Arc Length Calculator

Calculate arc length based on radius, central angle, chord length, or sector area. Supports Huygens' formula and provides single and batch calculations.

Bug report

Browser execution mode: Your data is processed in your browser and is not uploaded to the server.

Speed and Stability: Processing speed depends on your device and browser. For large batch work, the desktop version may be more stable.

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If the online tool fails to load or run, try the desktop tool.https://tools.yikeaigc.com/

Tool Usage

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Set known values Calculate by radius & angle, chord & sagitta, or sector area

Radius + central angle L = r × θ Chord + sagitta Find arc length after radius Sector area + radius L = 2A / r

Radius r

Central angle θ

Decimal places Live calculation

Derive parameters from arc length Calculate radius, central angle, or sector area from a known arc length

Find radiusKnown arc length and angle Find angleKnown arc length and radius Find areaKnown arc length and radius

Arc length L

Central angle θ

Batch import data One data set per line, or import CSV, TXT, XLSX files

Calculation Method Angle unit Length unit Decimal places

Bulk data

No files selected

Local history Save up to 30 results for comparison and reuse

Arc length L

Waiting for input Set parameters first, then click Calculate

Radius-

Central angle-

Chord length-

Sagitta-

Sector Area-

Circle Share-

Formula Tip Select a method and enter values to show the formula here.

Instructions

Software Usage Instructions

Select a calculation mode: The tool provides four modes: “Single Calculation,” “Reverse Calculation,” “Batch Calculation,” and “History.” You can switch between them step by step according to the page guidance.
Set known conditions:
- Radius + Central Angle: Suitable for calculating arc length when the circle radius and central angle are known.
- Chord Length + Arc Height: Suitable for reverse-calculating the radius, central angle, and arc length after measuring the chord length and sagitta.
- Sector Area + Radius: Suitable for deriving the arc length when the sector area and radius are known.
Select units and precision: Length supports mm, cm, m, km, inch, and ft; angles support degrees, radians, and gradians. Decimal places can be set as needed.
Enter data or use examples: You can manually enter parameters, or click “Sample Data” or scenario presets to quickly fill in data for pipe elbows, road curves, arch structures, and more.
Run the calculation: When real-time calculation is enabled, changing parameters will automatically update the result; you can also disable real-time calculation and click “Calculate Arc Length.”
View results: The results area displays arc length, radius, central angle, chord length, arc height, sector area, circumference percentage, formula explanation, and a graphical illustration.
Reverse calculation: You can calculate the radius from a known arc length and central angle, or calculate the central angle or sector area from a known arc length and radius.
Batch calculation: Enter two values per line, paste table data directly, or import CSV, TXT, or XLSX files. Multi-file import will process all files, and results can be downloaded as CSV or ZIP.
Save and reuse: You can save settings, copy results, download result files, and save frequently used calculation results to history.

FAQ

A: It uses L = r × θ, where θ must be converted to radians. If the input angle is in degrees, the tool automatically converts it using θ × π / 180 before calculating.

A: It is suitable for scenarios where only the chord length and sagitta can be measured on site, such as arch structures, circular arc edges, bent pipe sections, and template layout. The tool first reverse-calculates the radius, then calculates the central angle and arc length.

A: Yes. Arc height is also called sagitta, referring to the perpendicular distance from the midpoint of the chord to the corresponding point on the arc. When measuring, make sure the direction is perpendicular to the chord.

A: Yes. When the sector area A and radius r are known, the arc length can be calculated using L = 2A / r. If the derived central angle exceeds one full circle, the tool will prompt you to check the values or units.

A: Different drawings and engineering documents may use different angle units. Degrees use 360 for a full circle, radians use 2π for a full circle, and gradians use 400 for a full circle. The tool will automatically convert according to the selected unit.

A: Enter one set of data per line, separated by commas, spaces, or tabs. For example, in radius plus central angle mode, you can enter “10, 90”. When importing a spreadsheet file, it is recommended to keep two columns of pure numeric data.

A: The tool calculates using standard circular arc formulas and can be used for engineering measurement, layout, teaching, and parameter verification. For important projects, it is recommended to review the results together with measurement errors, material deformation, and site conditions.