Circle Calculator

Calculate circle properties including area, circumference, diameter, and radius. Perfect for geometry, engineering, and mathematical calculations involving circles.

Calculator Input

rd
Center & Radius --- Diameter

Circle Properties

Radius
5.0000 cm
Diameter
10.0000 cm
Circumference
31.4159 cm
Area
78.5398 cm²

Additional Properties

Radius (exact):5 cm
Diameter (exact):10 cm
Circumference (π form):10π cm
Area (π form):25π cm²
Sector (90°) Area:19.6350 cm²
Arc Length (90°):7.8540 cm

Unit Conversions

Radius (Millimeters):50.0000 mm
Radius (Meters):0.0500 m
Radius (Kilometers):0.0001 km
Radius (Inches):1.9685 in
Radius (Feet):0.1640 ft
Radius (Yards):0.0547 yd

Formulas Used

Radius: r = 5
Diameter: d = 2r = 10
Circumference: C = 2πr = π × 10 ≈ 31.4159
Area: A = πr² = π × 5² ≈ 78.5398

How to Use

Basic Steps

  1. Choose what measurement you know (radius, diameter, circumference, or area)
  2. Enter the known value in the input field
  3. Select the appropriate unit of measurement
  4. View all calculated circle properties instantly
  5. 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

Diameter = 2 × 15 = 30 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

A = πr² = 50
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

Radius = 26/2 = 13 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.