Pie Chart Angle Calculator
TOOLConvert values or percentages into pie-slice angles in degrees — and convert degrees back to percentages.
A pie chart angle (sector angle) is a slice's share of the full 360° circle. To convert a percentage to degrees, multiply it by 3.6, because 100% equals 360°. So 25% = 90°, 30% = 108° and 50% = 180°. For raw values, use (value ÷ total) × 360.
Each value becomes a slice. Angle = (value ÷ total) × 360°. Separate with commas, spaces or new lines.
How pie chart angles work
A pie chart is a full circle, and a full circle is 360 degrees. That circle represents the whole — 100% of your data. Every slice's angle is just its share of that whole scaled onto the 360°.
From a percentage to degrees
Because 100% maps to 360°, one percent maps to 3.6°. So the rule is simply angle = percentage × 3.6. A quarter of the pie, 25%, is 25 × 3.6 = 90°. A 30% slice is 30 × 3.6 = 108°. The full pie, 100%, is 100 × 3.6 = 360°, as it must be.
From raw values to degrees
If you have counts rather than percentages, first add them to get the total. Each slice's angle is then (value ÷ total) × 360. You do not need to convert to percentages first — though the calculator shows the percentage too, for reference.
From degrees back to a percentage
Reverse the rule by dividing: percentage = angle ÷ 3.6. A 90° slice is 90 ÷ 3.6 = 25%, and a semicircle of 180° is exactly 50% of the pie.
Suppose four slices hold the values 40, 30, 20, 10, summing to a total of 100. The first slice is (40 ÷ 100) × 360 = 144°, the second is (30 ÷ 100) × 360 = 108°, the third is 72°, and the last is 36°. Those four angles add back to 360°, the complete circle.
Worked examples
These are the questions people most often need to answer about sector angles, worked step by step. You can check any of them with the calculator above.
Is 30% a sector angle of 100° or 102°? (True or false)
False. 30 × 3.6 = 108°. Working backwards, 100° is 100 ÷ 3.6 ≈ 27.8% and 102° is 102 ÷ 3.6 ≈ 28.3%, so neither matches 30%.
If 30% = 108°, what is the total angle?
Divide the angle by the fraction it represents: 108° ÷ 0.30 = 360°. The total angle of any pie chart is always 360°, which is why 100% corresponds to a full circle.
What is 91 percent of 360 degrees?
0.91 × 360 = 327.6° (the same as 91 × 3.6). The remaining 9% of the pie is 360 − 327.6 = 32.4°.
What is the angle for 26% of a circle?
26 × 3.6 = 93.6° — just over a right angle, because 25% is exactly 90°.
The angles for 25%, 40% and 33%
25% = 90°, 40% = 144°, 33% = 118.8°. They add up to 352.8°, which is 98% of the circle; the missing 2% is a 7.2° sliver. If your percentages do not sum to 100%, the angles will not sum to 360°, so look for a missing category or rounding.
Pie chart angles of 45°, 90° and 135°
Going from degrees to percentages, divide by 3.6: 45° = 12.5%, 90° = 25%, 135° = 37.5%. Together they cover 270°, or 75% of the pie, leaving a 90° (25%) slice.
245 items out of 460
Angle = 245 ÷ 460 × 360 ≈ 191.7°. As a percentage that is 245 ÷ 460 × 100 ≈ 53.3%, a little more than half the pie.
If 2,800 is 50° on a pie chart, what is 360°?
First find the value of one degree: 2,800 ÷ 50 = 56. The whole circle is then 56 × 360 = 20,160. This is the total of all the data in the chart.
12 out of 40 compared with 12 percent
These are easy to mix up. 12 out of 40 is 12 ÷ 40 = 30%, so its slice is 30 × 3.6 = 108°. A slice of 12 percent is 12 × 3.6 = 43.2°, whatever the total.
Turning a table of amounts into angles
Suppose a monthly budget of £1,000 is split as below. Add the amounts, divide each by the total, then multiply by 360. A £250 item in a £1,000 total is a quarter of the pie, 90°.
| Category | Amount | Share | Angle |
|---|---|---|---|
| Rent | £500 | 500 ÷ 1,000 = 50% | 180° |
| Food | £250 | 250 ÷ 1,000 = 25% | 90° |
| Transport | £150 | 150 ÷ 1,000 = 15% | 54° |
| Savings | £100 | 100 ÷ 1,000 = 10% | 36° |
| Total | £1,000 | 100% | 360° |
Percent to degrees table (1% to 100%)
Every row below uses the same rule, percentage × 3.6. Read across the columns to find any whole-number percentage from 1% to 100% and its pie chart sector angle.
