Enter the chord length and arc height into the calculator to determine the radius of the circle. The calculator uses these two values to calculate the radius.
Chord to Radius Formula
The following formula is used to calculate the radius of a circle based on the chord length and arc height.
R = frac{H}{2} + frac{C^2}{8H}Variables:
- R is the radius of the circle (units)
- H is the arc height (units)
- C is the chord length (units)
To calculate the radius of a circle, add half of the arc height to the square of the chord length divided by eight times the arc height.
What is a Chord?
A chord is a straight line segment whose endpoints both lie on the circumference of a circle. The chord length is the distance between these two points. The arc height (also known as the sagitta) is the perpendicular distance from the midpoint of the chord to the arc of the circle. Together, these measurements can be used to determine the radius of the circle, which is the distance from the center of the circle to any point on its circumference.
How to Calculate Radius from Chord and Arc Height?
The following steps outline how to calculate the radius of a circle from the chord length and arc height.
- First, measure the chord length (C) of the circle.
- Next, measure the arc height (H) of the circle.
- Use the formula R = H/2 + C^2/(8H) to calculate the radius (R).
- Finally, enter the chord length and arc height into the calculator to get the radius.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Chord length (C) = 10 units
Arc height (H) = 2 units
