Chord Length Calculator | Circle Chord Formula & Geometry Tool

Input Parameters

Enter any two parameters to calculate chord length in real-time

Calculation Method

Select the parameters you have available

Circle Radius r

units

Distance from center to circle edge

Circle Diameter d = 2r

units

Twice the radius (d = 2 × r)

Central Angle θ

Angle between radii to chord endpoints

Sagitta (Height) s

units

Height from chord midpoint to arc

Chord Length c

units

Straight line distance between two circle points

Chord Length Formulas

c = 2r × sin(θ/2)

Where:

c = Chord Length
r = Circle Radius
θ = Central Angle (in radians)
s = Sagitta (Height from chord to arc)

Other useful formulas:

c = 2 × √(r² - (r - s)²)

Chord from radius and sagitta

Circle Visualization

Radius

Angle

0°

Chord

Sagitta

Calculation Results

Chord Length

0.00

Straight line between circle points

Arc Length

0.00

Curved distance along the circle

Segment Area

0.00

Area between chord and arc

Central Angle

0.00°

Angle at circle center

Sagitta

0.00

Height from chord to arc

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Understanding Chord Length: A Comprehensive Guide

A chord is a straight line segment whose endpoints lie on a circle. Calculating chord length is essential in geometry, engineering, architecture, and various technical fields.

What is Chord Length?

In geometry, a chord of a circle is a straight line segment connecting two points on the circle's circumference. The chord length varies based on its distance from the circle's center and the central angle it subtends.

How to Use This Chord Length Calculator

Our chord length calculator provides multiple methods to calculate chord measurements:

Using Radius and Central Angle: Enter the circle's radius and the central angle in degrees or radians.
Using Radius and Sagitta: Input the radius and the sagitta (height from chord midpoint to the arc).
Using Diameter and Central Angle: Provide the circle diameter and central angle.
Reverse Calculation: Find the central angle when you know the radius and chord length.

Practical Applications of Chord Length Calculations

Chord length calculations have numerous real-world applications:

Architecture: Designing arched windows, doorways, and vaulted ceilings
Engineering: Calculating material lengths for circular structures
Manufacturing: Designing circular components and fittings
Land Surveying: Measuring circular plots and boundaries
Computer Graphics: Rendering circular elements accurately

Key Mathematical Formulas

The primary formula for chord length calculation is:

Chord Length (c) = 2 × r × sin(θ/2)

Where r is the radius and θ is the central angle in radians.

For calculations using sagitta (s):

Chord Length (c) = 2 × √(2 × r × s - s²)

Tips for Accurate Calculations

Ensure consistent units for all measurements
Convert angles to radians when necessary (π radians = 180°)
Remember that diameter = 2 × radius
The maximum chord length equals the diameter (when the chord passes through the center)
Sagitta cannot exceed the radius value

Our chord length calculator automatically handles unit conversions and validates inputs to ensure accurate results. Try different calculation methods and explore the visual representation to better understand the geometric relationships.