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 ( r^2  - L/2^2 )
  • 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