Enter the radius of the arc and the length of the base (chord) of the arc into the calculator to determine the arc height(s).

## Arc Height Formula

The following formula is used to calculate the height of an arc.

s = r +/- SQRT ( r2 – L/22 )

• Where s is the arc height
• r is the radius of the arc
• L is the base of the arc (chord length)

In this case, the formula solves for both the small and larger sagitta, since in a full circle, there would be two different arc heights.

## Arc Height Definition

What is an arc height?

An arc height, also commonly referred to as a sagitta, is a measure of the distance from the base of a circular segment to the peak of the arc.

The distance is measured from the center of the base (chord) to the peak.

## How to calculate arc height?

Arc Height Example Problem:

The following example problem is a step-by-step guide on how to calculate an arc height.

First, determine the radius of the arc. In this example, the radius is measured as 5 inches.

Next, measure the base of the arc. For this problem, the chord is measured to be 7 inches.

Finally, calculate the arc height using the formula above:

s = r +/- SQRT ( r2 – L/22 )

s = 5 +/- SQRT ( 52 – (7/2)2 )

s = 8.570 or 1.429