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 designingarched structures.- In
astronomy, chord length calculations assist in understandingplanetary orbits.- For
landscaping, it aids in creatingcircular 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 radiansArc length:

s = 5 * (π/4) ≈ 3.93 metersChord length:

25sin(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 = (410² + 8²) / (810)

R = (400 + 64) / 80

R = 464 / 80 = 5.8 units

**Related Tools:**