The Arc Height (Sagitta) Calculator simplifies the process of determining the height of an arc (sagitta) from the base of the chord to the top of the arc. This measurement is vital in many construction and design tasks where precise curvature is required to meet specific aesthetic or structural demands.
Formula of Arc Height (sagitta) Calculator
To calculate the arc height or sagitta of a circle segment, the following formula is used:
Where:
- Radius (R): The radius of the circle.
- Chord Length (C): The horizontal line segment that spans from one point on the circle’s edge to another, passing underneath the arc.
This formula provides a direct method for calculating the sagitta, enabling precise and efficient assessments of the curvature for any segment of a circle.
General Terms and Conversion Table
For better understanding, here is a table of terms related to the arc height calculation:
| Term | Definition |
|---|---|
| Sagitta | The height of an arc segment in a circle. |
| Radius | The distance from the center of the circle to any point on its perimeter. |
| Chord | A straight line connecting two points on a circle. |
| Arc | A portion of the circumference of a circle. |
| Circumference | The complete distance around the circle. |
Example of Arc Height (sagitta) Calculator
Consider a circular window that is to be install in a chapel, with the window having a radius of 5 meters and a chord length of 8 meters. Using the Arc Height Calculator, the sagitta can be calculated as follows:
Radius = 5 meters Chord Length = 8 meters
Arc Height = 5 – √(5² – (8 / 2)²) Arc Height = 5 – √(25 – 16) Arc Height = 5 – 3 Arc Height = 2 meters
This result helps in designing the frame and the arch of the window accurately, ensuring that it fits perfectly within the intended space.
Most Common FAQs
Calculating the sagitta helps in determining the exact curvature of an arc, which is crucial for precise fabrication and aesthetics in construction and design projects.
Yes, the sagitta calculator can be apply to any circle. As long as the radius and the chord length are know.
Ensure accurate measurement of the radius and chord length. As small errors can significantly affect the calculation of the sagitta.