How this instrument works
A pie chart is a full circle — 360 degrees — split among categories in proportion to their share of the total. The angle for any one slice is that slice's fraction of the whole (value divided by total) multiplied by 360. A slice worth half the total gets 180 degrees, exactly half the circle; a slice worth a tenth of the total gets 36 degrees, exactly a tenth of the circle.
This is the number needed for physically constructing a pie chart — placing a protractor at the circle's center and marking off the slice's degree span, or passing a start-angle and sweep-angle into a charting library that draws in degrees or radians rather than raw percentages. It's a different unit from the percentage figure you'd put in a data table, even though both describe the same underlying share of the total.
Because every slice's angle is computed against the same 360-degree total, the full set of angles for every category in a pie chart always sums to exactly 360 — a useful check if you're computing several slices by hand and want to confirm nothing was double-counted or left out.
- Enter the slice's value into Slice value — the raw amount this one category represents.
- Enter the sum of every slice into Total — all categories combined, including this one.
- Read Slice angle — the number of degrees, out of 360, this slice should span.
- Repeat for each category; the angles across all categories should sum to 360 degrees.
Worked example — one quarter of a pie chart
A budget category accounts for 1 dollar out of every 4 dollars spent (value = 1, total = 4). Enter those two numbers into the calculator.
Angle = (1/4) × 360 = 90 degrees exactly. If drawing this slice by hand, you'd place a protractor at the circle's center and mark off a 90-degree wedge — exactly a quarter turn of the full circle, matching the fact that this category is exactly a quarter of the total.
Questions
Why 360 and not some other number?
360 is simply the number of degrees in a full circle, by definition — a pie chart is a circle divided proportionally, so scaling each slice's fraction of the total by 360 converts that fraction into the actual angle you'd mark off with a protractor or set in drawing code. There's nothing special about the value 360 mathematically; it's just the standard unit for measuring a full rotation.
How is this different from the pie-chart-percentage calculator?
Both start from the same value-and-total input and compute the same underlying fraction — this calculator scales that fraction to degrees, out of 360, for drawing or plotting a slice, while pie-chart-percentage scales it to a percent, out of 100, for a data table or label. If you need both numbers at once, this site's combined pie-chart calculator returns percentage and angle together from a single input.
What if my slice angles don't add up to 360?
That means the total used for one or more slices doesn't actually match the sum of every category's value. Recheck that the total entered for each slice calculation is the true grand total across all categories — if even one category's value was left out of that sum, every angle computed against it will be slightly off, and the full set won't close back to exactly 360 degrees.
Can I convert the angle to radians instead?
Yes — multiply the degree figure by pi/180 to convert to radians, since 360 degrees equals 2×pi radians. Some charting libraries, particularly lower-level graphics APIs, expect angles in radians rather than degrees, so this conversion is common when taking this calculator's output and feeding it into code.