Circular Sector Calculator

Calculate sectors from multiple known values accurately. Switch units, review formulas, and inspect geometric relationships. Visualize results, compare values, and export polished reports instantly.

Calculator Form

Choose the input pair you already know.
All formulas are converted internally to radians.
Choose how many decimal places to show.
Used in displayed results and exports.
Use a value greater than 0 and less than 360°.
Known distance from center to arc.
Full width across the circle.
Measured along the curved boundary.
Area enclosed by two radii and the arc.
Straight line joining the arc endpoints.

Example Data Table

Mode Known Values Radius Arc Length Sector Area Chord Perimeter
Radius + Angle r = 8, θ = 60° 8 8.3776 33.5103 8 24.3776
Diameter + Angle d = 20, θ = 90° 10 15.7080 78.5398 14.1421 35.7080
Arc Length + Angle L = 15, θ = 120° 7.1620 15 53.7148 12.4049 29.3239

Formula Used

Use θ in radians for the formulas below.

Arc length: L = rθ
Sector area: A = ½r²θ
Chord length: c = 2r sin(θ/2)
Perimeter: P = 2r + L
Triangle area: T = ½r² sin(θ)
Minor segment area: Aseg = ½r²(θm - sin θm)
Center to chord distance: d = r cos(θm/2)
Sagitta: s = r(1 - cos(θm/2))
Sector centroid distance: rc = 4r sin(θ/2) / 3θ
Circle fraction: f = θ / 2π

Here, θm is the smaller enclosed angle used for minor segment geometry.

How to Use This Calculator

  1. Select the solve mode that matches the measurements you already know.
  2. Choose whether your angle is in degrees or radians.
  3. Enter a unit label such as cm, m, ft, or in.
  4. Type the central angle and the required matching input for that mode.
  5. Set your preferred decimal precision for cleaner output.
  6. Press Calculate Sector to show the results above the form.
  7. Review the Plotly graph to understand the sector geometry visually.
  8. Use the CSV or PDF export buttons to save the result set.

FAQs

1. What measurements can this calculator solve from?

It solves from five input pairs: radius and angle, diameter and angle, arc length and angle, sector area and angle, or chord length and angle.

2. Why does the tool ask for the angle every time?

A sector is defined by both radius-related size and central angle. Without the angle, the curved span and enclosed portion of the circle remain unknown.

3. Does the calculator accept radians?

Yes. Choose radians from the angle unit menu. The calculator also displays the converted value in degrees and radians in the results.

4. What is the difference between arc length and chord length?

Arc length follows the curved boundary of the sector. Chord length is the straight line joining the arc endpoints. They are equal only in special limiting cases.

5. What happens when the sector angle is greater than 180°?

Sector area and perimeter still use the entered angle. Minor segment outputs use the smaller complementary angle, which matches standard minor segment geometry.

6. What is sagitta in this context?

Sagitta is the maximum height of the arc above its chord. It is useful in construction, machining, drafting, and geometric layout problems.

7. Why export the result to CSV or PDF?

CSV is convenient for spreadsheets, audits, and batch records. PDF is better for reports, client sharing, printed calculations, and documentation archives.

8. Can I use any unit system?

Yes. Enter a simple unit label such as mm, cm, m, in, or ft. The formulas remain valid as long as all length inputs use the same base unit.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.