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Circle Calculator

Calculate radius, diameter, circumference, and area of a circle from any single value. Includes arc length, sector area, chord length, and segment area calculations with step-by-step solutions and interactive diagram.

Circle Calculator

Embed Circle Calculator Widget

About Circle Calculator

Welcome to the Circle Calculator, a comprehensive geometry tool that calculates all properties of a circle from any single known measurement. Enter the radius, diameter, circumference, or area, and instantly get all other values plus optional arc length, sector area, and segment area calculations. Results are displayed in both decimal and exact π notation for maximum precision.

What is a Circle?

A circle is a two-dimensional shape consisting of all points in a plane that are equidistant from a central point called the center. This constant distance from the center to any point on the circle is called the radius. Circles are fundamental shapes in mathematics, appearing throughout nature, engineering, and everyday life.

Circle Formulas

Basic Relationships

Diameter from Radius
$$d = 2r$$
Radius from Diameter
$$r = \frac{d}{2}$$

Circumference (Perimeter)

The circumference is the distance around the circle:

Circumference Formula
$$C = 2\pi r = \pi d$$

Area

The area is the space enclosed by the circle:

Area Formula
$$A = \pi r^2 = \frac{\pi d^2}{4}$$

Advanced Circle Calculations

Arc Length

An arc is a portion of the circumference. Given a central angle θ:

Arc Length Formula
$$L_{arc} = \frac{\theta}{360°} \times 2\pi r = \frac{\theta \pi r}{180}$$

Sector Area

A sector is a "pie slice" of the circle bounded by two radii and an arc:

Sector Area Formula
$$A_{sector} = \frac{\theta}{360°} \times \pi r^2 = \frac{\theta \pi r^2}{360}$$

Chord Length

A chord is a straight line connecting two points on the circle:

Chord Length Formula
$$c = 2r \sin\left(\frac{\theta}{2}\right)$$

Segment Area

A segment is the region between a chord and its arc:

Segment Area Formula
$$A_{segment} = A_{sector} - A_{triangle} = \frac{r^2}{2}\left(\frac{\theta \pi}{180} - \sin\theta\right)$$

How to Use This Calculator

  1. Select what you know: Choose Radius, Diameter, Circumference, or Area from the dropdown
  2. Enter your value: Input the known measurement
  3. Choose a unit (optional): Select from mm, cm, m, km, in, ft, yd, or mi
  4. Add an angle (optional): Enter a central angle in degrees to calculate arc length, sector area, chord length, and segment area
  5. Click Calculate: View all circle properties with both decimal and π notation, plus an interactive diagram

Understanding π (Pi)

Pi (π) is the ratio of a circle's circumference to its diameter. It is an irrational number, meaning its decimal representation never ends and never repeats:

π ≈ 3.14159265358979323846...

Common approximations include 3.14159 or 22/7. This calculator uses high-precision arithmetic and shows results in exact π notation when possible.

Real-World Applications

🍕
Pizza Sizing
12" pizza = 113 in² area
🚗
Tire Diameter
26" wheel = 81.7" circumference
🏊
Pool Covers
18ft diameter = 254 ft² area
🎯
Dart Board
17.75" diameter = 247 in² area

Circle Properties Summary

PropertySymbolFormulaDescription
Radiusrd/2 or C/(2π)Distance from center to edge
Diameterd2rDistance across through center
CircumferenceC2πr or πdPerimeter (distance around)
AreaAπr²Space enclosed by the circle
Arc LengthLθπr/180°Length of a portion of circumference
Sector AreaAsθπr²/360°Area of a "pie slice"
Chord Lengthc2r·sin(θ/2)Straight line between two points on circle
Segment AreaAsegSector - TriangleArea between chord and arc

Frequently Asked Questions

What is the formula for the area of a circle?

The area of a circle is calculated using the formula A = πr², where r is the radius. For example, a circle with radius 5 units has an area of π × 5² = 25π ≈ 78.54 square units. Alternatively, using the diameter d, the formula is A = π(d/2)² = πd²/4.

How do you calculate the circumference of a circle?

The circumference (perimeter) of a circle is calculated using C = 2πr or C = πd, where r is the radius and d is the diameter. For example, a circle with radius 7 units has a circumference of 2 × π × 7 = 14π ≈ 43.98 units.

What is the relationship between radius and diameter?

The diameter of a circle is exactly twice the radius. Expressed as formulas: d = 2r and r = d/2. The radius is the distance from the center to any point on the circle, while the diameter is the distance across the circle through its center.

What is arc length and how is it calculated?

Arc length is the distance along the curved line of a circle between two points. It is calculated using the formula: Arc Length = (θ/360°) × 2πr, where θ is the central angle in degrees and r is the radius. Alternatively, in radians: Arc Length = θ × r.

What is the difference between a sector and a segment of a circle?

A sector is a "pie slice" of a circle bounded by two radii and an arc. A segment is the region between a chord and its arc. Sector area = (θ/360°) × πr². Segment area = Sector area - Triangle area, where the triangle is formed by the two radii and the chord.

What is the value of π (pi)?

Pi (π) is a mathematical constant representing the ratio of a circle's circumference to its diameter. Its value is approximately 3.14159265358979... and it is an irrational number, meaning its decimal representation never ends and never repeats. For calculations, π ≈ 3.14159 or 22/7 are common approximations.

Additional Resources

Reference this content, page, or tool as:

"Circle Calculator" at https://MiniWebtool.com/circle-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Feb 01, 2026

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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