Calculator
Choose one method. Only fields needed for that method are required.
Formula Used
Chord length = 2r × sin(θ ÷ 2)
Chord length = 2 × √(r² − d²)
Chord length = 2 × √(2rs − s²)
θ = arc length ÷ radius, then chord length = 2r × sin(θ ÷ 2)
Radius = circumference ÷ (2π), then chord length = 2r × sin(θ ÷ 2)
How to Use This Calculator
- Select the solving method that matches your known circle values.
- Enter the required inputs for that method.
- Choose degrees or radians when angle input is used.
- Set the unit label and decimal precision you want.
- Press Calculate Chord Length to show the results above the form.
- Review the table, graph, and derived measurements.
- Use the export buttons to save a CSV or PDF summary.
Example Data Table
| Method | Radius | Angle / Other Input | Chord Length |
|---|---|---|---|
| Radius + Angle | 10 | 60° | 10.0000 |
| Radius + Distance | 12 | 5 | 21.8174 |
| Radius + Sagitta | 15 | 3 | 18.0000 |
| Radius + Arc | 8 | 6 | 5.8603 |
| Circumference + Angle | 10 | 90° | 14.1421 |
FAQs
1. What is a chord in a circle?
A chord is a straight line segment connecting two points on a circle. Its length depends on the circle’s radius and the chord’s position.
2. Which method should I choose?
Choose the method that matches the values you already know. Radius and angle is common, while sagitta or center distance is useful in geometry and engineering layouts.
3. What is sagitta?
Sagitta is the height from the midpoint of a chord to the arc above it. It is often used in segment calculations and curved surface work.
4. Can I use radians instead of degrees?
Yes. The calculator supports both. Select radians when your angle is already in radian measure.
5. Why does the calculator use a minor angle?
Minor angles keep the geometry clear and return the standard chord configuration. Angles less than 180 degrees also keep the center-to-chord distance positive.
6. Do units matter?
Yes, but only for consistency. Enter all length values in the same unit, then the chord and related outputs will use that unit.
7. What does the graph show?
The graph plots the circle and the computed chord. It helps you verify the geometry visually and understand where the chord sits inside the circle.
8. What can I export?
You can export the result summary as a CSV file or a PDF report. This is useful for documentation, study notes, or sharing.