Chord Length Calculator
Verified Calculation Engine
The online Chord Length Calculator helps you calculate instantly and solve problems related to Coordinate Geometry Conics. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Calculates length of chord of circle: L = 2√(r² - d²) where r is radius and d is perpendicular distance from center to chord.
Chord length L = 2√(r² - d²)
where r = radius, d = perpendicular distance from center to line
Or: L = 2√(r² - p²) where p is distance from center to chord
Chord length using radius and distance from center
Inputs
Results
Worked Examples
Example 1: Basic
Find chord length of circle x² + y² = 25 cut by line x = 3
- circle: x^2 + y^2 = 25
- line: x = 3
- chordLength: 8
- distanceFromCenter: 3
Example 2: Board Level
Find chord length of circle x² + y² - 4x - 6y + 9 = 0 cut by line x + y = 5
- circle: x^2 + y^2 - 4x - 6y + 9 = 0
- line: x + y = 5
- chordLength: 2.8284
- distanceFromCenter: 0.7071
About this calculator
Overview
Chord Length Calculator evaluates Chord Length for the math / coordinate-geometry-conics library. Primary input cue: Circle Equation [required]. Method anchor: Chord length L = 2√(r² - d²) where r = radius, d = perpendicular distance from center to line Or: L = 2√(r² - p²) where p is distance from center to chord. Chor.
When to use
Use Chord Length Calculator when you already know the inputs and need chord length without setting up a spreadsheet.
Inputs explained
- Circle Equation [required]
- Line (Chord) [required]: Line equation that intersects circle
Formula / method
Chord length L = 2√(r² - d²) where r = radius, d = perpendicular distance from center to line Or: L = 2√(r² - p²) where p is distance from center to chord. Chord length using radius and distance from center (calculator id: chord-length-calculator).
Worked example
Worked values: circle = x^2 + y^2 = 25, line = x = 3 → chordLength = 8, distanceFromCenter = 3
Interpreting results
Read the primary output as chord length under the method on this page.
Assumptions
- Chord Length is computed only from the fields you enter on this calculator. [chord-length-calculator]
- The wired execution function for `chord-length-calculator` is the source of numerical behavior.
- Real-number arithmetic is used unless chord length explicitly needs integers.
Limitations
- Edge cases outside the intended domain of chord length may error or look unstable—treat them as out of scope.
- If multiple conventions exist for chord length, this calculator uses the convention implemented in its engine path.
- Complex/branch cuts and undefined points are not always interactively annotated for chord length.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Chord length L = 2√(r² - d²) where r = radius, d = perpendicular distance from center to line Or: L = 2√(r² - p²) where p is distance from center to chord. Chord length using radius and distance from center (calculator id: chord-length-calculator).
Example Calculation
Worked values: circle = x^2 + y^2 = 25, line = x = 3 → chordLength = 8, distanceFromCenter = 3
Frequently Asked Questions
What is Chord Length Calculator?
- Chord Length Calculator evaluates Chord Length for the math / coordinate-geometry-conics library. Primary input cue: Circle Equation [required]. Method anchor: Chord length L = 2√(r² - d²) where r = radius, d = perpendicular distance from center to line Or: L = 2√(r² - p²) where p is distance from center to chord. Chor.
How does Chord Length Calculator work?
- Chord length L = 2√(r² - d²) where r = radius, d = perpendicular distance from center to line Or: L = 2√(r² - p²) where p is distance from center to chord. Chord length using radius and distance from center (calculator id: chord-length-calculator).
Why use this Math Numbers calculator?
- Use Chord Length Calculator when you already know the inputs and need chord length without setting up a spreadsheet.