Chord Length Calculator

Chord Length Calculator

Calculate chord length from a central angle, arc length, or sagitta with the geometry checks built in.

Last updated: June 2026 | By Patchworkr Team

Chord Solver

Live results update as you type

Radius needs a real number.

Sagitta is the segment height from the chord to the arc. For a circle, it cannot exceed the radius.
Results
Enter values to calculate the chord length.

What Is a Chord?

A chord is a straight line segment that connects two points on a circle.

The longest chord is the diameter. That gives a built-in limit: chord length cannot exceed 2r.

This calculator checks that limit before it computes a value.

Chord Length Formulas

From Angle
c = 2r * sin(theta / 2)
From Arc
theta = s / r
From Sagitta
c = 2 * sqrt(2rh - h^2)

How to Use This Calculator

  1. Choose the known quantity: angle, arc length, or sagitta.
  2. Enter the radius and the known value.
  3. Read the chord length and related outputs on the right.
  4. Check the diameter limit if you are using chord length directly.

Worked Example

For a radius of 10 and a central angle of 60 deg, the chord length is 2 * 10 * sin(30 deg) = 10.

Chord length = 10
Arc length = 10.4719755
Sagitta = 1.33974596

The chord is shorter than the arc, which is exactly what the geometry predicts.

Frequently Asked Questions

Can sagitta be larger than the radius?

No. That would describe a circle segment that is not possible in this model.

Can the angle be zero?

Yes. A zero angle gives a zero-length chord as a degenerate boundary case.

Why do you use radians internally?

The sine function in the chord formula expects radians, so degrees are converted before calculation.

What if the chord is the diameter?

Then the angle is 180 deg and the chord length is exactly 2r.

Related Tools