How it works
Use the central angle subtending the chord. The minor arc of at most 180° is selected; sagitta is the perpendicular distance from chord midpoint to that arc. This form solves for angle; enter the known quantities in Chord length, Radius.
Inputs and units
| Input | Example value | What to enter |
|---|---|---|
| Chord length | 5 cm | Formula symbol: c. Required unit: cm. Must be greater than zero. |
| Radius | 5 cm | Formula symbol: r. Required unit: cm. Distance from the centre to the edge; half the diameter. Must be greater than zero. |
Worked example
Show example inputs and results
This example is generated by the same calculation engine using the starting values in the form. Your own inputs produce your own result.
- Chord length
- 5 cm
- Radius
- 5 cm
Complete example results
- Angle
- 60 °
Reading the result
The result solves for angle from the entered quantities. Check the result unit and the formula conditions before using it.
Questions and answers
Can I use the example values for my own calculation?
The example values illustrate the calculation. Replace every input with your own information, especially dates, rates and the selected operation.
When can I use the angle result?
Lengths use cm, areas cm² and volumes cm³ on one consistent scale. The positive real branch is selected; the supplied quantities must describe the stated shape.
Why are some results rounded?
Results display up to 8 decimal places. Calculations use the unrounded values; very small values use scientific notation. JavaScript floating-point arithmetic can introduce tiny rounding differences.
Are my inputs sent to a server?
The calculator processes inputs in your browser. Its code does not send your values to a server.
Method sources: openstax.org