Arc Height (sagitta) Calculator



Arc Height Small (ssmall):

Arc Height Large (slarge):

 

Introduction

The Arc Height Calculator is a handy tool for calculating the height of an arc segment within a circle, based on its radius, base (chord), and arc heights. Whether you’re working on geometry problems, engineering projects, or any other application that involves arcs, this calculator simplifies the process.

How to Use

To use the Arc Height Calculator, follow these steps:

  1. Enter the radius of the circle in the “Radius” field.
  2. Input the length of the base (chord) in the “Base” field.
  3. Fill in either the “Arc Height Small” or “Arc Height Large” field with the appropriate value.
  4. Click the “Calculate” button to find the arc height of the segment.

Formula

The formula for calculating the arc height of a segment is as follows:

s = r ± √(r² – (L/2)²)

Where:

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

Example

Let’s say you have a circle with a radius (r) of 10 units and a base (chord) length (L) of 6 units. You want to calculate the arc height. Using the formula:

s = 10 ± √(10² – (6/2)²)

s = 10 ± √(100 – 9) s = 10 ± √91

So, the arc height is approximately 10 ± 9.54 units, which means the arc height could be either approximately 19.54 units or approximately 0.46 units, depending on whether you choose the positive or negative square root in the formula.

FAQs

1. What is the arc height in a circle?

The arc height is the vertical distance from the midpoint of the base (chord) of an arc to the edge of the circle.

2. Can I use this calculator for any type of arc?

Yes, this calculator can be used for calculating the arc height of any arc within a circle, regardless of its size or position.

3. What is the significance of the positive and negative square root in the formula?

The positive square root represents the larger arc height, while the negative square root represents the smaller arc height. You can choose the appropriate result based on your specific application.

Conclusion

The Arc Height Calculator simplifies the process of determining the arc height of a segment within a circle. Whether you are a student working on geometry problems or an engineer involved in designing circular structures, this calculator can save you time and effort. Just input the necessary values, and you’ll have the arc height in no time, thanks to the user-friendly interface and the straightforward formula provided.

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