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).

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## 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 ( r^{2 } – L/2^{2} )

s = 5 +/- SQRT ( 5^{2 } – (7/2)^{2} )

s = 8.570 or 1.429