Calculator Inputs
Use any supported mode to solve the central angle of a pie slice. Radius is optional in percent and fraction modes, but needed for arc, area, and chord outputs.
Formula Used
θ(rad) = s / r, then θ(deg) = θ(rad) × 180 / π
θ(rad) = 2A / r², then θ(deg) = θ(rad) × 180 / π
θ(deg) = (p / 100) × 360, then θ(rad) = θ(deg) × π / 180
θ(deg) = (n / d) × 360, arc length = rθ, area = ½r²θ, chord = 2r sin(θ / 2)
How to Use This Calculator
- Choose the mode that matches the values you already know.
- Enter the radius when you want arc, area, and chord outputs.
- Type arc length, sector area, percent, or fraction values.
- Set the decimal precision and your preferred unit label.
- Press the calculate button to show the result above the form.
- Use the export buttons to download the summary as CSV or PDF.
Example Data Table
| Case | Input | Radius | Angle | Arc Length | Sector Area |
|---|---|---|---|---|---|
| Quarter Pie | 25% | 8 cm | 90° | 12.566 cm | 50.265 cm² |
| Sixth Slice | 1 / 6 | 9 cm | 60° | 9.425 cm | 42.412 cm² |
| Arc Method | Arc = 15.708 cm | 10 cm | 90° | 15.708 cm | 78.540 cm² |
| Area Method | Area = 31.416 cm² | 6 cm | 100° | 10.472 cm | 31.416 cm² |
Why This Matters in Physics
Pie angles model detector sectors, rotational sweeps, beam apertures, and circular motion partitions. By linking angle, arc length, and area, the calculator helps convert geometry into usable physics quantities quickly and consistently.
FAQs
1) What is a pie angle?
A pie angle is the central angle that defines a sector of a circle. It tells you how large the slice is relative to the whole pie.
2) Which mode should I choose?
Use arc plus radius when you know the curved edge. Use area plus radius for sector area data. Use percent or fraction for direct slice portions.
3) Why does the calculator show radians and degrees?
Physics formulas often use radians, while design and geometry problems often use degrees. Showing both avoids manual conversion and reduces mistakes in later calculations.
4) Can a pie angle exceed 360°?
Not for a single slice of one full circle. If your computed value is above 360°, the entered data does not represent one valid pie sector.
5) Do I need the radius in percent mode?
You only need radius if you also want arc length, sector area, and chord length. Without radius, the calculator still gives the central angle and percent.
6) What does chord length mean here?
Chord length is the straight-line distance between the two ends of the slice. It is useful when replacing a curved edge with a direct span.
7) What do the CSV and PDF downloads include?
They include the visible result summary from your latest calculation. This makes it easier to document pie angle work in reports, lab notes, or estimates.
8) Where is this useful in physics?
It is useful for circular motion, angular sweeps, sensor sectors, beam spread regions, and any situation where a partial circle must be measured precisely.