Geometry Tool

Circle Calculator

Calculate Area and Circumference from Radius or Diameter.

Σ The Formula

Area = πr² | Circumference = 2πr | Diameter = 2r

Real World Examples

Pizza Size
r=8 inches → Area=201.06 in², C=50.27 in
Garden Circle
d=10m → r=5m, Area=78.54 m²
Wheel Circumference
r=30cm → C=188.5cm (distance per rotation)
Circular Pool
d=15ft → r=7.5ft, Area=176.71 ft²

# About This Calculator

A circle is a perfectly round 2D shape where every point on the edge is equidistant from the center. This distance is the radius (r), while the diameter (d) is twice the radius. Circles are fundamental in geometry, appearing everywhere from wheels to planets to pizza.

Circle calculations are essential in countless applications: engineering (gears, pipes, tanks), architecture (domes, arches), landscaping (circular gardens, fountains), manufacturing (wheels, discs), and everyday life (pizza sizes, plate areas). Understanding area and circumference helps with material estimation and design.

The formulas use π (pi ≈ 3.14159), the ratio of circumference to diameter. Area = πr² gives the space inside the circle, while circumference = 2πr (or πd) gives the distance around it. These formulas have been known since ancient times and are among the most important in mathematics.

This calculator handles both radius and diameter inputs, automatically computing area, circumference, and the complementary measurement. It's perfect for determining pizza sizes, calculating fence length for circular gardens, finding wheel rotations, or any circular measurement task.

How To Use

  1. Select determining variable (Radius/Diameter).
  2. Enter value.
  3. Click Calculate.

Frequently Asked Questions

What's the difference between radius, diameter, and circumference?+

Radius (r) is the distance from center to edge. Diameter (d) is the distance across the circle through the center (d = 2r). Circumference (C) is the distance around the circle (C = πd = 2πr). Think: radius is half-width, diameter is full-width, circumference is perimeter.

Why is π (pi) used in circle formulas?+

π is the ratio of circumference to diameter for ANY circle - it's always approximately 3.14159. This constant relationship means C = πd and A = πr². π is one of mathematics' most important constants, appearing in circles, waves, probability, and countless other areas.

How do I find the area if I only know the circumference?+

First find radius from circumference: r = C/(2π). Then calculate area: A = πr². For example, if C = 31.42: r = 31.42/(2×3.14159) = 5, so A = π×5² = 78.54. This calculator does this automatically!

Which pizza is a better deal: 12-inch or two 8-inch?+

Calculate areas! 12-inch (r=6): A = 113 in². Two 8-inch (r=4 each): A = 50.3 × 2 = 100.6 in². The single 12-inch has MORE pizza! Area grows with the square of radius, so bigger circles are usually better value.

How many times does a wheel rotate to travel a certain distance?+

Divide distance by circumference. A wheel with r=30cm has C=188.5cm. To travel 10 meters (1000cm): 1000/188.5 = 5.3 rotations. This is crucial for odometers, robotics, and engineering calculations.

Is Circle Calculator free to use?+

Yes, Circle Calculator on Matheric is completely free to use. We believe in accessible education and utility for everyone.

About

A circle is a perfectly round 2D shape where every point on the edge is equidistant from the center. This distance is the radius (r), while the diameter (d) is twice the radius. Circles are fundamental in geometry, appearing everywhere from wheels to planets to pizza.

Circle calculations are essential in countless applications: engineering (gears, pipes, tanks), architecture (domes, arches), landscaping (circular gardens, fountains), manufacturing (wheels, discs), and everyday life (pizza sizes, plate areas). Understanding area and circumference helps with material estimation and design.

The formulas use π (pi ≈ 3.14159), the ratio of circumference to diameter. Area = πr² gives the space inside the circle, while circumference = 2πr (or πd) gives the distance around it. These formulas have been known since ancient times and are among the most important in mathematics.

This calculator handles both radius and diameter inputs, automatically computing area, circumference, and the complementary measurement. It's perfect for determining pizza sizes, calculating fence length for circular gardens, finding wheel rotations, or any circular measurement task.

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