Math July 13, 2026 · 8 Min Read

Chord Length Calculator – Guide & Formulas

Calculate the length of a chord in a circle using the radius and distance from center, or radius and central angle. Step-by-step results.

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Put these formulas into practice with our instant, step-by-step Chord Length Calculator.

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The Chord Length Calculator computes the length of a chord in a circle using either the radius and perpendicular distance from center, or the radius and central angle. It also calculates related values like sagitta (arrow height) and arc length.

Key Takeaway

Use the free Chord Length Calculator to calculate the length of a chord in a circle using the radius and distance from center, or radius and central angle. step-by-step results. Get instant results with step-by-step explanations.

How to Use the Chord Length Calculator

  1. Choose your calculation mode: Radius + Distance, or Radius + Angle.
  2. Enter the radius of the circle.
  3. Enter the perpendicular distance from center (Mode 1) or the central angle in degrees (Mode 2).
  4. Review the chord length, sagitta, arc length, and segment area.

The Formula

Chord length = 2 × √(r² — d²) where r = radius, d = perpendicular distance from center

Variable Definitions

  • c: Length of the chord
  • r: Radius of the circle
  • d: Perpendicular distance from the center of the circle to the chord
  • θ: Central angle subtended by the chord (in degrees or radians)

Example: Chord in a Circle with r=10, d=6

Find the chord length when the radius is 10 and the distance from center is 6.

  1. Step 1: Identify the formula: c = 2√(r² — d²).
  2. Step 2: Substitute values: c = 2√(10² — 6²).
  3. Step 3: Calculate inside the square root: 100 — 36 = 64.
  4. Step 4: Take the square root: √64 = 8.
  5. Step 5: Chord length: c = 2 × 8 = 16 units.

Frequently Asked Questions