Circle Calculator
Find radius, diameter, area, and circumference from any one circle measurement
By Drew Budwin · Last updated July 2026 · Methodology
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Radius
Diameter
Area
Circumference
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Circle Calculator Formula
Area of a circle:
A = π × r²
r = radius.
Circumference of a circle:
C = 2π × r
r = radius.
Diameter of a circle:
d = 2r
r = radius.
Radius from area:
r = √(A / π)
A = area.
Radius from circumference:
r = C / (2π)
C = circumference.
How to Use This Calculator
- Choose what you already know: Radius, Diameter, Area, or Circumference.
- Enter your known value in the field.
- Click Calculate to see all four circle measurements instantly.
Frequently Asked Questions
What is the formula for the area of a circle?
The area is A = π × r², where r is the radius. Because area grows with the square of the radius, doubling the radius quadruples the area. To find the area of a partial circle, see the Sector Calculator.
How do I find the circumference of a circle if I only know the area?
First find the radius from the area: r = √(A / π). Then the circumference is C = 2π × r. This calculator does both steps for you: enter the area in the Area tab and all other values appear instantly.
What is the difference between radius and diameter?
The diameter is any straight line that passes through the center of the circle from one side to the other. The radius is half the diameter, running from the center to the edge. Every formula in this calculator converts between them with d = 2r.
Why does the circumference formula use π?
π (pi ≈ 3.14159) is the ratio of a circle's circumference to its diameter, the same for every circle regardless of size. The circumference formula C = 2πr is just π × d, which directly states that relationship.
What is a unit circle?
A unit circle has a radius of 1. Its area is π ≈ 3.14159, its diameter is 2, and its circumference is 2π ≈ 6.28319. Unit circles are the foundation of trigonometry because every angle maps to a point on the unit circle.
How do I find the area of a circle from its diameter?
Substitute r = d/2 into the area formula: A = π × (d/2)² = πd² / 4. You can use the Diameter tab here to go straight from diameter to area without doing the algebra yourself.
How do I calculate the area of a circular ring (annulus)?
Subtract the inner circle's area from the outer: A = π(R² − r²). For a flower bed with outer radius 3 m and inner radius 1.5 m, the ring area is π(9 − 2.25) ≈ 21.2 m². Calculate each circle here separately, then subtract.
How much fencing is needed to enclose a circular plot?
The fencing equals the circumference: C = 2πr. A circular plot with a 10-meter radius needs about 62.8 meters of fencing. Enter the radius in the Radius tab and read the circumference directly.
Why does a small increase in radius have a large effect on area?
Area scales with the square of the radius. A 10% increase in radius produces a 21% increase in area (1.1² = 1.21). That's why irrigation circles cover more ground than you might expect when expanded slightly, and why pipe diameter matters so much for flow capacity.