To find the radius from a chord, square the height (H), then add the result to the chord squared (C²) divided by 8 times the height (H). This gives the radius (R).
The Chord to Radius Calculator allows you to find the radius of a circle using the chord length and the height (also known as the sagitta).
Formula:
R = (H² + (C² ÷ 8H))
| Symbol | Meaning |
|---|---|
| R | Radius of the Circle |
| H | Height (distance from chord to arc) |
| C | Chord Length |
Solved Calculation:
Example 1:
| Calculation | Instructions |
|---|---|
| Given: H = 4 cm, C = 10 cm | Start with the given height and chord length. |
| R = (4² + (10² ÷ 8 × 4)) | Square the height and chord, then divide the chord squared by 8 times the height. |
| R = (16 + (100 ÷ 32)) | Perform the division and addition. |
| R = (16 + 3.125) | Add the results together. |
| R = 19.125 cm | The radius of the circle is 19.125 cm. |
Answer: The calculated radius is 19.125 cm.
Example 2:
| Calculation | Instructions |
|---|---|
| Given: H = 5 cm, C = 12 cm | Start with the given height and chord length. |
| R = (5² + (12² ÷ 8 × 5)) | Square the height and chord, then divide the chord squared by 8 times the height. |
| R = (25 + (144 ÷ 40)) | Perform the division and addition. |
| R = (25 + 3.6) | Add the results together. |
| R = 28.6 cm | The radius of the circle is 28.6 cm. |
Answer: The calculated radius is 28.6 cm.
What is Chord to Radius Calculator ?
A Chord to Radius Calculator helps you find the radius of a circle when you know the length of the chord. A chord is a straight line that connects two points on a circle. To calculate the radius, you can use a specific formula that takes into account the chord’s length and how far it is from the center of the circle.
If you’re not sure how to find the radius from a chord, you can use tools like a chord length calculator app. These apps make it easy to input the chord length and get the radius quickly.
Some calculators even show you the steps, making the math simpler. Understanding how a chord and radius relate helps in many areas, like geometry and design. Whether you are studying or working on a project, knowing how to find the radius can be very useful.
Final Words:
The Chord to Radius Calculator simplifies the process of determining the radius of a circle when given the chord length and arc height. Its versatility and accuracy make it a valuable tool in engineering, mathematics, design, and other fields where precise circular calculations are required.
