A chord length calculator is designed to determine the length of a chord in a circle or arc. A chord is a line segment that connects two points on the circumference of a circle.
Examples:
- In construction, calculating chord length helps in designing arched structures.
- In astronomy, chord length calculations assist in understanding planetary orbits.
- For landscaping, it aids in creating circular garden designs.
This calculator is particularly useful in geometry, engineering, and various practical applications.
Chord Length Calculator
| Radius (R) | Central Angle (θ) | Chord Length (c) | Conversion Notes |
|---|---|---|---|
| 5 m | 60° (π/3 rad) | 5 m | θ(rad) = θ(deg) * π/180 |
| 10 ft | 45° (π/4 rad) | 7.65 ft | c = 2R * sin(θ/2) |
| 15 cm | 90° (π/2 rad) | 21.21 cm | Round to 2 decimal places |
| 8 in | 120° (2π/3 rad) | 13.86 in | 1 ft = 12 in |
| 20 km | 30° (π/6 rad) | 10 km | Large scale application |
Chord Length Calculator Formula
The formula for calculating chord length is:
Chord Length = 2R * sin(θ/2)
Where:
- R is the radius of the circle
- θ (theta) is the central angle in radians
Example:
For a circle with a radius of 10 units and a central angle of 60°:
- Convert 60° to radians: π/3
- Apply the formula: 2 10 sin(π/6) ≈ 10 units
How do you find the chord length of an arc?
Finding the chord length of an arc involves these steps:
- Identify known values: Determine the radius (R) and either the central angle (θ) or arc length (s).
- Convert angle to radians: If given in degrees, multiply by π/180.
- Calculate arc length: If not given, use s = R * θ.
- Apply chord length formula: Use 2R * sin(θ/2).
Detailed Example:
Given an arc with a radius of 5 meters and a central angle of 45°:
Convert 45° to radians: 45 * (π/180) = π/4 radians
Arc length: s = 5 * (π/4) ≈ 3.93 meters
Chord length: 2 5 sin(π/8) ≈ 3.83 meters
What is the formula for the length of a chord on a circle calculator?
The formula remains consistent: 2R * sin(θ/2).
- Given radius and central angle: Use the standard formula.
- Given diameter and central angle: Chord Length = D * sin(θ/2), where D is diameter.
- Given radius and arc length: First calculate θ using θ = s/R, then apply the standard formula.
Consider a circle with a diameter of 12 units and a central angle of 30°:
Radius R = 12/2 = 6 units
Convert 30° to radians: π/6
Apply formula: 2 6 sin(π/12) ≈ 3.12 units
How to calculate radius from arc length and chord length?
Calculating radius from arc length (s) and chord length (c) involves these steps:
- Use the formula: R = (4s² + c²) / (8s)
- Ensure s and c are in the same units.
Given arc length 10 units and chord length 8 units:
Apply formula: R = (4 10² + 8²) / (8 10)
R = (400 + 64) / 80
R = 464 / 80 = 5.8 units
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