| % | Angle | % | Angle | % | Angle | % | Angle | % | Angle |
|---|---|---|---|---|---|---|---|---|---|
| 1% | 3.6° | 21% | 75.6° | 41% | 147.6° | 61% | 219.6° | 81% | 291.6° |
| 2% | 7.2° | 22% | 79.2° | 42% | 151.2° | 62% | 223.2° | 82% | 295.2° |
| 3% | 10.8° | 23% | 82.8° | 43% | 154.8° | 63% | 226.8° | 83% | 298.8° |
| 4% | 14.4° | 24% | 86.4° | 44% | 158.4° | 64% | 230.4° | 84% | 302.4° |
| 5% | 18° | 25% | 90° | 45% | 162° | 65% | 234° | 85% | 306° |
| 6% | 21.6° | 26% | 93.6° | 46% | 165.6° | 66% | 237.6° | 86% | 309.6° |
| 7% | 25.2° | 27% | 97.2° | 47% | 169.2° | 67% | 241.2° | 87% | 313.2° |
| 8% | 28.8° | 28% | 100.8° | 48% | 172.8° | 68% | 244.8° | 88% | 316.8° |
| 9% | 32.4° | 29% | 104.4° | 49% | 176.4° | 69% | 248.4° | 89% | 320.4° |
| 10% | 36° | 30% | 108° | 50% | 180° | 70% | 252° | 90% | 324° |
| 11% | 39.6° | 31% | 111.6° | 51% | 183.6° | 71% | 255.6° | 91% | 327.6° |
| 12% | 43.2° | 32% | 115.2° | 52% | 187.2° | 72% | 259.2° | 92% | 331.2° |
| 13% | 46.8° | 33% | 118.8° | 53% | 190.8° | 73% | 262.8° | 93% | 334.8° |
| 14% | 50.4° | 34% | 122.4° | 54% | 194.4° | 74% | 266.4° | 94% | 338.4° |
| 15% | 54° | 35% | 126° | 55% | 198° | 75% | 270° | 95% | 342° |
| 16% | 57.6° | 36% | 129.6° | 56% | 201.6° | 76% | 273.6° | 96% | 345.6° |
| 17% | 61.2° | 37% | 133.2° | 57% | 205.2° | 77% | 277.2° | 97% | 349.2° |
| 18% | 64.8° | 38% | 136.8° | 58% | 208.8° | 78% | 280.8° | 98% | 352.8° |
| 19% | 68.4° | 39% | 140.4° | 59% | 212.4° | 79% | 284.4° | 99% | 356.4° |
| 20% | 72° | 40% | 144° | 60% | 216° | 80% | 288° | 100% | 360° |
Out of 360 or out of 100? Converting between the two
A pie chart can be described on two scales: degrees, where the whole is 360, and percentages, where the whole is 100. Converting between them is a single multiplication or division because 360 ÷ 100 = 3.6.
- Percent to degrees: multiply by 3.6 (e.g. 15% × 3.6 = 54°).
- Degrees to percent: divide by 3.6 (e.g. 54° ÷ 3.6 = 15%).
- Value to degrees: value ÷ total × 360 (no percentage step needed).
- Degrees to value: angle ÷ 360 × total.
To draw the chart by hand, start with a radius pointing straight up, measure the first angle clockwise with a protractor, then measure each next slice from the edge of the previous one. The last slice should close the circle exactly.
Common mistakes
- Multiplying raw counts by 3.6. That only works when the counts happen to total 100. Otherwise divide by the total first.
- Angles that add to 359° or 361°. This is rounding. Keep one decimal place, or adjust the largest slice so the total is exactly 360°.
- Percentages above 100% in total. Survey questions where people can pick several answers produce shares that overlap; they cannot be drawn as a pie. Use a bar chart instead.
- Too many thin slices. Slices under about 2% (7.2°) are hard to see. Group them into an "Other" slice. See pie chart vs bar chart for when a bar works better.
Turn the numbers into a chart
Once you know the angles, the easiest way to draw the slices accurately is to let a tool do it. The pie chart maker takes your labels and values, computes the angles for you, and exports a clean PNG or SVG. If you want to understand when a pie is the right choice in the first place, the pie chart guide walks through how to read one and the common mistakes to avoid.
Frequently asked questions
How do I convert a percentage to a pie chart angle?
Multiply the percentage by 3.6, because a full circle of 360 degrees represents 100%. So 25% becomes 90°, 30% becomes 108° and 91% becomes 327.6°. The whole pie, 100%, is 360°.
On a pie chart, is it true or false that 30% represents a sector angle of 100 or 102 degrees?
False. 30% × 3.6 = 108°, so a 30% slice has a sector angle of 108 degrees. An angle of 100° is only about 27.8% of the circle, and 102° is about 28.3%.
In a pie chart, if 30% = 108°, what is the total angle?
The total angle is 360°. Dividing 108° by 0.30 gives 360°, the full circle. Every pie chart's slices add up to 360°, whatever the data.
What angles do 25%, 40% and 33% make in a pie chart?
25% is 90°, 40% is 144° and 33% is 118.8°. Together they cover 98% of the pie (352.8°), so a 2% slice of 7.2° is needed to complete the circle.
How do I turn numbers in a table into angles in a pie chart?
Add all the numbers to get the total, divide each number by that total, then multiply by 360. For example, 245 items out of 460 is 245 ÷ 460 × 360 ≈ 191.7°. Check that the angles add up to 360°.
How do I convert a pie chart angle back to a percentage?
Divide the angle by 3.6, or divide by 360 and multiply by 100. For example, 90° ÷ 3.6 = 25%, 45° is 12.5% and 135° is 37.5%.