Circle Calculator

Calculate area, circumference, diameter, and radius of any circle instantly

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Value (units):

Calculation Results

Enter a circle measurement to calculate all properties.

Circle Diagram

The Circle: A Fundamental Geometric Shape

A circle is one of the most fundamental and symmetrical shapes in geometry. It is defined as the set of all points in a plane that are at a fixed distance (called the radius) from a central point (called the center).

Key Properties of a Circle

Radius (r) - The distance from the center to any point on the circle.
Diameter (d) - The longest distance across the circle, passing through the center (d = 2r).
Circumference (C) - The perimeter or distance around the circle (C = 2πr or C = πd).
Area (A) - The space enclosed within the circle (A = πr²).
Chord - A straight line connecting two points on the circle (the diameter is the longest chord).
Arc - A segment of the circumference.
Sector - A "pie slice" of the circle, bounded by two radii and an arc.
Segment - A region between a chord and its corresponding arc.

Mathematical Equations of a Circle

Standard Equation (Center at Origin)
x² + y² = r²
Standard Equation (Center at (h, k))
(x - h)² + (y - k)² = r²
Parametric Equations
x = r cosθ, y = r sinθ (0 ≤ θ < 2π)

Why Are Circles Important?

Symmetry & Balance - Circles appear in nature (planets, bubbles, ripples) and man-made objects (wheels, clocks, coins).
Engineering & Design - Used in gears, pipes, and circular structures for optimal strength and efficiency.
Mathematics & Physics - Essential in trigonometry, circular motion, and wave mechanics.
Everyday Life - Used in sports (basketballs, rings), art, and architecture.

Facts About Circles

The word "circle" comes from the Greek word "kirkos," meaning "ring" or "hoop."
A circle has infinite lines of symmetry.
π (Pi) is a mathematical constant crucial in circle calculations, representing the ratio of circumference to diameter.

Circles are everywhere—from tiny atoms to massive planets! Understanding their properties helps in math, science, and real-world applications.

Circle Formulas

Radius (r): r = d/2 = C/(2π) = √(A/π)
Diameter (d): d = 2r = C/π = 2√(A/π)
Circumference (C): C = 2πr = πd = 2√(πA)
Area (A): A = πr² = (πd²)/4 = C²/(4π)

Where π (pi) ≈ 3.141592653589793

Radius (r)

Diameter (d)

Circumference (C)

Area (A)

How to Use the Circle Calculator

This Circle Calculator helps you quickly compute the properties of a circle like Radius, Diameter, Circumference, Area based on the input you provide. Below is a step-by-step guide on how to use it.

1 Select the Input Type

Choose what you already know about the circle:

Radius (r) - Distance from the center to the edge.
Diameter (d) - The longest distance across the circle (2 × radius).
Circumference (C) - The total distance around the circle.
Area (A) - The space enclosed within the circle.

Example: If you know the radius, select "Radius" from the dropdown.

2 Enter the Known Value

Type in the numerical value in the input box.

Make sure to enter a positive number.
You can use decimals (e.g., 5.5).

Example: If the radius is 7, enter 7 in the input field.

3 Click "Calculate"

Press the Calculate button to get results.

The calculator will automatically compute:

Radius (r)
Diameter (d)
Circumference (C)
Area (A)

Example Output:

If you entered Radius = 7, the results will show:

Diameter = 14
Circumference ≈ 43.98
Area ≈ 153.94

Example Use Cases

Finding the circumference of a circular track (if you know the radius).
Calculating the area of a circular garden (if you know the diameter).
Determining the radius of a pipe (if you know the circumference).

Example Calculations

Example 1: For a circle with radius 5 units:
- Diameter = 10 units
- Circumference ≈ 31.42 units
- Area ≈ 78.54 square units
Example 2: For a circle with circumference 20π units:
- Radius = 10 units
- Diameter = 20 units
- Area ≈ 314.16 square units
Example 3: For a circle with area 50 cm²:
- Radius ≈ 3.99 cm
- Diameter ≈ 7.98 cm
- Circumference ≈ 25.06 cm

Frequently Asked Questions

1. What is the difference between circumference and area?

Circumference is the perimeter of the circle - the distance around it, measured in linear units (cm, m, etc.).

Area is the space contained within the circle, measured in square units (cm², m², etc.).

For a circle with radius r:

Circumference = 2πr
Area = πr²

2. Why is π (pi) used in circle calculations?

π (pi) is the ratio of a circle's circumference to its diameter. This ratio is constant for all circles, making π a fundamental constant in circle geometry.

Key facts about π:

π ≈ 3.141592653589793
It's an irrational number (infinite non-repeating decimal)
Appears in many mathematical formulas beyond circles
First calculated by ancient mathematicians measuring circles

3. How do you find the radius if you know the area?

You can find the radius from the area using the formula:

r = √(A/π)

Where:

r = radius
A = area
π ≈ 3.14159

Example: For area = 78.54 square units:

r = √(78.54/π) ≈ √(78.54/3.14159) ≈ √25 ≈ 5 units

4. What are some real-world applications of circle calculations?

Circle calculations are used in many practical situations:

Construction: Calculating materials for circular structures
Engineering: Designing gears, wheels, and pipes
Astronomy: Calculating orbits of celestial bodies
Manufacturing: Determining material needed for circular products
Sports: Marking circular fields and tracks
Art: Creating precise circular designs