the circle. All four are linked by π: given any one, the other three are fixed.
What is π (pi)? ▾
π is the ratio of a circle's circumference to its diameter — about 3.14159. It's the same for every circle, no matter the size, which is why it appears in every circle formula. The calculator uses JavaScript's Math.PI, which is accurate to about 15 decimal places.
How are the formulas derived? ▾
From π = circumference / diameter, the basic circle equations follow: C = π × d = 2 × π × r, and (using calculus) A = π × r². The diameter = 2 × r relationship is just the geometric definition. The calculator lets you go from any one measurement to all four by solving for r first, then deriving the rest.
What if I only know the area? Can I find the radius? ▾
Yes. Rearranging A = π × r² gives r = √(A / π). Pick 'Area' as the input and enter the area; the calculator derives the radius, diameter and circumference from there.
Are radius and diameter the same as semi-diameter? ▾
The semi-diameter is the radius — same thing, different name. It comes up mostly in older mathematics and engineering texts. Modern usage almost always says 'radius'.
How do I calculate arc length and sector area? ▾
Switch to the Arc & Sector tab. Arc length is the distance along a portion of the circle's edge: s = r × θ (with the angle θ in radians). Sector area is the pie-slice region between two radii: A = ½ × r² × θ. The calculator also returns the chord (straight line between the two arc endpoints) for free, since it's a one-liner derived from the same inputs: c = 2r × sin(θ/2).