Last updated: April 2026 · Reviewed by Calculatormatics Editorial Team

Circle Calculator

A free circle calculator that takes any single measurement of a circle — radius, diameter, circumference, or area — and instantly computes the other three, plus shows every formula being applied. All four are linked through one constant: π ≈ 3.14159, the universal ratio of any circle's circumference to its diameter. The calculator uses d = 2r, C = 2πr, and A = πr², with the inverse r = √(A/π) when you start from area. Because area scales with the square of the radius, doubling a circle's radius produces four times the area — which is why a 16-inch pizza has four times the food of an 8-inch pizza, not twice as much. Useful for geometry homework, sizing pipes, calculating round-pool volume (pair with the volume calculator for cylinders), working out fabric for circular cutouts, and any everyday problem that involves a round shape. Enter one measurement below to compute the rest.

Given: radius = 5

Step 1 — Find radius:
  r = 5 (given)

Step 2 — Diameter:
  d = 2r = 2 × 5 = 10

Step 3 — Circumference:
  C = 2πr = 2 × 3.14159265 × 5
  C = 31.41592654

Step 4 — Area:
  A = πr² = 3.14159265 × 5²
  A = 3.14159265 × 25
  A = 78.53981634

Circle Formulas

All circle formulas derive from one number: the radius r, the distance from the center to the edge. The constant π ≈ 3.14159265 links linear measurements (radius, diameter) to curved measurements (circumference) and area.

Finding Any Measurement from Any Other

If you know any single measurement, you can find all others by rearranging the formulas:

What Is Pi (π)?

Pi (π) is the ratio of any circle's circumference to its diameter: π = C / d. This ratio is exactly the same for every circle, from a coin to a planet. Pi is irrational (cannot be expressed as a fraction) and transcendental (not a root of any polynomial with rational coefficients).

Approximations used in practice:

• 22/7 ≈ 3.142857 (accurate to 2 decimal places)
• 355/113 ≈ 3.1415929 (accurate to 6 decimal places)
• 3.14159265358979... (exact to 15 places)

For most engineering and everyday calculations, π ≈ 3.14159 is more than sufficient.

Arc Length and Sector Area

A sector is a "pie slice" of a circle with central angle θ:

• Arc length = (θ / 360°) × 2πr   (portion of circumference)
• Sector area = (θ / 360°) × πr²   (portion of total area)

For a semicircle (θ = 180°): arc = πr, area = πr²/2.
For a quarter circle (θ = 90°): arc = πr/2, area = πr²/4.

Real-World Circle Calculations

• Wheel travel distance: One revolution = circumference = 2πr. A tire with 14-inch radius travels 2π×14 ≈ 87.96 inches per revolution.
• Pizza area: A 16-inch diameter pizza has area π × 8² ≈ 201 sq in. A 12-inch pizza has area π × 6² ≈ 113 sq in. The 16-inch is 78% larger, not 33%.
• Pipe cross-section: Flow rate depends on pipe area = πr². Doubling the radius quadruples the flow capacity. Use the Exponent Calculator to verify squaring and cubing calculations.
• Circular garden: A garden with 10 ft radius has area π × 100 ≈ 314 sq ft, needing about 314 sq ft of sod. Use our Square Footage Calculator for irregular garden shapes.

Frequently Asked Questions