Chord Length Calculator - Free Online Calculator | yourcalculator.app
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Chord c = 2 r sin(θ/2) | Sagitta h = r (1 - cos(θ/2))

Chord Length Calculator

Calculate straight line chord length across a circle and sagitta arc height.

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Formula & Mathematical Method

This calculator uses standard deterministic mathematical algorithms to process user inputs in real time. Calculations are performed client-side for maximum speed and privacy.

Reviewed by Geometry Desk
Checked for AccuracyLast Reviewed: August 2026

Circle Chord & Sagitta Properties

Theoretical background and practical computational guidance

A chord is a straight line segment joining two points on a circular curve.

Sagitta (h) is the height of the arc above the chord midpoint.

Chord & Sagitta EquationsMathematical Standard
c = 2 r \sin\left(\frac{\theta}{2}\right) \quad | \quad h = r \left(1 - \cos\left(\frac{\theta}{2}\right)\right)

Solves chord length c and arc height h.

Worked Calculation Walkthrough & Analytical Steps

To evaluate a typical problem using the Chord Length Calculator, identify your known baseline inputs, convert all measurements to congruent units, and apply the governing formula sequentially. Below is a structured breakdown of the computational workflow:

  1. Data Ingestion & Unit Harmonization: Enter the primary parameters into the input fields. If working with mixed metric or imperial dimensions, use the unit selector above to align scales.
  2. Intermediate Term Evaluation: The algorithm evaluates inner parentheses, rate exponents, and coefficient ratios in strict compliance with mathematical precedence.
  3. Final Transformation & Precision Rounding: The final numerical figure is determined, formatted to user-selected decimal precision, and mapped against relevant diagnostic or diagnostic thresholds.

Key Insights & Operational Tips

  • The longest chord in any circle is its diameter.

Frequently Asked Questions (FAQs)

Authoritative answers to common computational and formula questions

The perpendicular height from chord midpoint to arc crest.

Authoritative Citations & Institutional References

Disclaimer & Methodological Transparency Notice

Academic Notice: Circle chord formulas.