Example Data Table
| Known input | Example value | Computed angle (deg) | Notes |
|---|---|---|---|
| Percent of whole | 25% | 90 | Quarter slice of a full circle. |
| Slice value / Total value | 30 / 120 | 90 | Same fraction as 25%. |
| Sector area and radius | 18.85 cm², radius 5 cm | 43.2 | Uses A = ½ r²θ. |
| Arc length and radius | 7.85 cm, radius 5 cm | 90 | Uses s = rθ. |
| Chord length and radius | 7.07 cm, radius 5 cm | 90 | Uses c = 2r·sin(θ/2). |
| Multiple slices list | Rent 800, Food 350, Transport 150 | See breakdown table | Auto-generated |
Numbers are rounded for readability.
Formula Used
- Fraction of circle: f = value / total and θ = 360° × f
- Percent method: f = percent / 100 and θ = 360° × f
- Sector area: A = ½ r² θ (θ in radians), so θ = 2A / r²
- Arc length: s = r θ (θ in radians), so θ = s / r
- Chord length: c = 2r·sin(θ/2), so θ = 2·asin(c/(2r))
- Derived values: arc = rθ, sector area = ½r²θ, segment area = ½r²(θ − sinθ)
How to Use This Calculator
- Select a method that matches the data you have.
- Enter your values. Use consistent units for lengths.
- Optionally enter radius or diameter to unlock geometry outputs.
- Pick the length unit and decimal precision you prefer.
- Click Calculate to see the central angle and related results.
- Use the export buttons to save CSV or PDF.
Pie Angle Article
Why every chart totals 360 degrees
A full circle equals 360°, so every pie chart slice must share that total. If your slices are complete, all angles add to 360° and all percents add to 100%. When totals miss, rounding or missing categories are usually the reason.
Convert percent to central angle
Percent is the fastest input. Multiply percent by 3.6 to get degrees, then divide degrees by 57.2958 to get radians. For example, 12.5% becomes 45° (0.785 rad) and 25% becomes 90° (1.571 rad). This is ideal for reports and classroom demonstrations too.
Use values and a total
When you have raw counts, compute the fraction f = value/total. A slice of 30 out of 120 gives f = 0.25, so θ = 360×0.25 = 90°. If totals are large, keep at least 2–4 decimals to avoid drift across many slices.
Arc length with a radius
If you know radius r and arc length s, use θ = s/r in radians. With r = 5 cm and s = 7.85 cm, θ = 1.57 rad, which is about 90°. Doubling the radius halves the angle for the same arc, so units matter.
Sector area method
For a sector area A, use θ = 2A/r² (radians). With r = 5 cm and A = 18.85 cm², θ = 1.508 rad, or about 86.43°. This method is common in machining, land plots, and circular logos.
Chord length method checks
Chord length c must be between 0 and 2r. The formula θ = 2·asin(c/(2r)) returns a valid central angle. With r = 5 cm and c = 7.07 cm, the angle is near 90°. If c is close to 2r, the slice approaches 180°.
Build a full pie from a slice list
Paste multiple lines like “Rent, 800”, “Food, 350”, and “Transport, 150”. The calculator totals values, converts each to percent, then outputs degrees and radians. The footer confirms 100% and 360°.
FAQs
1) What is a pie angle?
A pie angle is the central angle of a slice, measured at the circle’s center. It represents the slice’s share of the whole: 360° for the full circle, or 2π radians.
2) Do angles always add to 360°?
Yes, for a complete chart. Small differences can happen due to rounding, especially when many slices are shown with limited decimals. Increase precision or normalize your inputs to reduce drift.
3) Which input method should I use?
Use percent when you already have percentages. Use value/total for counts or money. Use arc, chord, or sector area when you measured a physical circle. Use “central angle given” when the angle is known.
4) Why do I see dashes in arc, chord, or area?
Those geometry values require a radius (or diameter). Enter one in the optional settings, choose the correct length unit, and recalculate to get arc length, chord length, sector area, and segment area.
5) How does normalization work for percent lists?
In percent-list mode, entries are scaled so their sum becomes 100%. For example, if your lines total 102%, each value is multiplied by 100/102. The output angles will then sum to 360°.
6) Can I download results for documentation?
After calculating, use the Download CSV button for spreadsheets and the Download PDF button for a printable report. CSV includes inputs and computed angles, and PDF includes a readable summary of the results.