How this instrument works
A pie chart divides a full circle — 360 degrees — proportionally among categories, so each slice's share of the circle matches its share of the total. Converting a raw value into a slice means answering two closely related questions: what percentage of the whole does this value represent, and how many of the circle's 360 degrees should the slice span? Both answers come from the exact same ratio, value divided by total, just scaled differently — by 100 for a percentage, by 360 for an angle.
Percentage and angle serve different purposes: percentage is what you'd put in a data table or a legend label, while angle in degrees is what you'd actually need if drawing the slice by hand with a protractor, or programmatically setting the start and sweep angle for a chart library. Because they come from the same underlying fraction, a slice that's 25% of the total is always exactly 90 degrees — a quarter of the circle — no matter what the raw numbers happen to be.
This calculator reports both figures from a single value-and-total input, so you don't have to run the ratio twice. If you only ever need one of the two — just the percentage for a table, or just the angle for drawing — this site also has dedicated single-output versions of this same calculation.
- Enter the slice's value into Slice value — the raw count or amount this category represents.
- Enter the sum of every slice into Total — all categories combined, including this one.
- Read Slice percentage — this slice's share of the whole, as a percent.
- Read Slice angle — the same share expressed in degrees out of the circle's 360.
Worked example — a quarter-circle slice
A survey category received 90 responses out of 360 total responses. Enter 90 into Slice value and 360 into Total.
Percentage = (90/360) × 100 = 25% exactly. Angle = (90/360) × 360 = 90 degrees exactly — a clean quarter of the circle, which makes sense: 25% of anything is one quarter, and one quarter of a 360-degree circle is 90 degrees.
Questions
Why do percentage and angle always match up?
Because both are the exact same fraction — value divided by total — just expressed on two different scales. Percentage scales that fraction to a total of 100, while angle scales it to a total of 360, the number of degrees in a full circle. A slice that's 10% of the total is always exactly 36 degrees (10% of 360), no matter what the underlying value and total actually are.
Do all the slice angles in a pie chart have to add up to 360?
Yes, always — if you compute every category's angle using its own value divided by the same grand total, the angles are guaranteed to sum to exactly 360 degrees, because the percentages they're based on are guaranteed to sum to 100%. If your angles don't add up to 360, the most common cause is that the total used for one or more slices didn't actually match the sum of all the category values.
Can the slice value be larger than the total?
No — a single slice can't logically be bigger than the whole pie it's part of, so this calculator flags it as invalid input if the value you enter for a slice exceeds the total. If you're getting this error, double check that total really is the sum of every category, including the one you're currently calculating.
Is there a single-purpose version if I only need the angle or the percentage?
Yes — this calculator returns both figures at once from the same value-and-total input, since they're derived from an identical ratio either way. If you only ever need one of them, this site also has a dedicated pie-chart-angle calculator (angle only) and a dedicated pie-chart-percentage calculator (percentage only), each stripped down to a single output for that specific use case.