Geometry

Circle Chord Length Calculator

Easily calculate the chord length of a circle using its radius and the distance from the center. Visualize the chord and understand the geometry behind it.

Input Values

Enter the radius of the circle and the distance from the center of the circle to the chord to calculate the chord length.

units
units

Result

Chord Length (L):

Visualization

Visual representation of the circle, radius, distance from center, and the calculated chord.

Distance (d)Radius (r)CenterChord EndChord EndChord (L)

Understanding Circle Chords

In geometry, a chord of a circle is a line segment whose endpoints both lie on the circle. The straight line distance from the center of the circle to the chord is called the distance from the center to the chord.

The formula to calculate the length of a chord (L) given the radius (r) of the circle and the distance (d) from the center to the chord is derived from the Pythagorean theorem:

$$ L = 2 \sqrt{r^2 - d^2} $$

This calculator simplifies the process of finding the chord length by just requiring the radius and the distance from the center as inputs. It's useful in various applications, from geometry problems to practical constructions involving circular shapes.

Learn more about circle chords on Wikipedia.

Frequently Asked Questions

What is the Circle Chord Length Calculator?
The Circle Chord Length Calculator is an online Geometry calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Circle Chord Length Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Circle Chord Length Calculator for professional Geometry projects?
Yes. The math behind it is standard Geometry, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Circle Chord Length Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Circle Chord Length Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.