Chord to Radius Calculator

How to Use This Calculator

1. Enter the length of the chord (c) in your circle. This is the straight line distance between two points on the circle's circumference.
2. Enter the perpendicular distance from the center of the circle to the chord (d). This is the shortest distance from the center to the chord.
3. Click the "Calculate" button to compute the radius.
4. The calculator will display the radius of the circle based on your inputs.

Principle Behind the Calculation

The radius of a circle can be calculated when you know the chord length and the distance from the center to the chord using the following formula:

r = √(d² + (c/2)²)

This formula works because when you draw a perpendicular from the center of the circle to the chord, you create a right triangle where:

• The radius (r) is the hypotenuse
• The distance from the center to the chord (d) is one leg of the triangle
• The half chord length (c/2) is the other leg of the triangle

Example

If you have a chord that is 10 units long and is 3 units away from the center of the circle, the radius would be:

r = √(3² + (10/2)²) = √(9 + 25) = √34 ≈ 5.83 units

Applications

This calculator is useful in various fields including:

• Architecture and engineering for designing circular structures
• Cartography for map-making
• Surveying and geometry problems
• Manufacturing for circular components