The circle calculator computes area, circumference, diameter, and radius from any one measurement. Enter a value in any field to calculate all other circle dimensions instantly.
Circle Calculator
How to Use the Circle Calculator
The circle calculator finds all circle measurements from any one known value. Enter the radius, diameter, circumference, or area, and all others are computed automatically.
The Key Formulas
Radius r → diameter d = 2r → circumference C = 2πr = πd → area A = πr². All four formulas are derived from the radius. π ≈ 3.14159265. For a circle with radius 5: d=10, C=31.416, A=78.540.
Finding Radius from Area
If you know the area: r = √(A/π). A pizza has area 78.54 in²: r = √(78.54/π) = √25 = 5 inches. Diameter = 10 inches. A standard 12-inch pizza has r=6, A = π×36 = 113.1 in².
Circumference Applications
Car tire diameter 25 inches: C = π×25 = 78.54 inches per rotation. At 60 mph (63,360 in/min): 63,360/78.54 ≈ 807 rotations per minute (RPM) of the tire. GPS distance counters use circumference × rotations to measure distance.
Frequently Asked Questions
What is the formula for circle area?
A = π × r² where r is the radius. Example: r = 5 cm → A = π × 25 ≈ 78.54 cm². Equivalently A = π × (d/2)² = π × d²/4 where d is diameter. The area doubles when radius increases by √2 ≈ 1.414.
What is circumference?
Circumference C = 2πr = πd is the perimeter of a circle. Example: d = 10 cm → C = π × 10 ≈ 31.42 cm. A car tire with diameter 26 inches travels π × 26 ≈ 81.7 inches per rotation. After 1 mile (63,360 in), the tire makes 63,360/81.7 ≈ 776 rotations.
Is this calculator free?
Yes, completely free with no signup required. All calculations run in your browser.
Is my data private?
Yes. All calculations run locally. Nothing is transmitted.
What is the relationship between diameter and radius?
Diameter = 2 × radius. The diameter passes through the center and touches both edges. Radius goes from center to edge. For area and circumference problems, use whichever you know — the calculator converts automatically.