🎯 Chord Length Calculator
Calculate the length of a chord in a circle
How to Use This Calculator
Choose Calculation Method
Select whether you know the central angle or the distance from the center to the chord.
Enter Values
Input the radius and either the central angle (in degrees) or the distance from center to chord.
Click Calculate
Press the "Calculate Chord Length" button to get the chord length.
Formula
Method 1: Using Radius and Central Angle
Chord Length = 2 × r × sin(θ/2)
Where θ is in radians (convert degrees to radians: θ_rad = θ_deg × π/180)
Method 2: Using Radius and Distance from Center
Chord Length = 2 × √(r² - d²)
Where d is the perpendicular distance from center to chord
Where:
- r = Radius of the circle
- θ = Central angle subtended by the chord
- d = Perpendicular distance from center to chord
Example 1 (Angle): Find chord length for a circle with radius = 10 and central angle = 60°
Chord Length = 2 × 10 × sin(60°/2)
Chord Length = 2 × 10 × sin(30°)
Chord Length = 2 × 10 × 0.5 = 10 units
Example 2 (Distance): Find chord length for a circle with radius = 10 and distance from center = 6
Chord Length = 2 × √(10² - 6²)
Chord Length = 2 × √(100 - 36)
Chord Length = 2 × √64 = 2 × 8 = 16 units
About Chord Length Calculator
The Chord Length Calculator finds the length of a chord in a circle. A chord is a line segment whose endpoints lie on the circle. You can calculate it using either the radius and central angle, or the radius and distance from the center to the chord.
When to Use This Calculator
- Geometry: Calculate chord lengths in circle geometry problems
- Engineering: Design circular components and measure distances
- Construction: Determine arc lengths and chord dimensions for circular structures
- Surveying: Calculate distances in circular land plots
- Education: Learn and practice circle geometry
- Architecture: Design circular elements and arches
Why Use Our Calculator?
- ✅ Two Methods: Calculate using angle or distance from center
- ✅ Instant Results: Get chord length immediately
- ✅ Flexible Input: Choose the method based on available data
- ✅ Step-by-Step Display: See the calculation formula
- ✅ 100% Accurate: Precise geometric calculations
- ✅ Completely Free: No registration required
Understanding Chords
A chord is a line segment connecting two points on a circle. Key properties:
- The longest chord is the diameter (passes through center)
- Chords equidistant from center have equal lengths
- The perpendicular from center to chord bisects the chord
- Central angle determines chord length for a given radius
- Chord length increases with central angle (up to 180°)
Real-World Applications
Bridge Construction: Calculate the span of a circular arch. For a bridge with radius 50 meters and central angle 90°, the chord length (span) is 2 × 50 × sin(45°) ≈ 70.71 meters.
Circle Cutting: When cutting a circle with a straight cut, the cut length is a chord. If you know the distance from center to cut and radius, you can find the chord length.
Arc Design: In architectural design, chord length helps determine arc dimensions and material requirements for curved structures.
Frequently Asked Questions
What is a chord in a circle?
A chord is a line segment whose endpoints lie on the circle. The diameter is a special chord that passes through the center and is the longest possible chord.
What's the difference between a chord and a diameter?
A diameter is a special type of chord that passes through the center of the circle. All diameters are chords, but not all chords are diameters. The diameter is the longest chord.
Can I calculate chord length if I only know the arc length?
Yes, but you'd need the radius too. From arc length (s) and radius (r), find the central angle: θ = s/r, then use the chord formula: Chord = 2r sin(θ/2).
What is the maximum chord length?
The maximum chord length is the diameter, which equals 2r. This occurs when the central angle is 180° (a semicircle).
How does the angle affect chord length?
Chord length increases with the central angle, from 0 (at 0°) to the diameter (at 180°). The relationship follows: Chord = 2r sin(θ/2), so larger angles give longer chords.
What if the distance from center equals the radius?
If the distance equals the radius, the chord length would be 0 (the chord is a single point at the circle's edge). The distance must be less than the radius for a valid chord.
Can I use this for ellipses?
No, this calculator is specifically for circles. Ellipses have different geometry and require different formulas for chord calculations.