Circle Calculator
Calculate circle area, circumference, diameter, and radius from any single measurement.
Circle Properties
Distance from center to edge
Distance across circle through center
Distance around the circle
Space inside the circle
Sector Calculator
Angle of the sector in degrees
📐 Circle Formulas
Circle Results
Area
square units
Circumference
linear units
Radius
from center to edge
Diameter
across the circle
Related Squares
Circle Properties
How it works
Every measurement of a circle flows from one number — the radius. Once you know the radius (or the diameter, which is twice the radius), the calculator derives the circumference (the distance around) and the area (the space inside) using the constant π ≈ 3.14159.
Circle measurements
Diameter = 2r Circumference = 2πr Area = πr²
- r
- radius — centre to edge
- π
- pi ≈ 3.14159, the ratio of circumference to diameter
Worked example
- Radius r = 5
- Circumference = 2 × π × 5 ≈ 31.42
- Area = π × 5² = π × 25 ≈ 78.54
Diameter 10, circumference ≈ 31.42, area ≈ 78.54 square units.
Good to know
- Watch radius vs diameter — they're the most common mix-up. If you measured across the whole circle, that's the diameter; halve it for the radius.
- π is irrational (never-ending), so answers are approximations; 3.14159 is plenty for everyday use.
- Circumference uses the radius to the first power, area to the second — so doubling the radius doubles the perimeter but quadruples the area.
Related Calculators
Frequently Asked Questions
What are the formulas for circle calculations?
Area = πr² (pi times radius squared). Circumference = 2πr or πd. Diameter = 2r. Radius = d/2. Where r is radius, d is diameter, and π (pi) ≈ 3.14159. These formulas are interconnected - knowing any one value lets you calculate all others.
How do I find the area of a circle from circumference?
First find radius: r = C/(2π). Then calculate area: A = πr². Example: If circumference is 31.416 units, radius = 31.416/(2π) = 5 units, so area = π(5)² = 78.54 square units.
What's the difference between diameter and radius?
Radius is the distance from the center to any point on the circle's edge. Diameter is the distance across the circle through the center, which equals 2 × radius. Diameter is always the longest distance across a circle.
How many decimal places should I use for pi (π)?
For most practical applications, 3.14159 (5 decimal places) is sufficient. Engineering often uses 3.14159265. For rough estimates, 3.14 or even 22/7 (≈3.14286) works. More precision rarely changes results significantly in real-world applications.
How do I calculate the area of a partial circle (sector)?
Sector area = (θ/360) × πr² where θ is the central angle in degrees. For radians: Area = (θ/2) × r². Example: A 90° sector of a circle with radius 10 has area = (90/360) × π(10)² = 78.54 square units.
What are common real-world applications of circle calculations?
Pizza sizes (area for pricing), wheels/tires (circumference for distance), pipes (cross-sectional area for flow), round tables (area for seating), irrigation systems (spray radius), and architecture (circular windows, domes). Engineering uses these constantly for gears, pulleys, and rotating machinery.