Math and Education
Arc Length Calculator
Arc Length Calculator calculate circular arc length, sector area, chord length, and sagitta from radius and central angle.
Math and Education
Arc Length Calculator
Calculate circular arc length, sector area, chord length, and sagitta from radius and central angle.
Formula
Arc length = radius x angle in radians; sector area = 1/2 x radius^2 x angle in radians.
About the Arc Length Calculator
Calculate circular arc length, sector area, chord length, and sagitta from radius and central angle.
How the Arc Length Calculator Works
The central angle is converted from degrees to radians and applied to exact circle relations for the arc, sector, chord, and segment rise.
Formula
Arc length = radius x angle in radians; sector area = 1/2 x radius^2 x angle in radians.
The calculation runs in your browser. Values are validated for required ranges, compatible units, and method-specific restrictions before results are displayed.
Required Inputs
- Circle radius (required).
- Central angle (required) - enter in degrees.
- Length unit label (optional).
Results Reported
The result panel reports the final answer and the intermediate quantities needed to check the calculation:
- Arc length
- Sector area
- Chord length
- Sagitta or segment rise
- Central angle (radians)
- Length unit used
Arc Length Calculator Example
Select Example Data in the calculator to load this reproducible input set:
| Input | Example value |
|---|---|
| Circle radius | 10 |
| Central angle | 60 degrees |
| Length unit label | cm |
How to Use the Calculator
- Confirm that the calculator title and formula match the quantity you need.
- Enter every required value using the unit shown with its field.
- Select Example Data to inspect a valid input set, or enter your own values and select Calculate.
- Review all reported values and the displayed formula before using the answer.
- Use Copy Result or Download CSV when you need a reusable record.
Accuracy and Limitations
This calculator is for circular arcs with a central angle from 0 through 360 degrees. Elliptical and arbitrary-curve arc length require different methods.
Keep units consistent, use measurements that represent the actual situation, retain full precision during the calculation, and round only the final answer. Professional decisions may require current official rules, field measurements, laboratory methods, or specialist review.
Frequently Asked Questions
What does the Arc Length Calculator calculate?
Calculate circular arc length, sector area, chord length, and sagitta from radius and central angle.
Which formula does the Arc Length Calculator use?
Arc length = radius x angle in radians; sector area = 1/2 x radius^2 x angle in radians. The central angle is converted from degrees to radians and applied to exact circle relations for the arc, sector, chord, and segment rise.
What should I check before using the Arc Length Calculator result?
This calculator is for circular arcs with a central angle from 0 through 360 degrees. Elliptical and arbitrary-curve arc length require different methods.