Circle Calculator
Calculate circle properties including area, circumference, diameter, and radius. Perfect for geometry, engineering, and mathematical calculations involving circles.
Calculator Input
Circle Properties
Additional Properties
Unit Conversions
Formulas Used
How to Use
Basic Steps
- Choose what measurement you know (radius, diameter, circumference, or area)
- Enter the known value in the input field
- Select the appropriate unit of measurement
- View all calculated circle properties instantly
- Check unit conversions and exact π formulas
Calculation Types
- From Radius: Calculate diameter, circumference, and area
- From Diameter: Find radius, circumference, and area
- From Circumference: Determine radius, diameter, and area
- From Area: Calculate radius, diameter, and circumference
Understanding Circle Geometry
Basic Circle Elements
Radius (r)
The distance from the center to any point on the circle. All radii of a circle are equal.
Diameter (d)
The distance across the circle through its center. Always twice the radius: d = 2r.
Circumference (C)
The distance around the circle. Calculated as C = 2πr or C = πd.
Area (A)
The space enclosed by the circle. Calculated as A = πr².
Circle Formulas
Basic Relationships:
d = 2r
r = d/2
C = 2πr = πd
A = πr² = π(d/2)²
Reverse Formulas:
r = C/(2π)
r = √(A/π)
d = C/π
The Constant π (Pi)
Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. It's approximately 3.14159, but it's an irrational number with infinite decimal places.
π ≈ 3.14159265358979323846...
In calculations: π ≈ 3.14159 (for most practical purposes)
Example Calculations
Example 1: Pizza Circle
Given: Pizza with radius = 15 cm
Circumference = 2π × 15 ≈ 94.25 cm
Area = π × 15² ≈ 706.86 cm²
Result: A 30cm diameter pizza has about 707 cm² of area.
Example 2: Garden Sprinkler
Given: Sprinkler covers area = 50 m²
r² = 50/π ≈ 15.92
r = √15.92 ≈ 3.99 m
Diameter ≈ 7.98 m
Result: The sprinkler has a radius of about 4 meters.
Example 3: Wheel Circumference
Given: Bicycle wheel diameter = 26 inches
Circumference = π × 26 ≈ 81.68 inches
Area = π × 13² ≈ 530.93 square inches
Result: One wheel rotation moves the bike about 81.7 inches forward.
Frequently Asked Questions
Why is π used in circle calculations?
Pi (π) represents the fundamental relationship between a circle's circumference and diameter. No matter the size of the circle, the circumference is always π times the diameter. This constant appears in all circle formulas because of this geometric relationship.
How accurate are the calculations?
Our calculator uses a high-precision value of π (3.141592653589793) for accurate results. The displayed results are rounded to 4 decimal places for readability, but internal calculations maintain full precision.
What's the difference between area and circumference?
Circumference is the distance around the circle (1-dimensional), measured in linear units like meters or inches. Area is the space inside the circle (2-dimensional), measured in square units like square meters or square inches.