Enter the total number of pie slices into the Pie Cut Angle Calculator. The calculator will evaluate the Pie Cut Angle.
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Pie Cut Formula
The calculator uses three core formulas depending on the mode you select.
Angle per slice = 360° / N
Arc length (rim spacing) = pi * D * (angle / 360)
Slice area = pi * (D/2)^2 * (angle / 360)
Chord = 2 * (D/2) * sin(angle / 2)
- N = number of equal slices
- angle = central angle of one slice, in degrees
- D = pie diameter (any length unit; output matches input)
- Arc length = distance along the rim between two cuts
- Chord = straight-line distance between two rim marks
The pie is treated as a perfect circle. For an even slice count, each straight cut crosses the center and produces two slices, so the number of cuts equals N/2. For an odd count, every cut runs from the center to the rim, so the number of cuts equals N.
Reference Tables
Common slice counts and the angle each slice covers:
| Slices | Angle | Share of pie | Cuts needed |
|---|---|---|---|
| 4 | 90° | 25% | 2 |
| 5 | 72° | 20% | 5 |
| 6 | 60° | 16.67% | 3 |
| 7 | ≈51.43° | 14.29% | 7 |
| 8 | 45° | 12.5% | 4 |
| 10 | 36° | 10% | 5 |
| 12 | 30° | 8.33% | 6 |
| 16 | 22.5° | 6.25% | 8 |
Rim spacing (arc length per slice) for common pie diameters:
| Diameter | 6 slices | 8 slices | 10 slices | 12 slices |
|---|---|---|---|---|
| 8 in | 4.19 in | 3.14 in | 2.51 in | 2.09 in |
| 9 in | 4.71 in | 3.53 in | 2.83 in | 2.36 in |
| 10 in | 5.24 in | 3.93 in | 3.14 in | 2.62 in |
| 11 in | 5.76 in | 4.32 in | 3.46 in | 2.88 in |
| 12 in | 6.28 in | 4.71 in | 3.77 in | 3.14 in |
Worked Example
A 9-inch pie cut into 8 equal slices:
- Angle per slice: 360 / 8 = 45°
- Rim spacing: π × 9 × (45 / 360) ≈ 3.53 in
- Slice area: π × 4.5² × (45 / 360) ≈ 7.95 sq in
- Cuts needed: 8 / 2 = 4 straight cuts through the center, rotating 45° each time
To mark the rim before cutting, place ticks every 3.53 in around the edge, then draw each cut from one tick straight across through the center to the opposite tick.
FAQ
Why does an odd slice count need more cuts? A single straight cut across the pie always produces two equal pieces. You can only get an odd number of equal slices by cutting from the center outward, one slice boundary at a time.
What if my angle does not divide 360 evenly? The Angle to Slices mode flags this and shows the nearest whole slice count along with the exact angle that count would require.
Does this work for round cakes or pizzas? Yes. The math applies to any flat circular shape. Use the diameter of the cake or pizza in place of the pie diameter.
