\[h = r - \sqrt{r^2 - \left(\frac{c}{2}\right)^2}\]
Variables
hsagitta height (m)
rradius (m)
cchord length (m)
Description
What is this formula?
This formula calculates the sagitta of a circular segment. The sagitta is the perpendicular distance from the midpoint of a chord to the arc of the circle.
When to use it
Use this formula when the radius and chord length of a circle are known and the height of the circular segment needs to be determined.
Example
If the radius is 10 m and the chord length is 12 m:
h = 10 - √(10² - (12/2)²) = 2 m
Applications
- Civil engineering
- Arch and bridge design
- Mechanical fabrication
- Geometry and drafting
- Circular tank and pipe calculations