What Is a Chord Calculator?
A chord calculator finds the length of a chord — a straight line connecting two points on a circle — from the circle's radius and the central angle, or from the radius and the perpendicular distance from the center to the chord. Chords appear in geometry, engineering, and design. Enter the known values and the calculator returns the chord length.
How to Use the Calculator
- Enter the radius of the circle.
- Enter the central angle (or the distance from center to chord).
- Calculate — see the chord length.
Chord Length Formulas
From the radius r and central angle θ:
Chord = 2r × sin(θ ÷ 2)
From the radius r and the perpendicular distance d from the center to the chord:
Chord = 2 × √(r² − d²)
Worked Example
For a circle of radius 10 with a central angle of 60°: chord = 2 × 10 × sin(30°) = 20 × 0.5 = 10. So the chord is 10 units long — equal to the radius in this case, forming part of an equilateral triangle.
Key Facts About Chords
| Chord | Property |
|---|---|
| Diameter | The longest possible chord, passing through the center |
| Equal chords | Are equidistant from the center |
| Perpendicular from center | Bisects the chord |
Where Chords Are Used
- Engineering: arcs, curves, and structural design.
- Construction: laying out curved walls and roads.
- Geometry: circle theorems and problems.
Frequently Asked Questions
What is a chord of a circle?
A chord is a straight line segment whose endpoints both lie on the circle. The diameter is the longest chord.
How do you find chord length?
From radius and central angle, use chord = 2r·sin(θ/2). From radius and distance to the chord, use chord = 2√(r² − d²).
Is the diameter a chord?
Yes — the diameter is the longest chord of a circle, passing through the center.
How does the central angle affect chord length?
A larger central angle produces a longer chord, up to the diameter at 180°. The chord grows as the angle approaches a straight line through the center.
Is this chord calculator free?
Yes — it is completely free, requires no signup, and finds chord length from your inputs.