Drawing a pie chart by hand comes down to one number per category: the angle at the centre of the circle. Divide a category’s count by the total and multiply by 360°. In a survey of 30 students where 12 walk to school, the “walk” slice is 12 ÷ 30 × 360° = 144°. If you already have percentages, the shortcut is to multiply by 3.6, because 1% of a full turn is 3.6°.
Rounding can leave the angles summing to 359° or 361°, which makes the last slice in a hand-drawn chart too big or too small. This calculator rounds with the largest-remainder method, so the rounded angles always add up to exactly 360°. It also lists where each slice starts and ends, measured clockwise from the 12 o’clock line, which is exactly what you mark off with a protractor.
Use whole degrees for drawing on paper and one or two decimals when you need precision for software or for checking homework answers.
How to use the Pie Chart Angle Calculator
- Categories – one “label, value” per line — For example “Walk, 12” or “Walk, 40%”.
- The values are
- Round to — Rounded values are adjusted (largest-remainder method) so they still add up exactly.
- Order of slices
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
Enter counts or percentages, one category per line. The tool converts each to a share of the whole, multiplies by 360°, rounds while keeping the total at 360°, and accumulates the angles to give the start and end positions of every slice.
Worked example
A class of 30 students travels to school by walking (12), bus (8), car (6) and bike (4). Each student is worth 360° ÷ 30 = 12°, so the angles are walk 12 × 12° = 144°, bus 96°, car 72° and bike 48° – a total of 360°. Measured clockwise from 12 o’clock, the walk slice runs from 0° to 144°, bus from 144° to 240°, car from 240° to 312° and bike from 312° to 360°.
Starting from percentages instead – 40%, 26.7%, 20% and 13.3% – multiply each by 3.6: 144°, 96.1°, 72° and 47.9° (to one decimal, adjusted so the sum stays 360°).
Drawing a pie chart by hand
- Work out every angle and check they add up to 360°.
- Draw a circle and a vertical radius from the centre to 12 o’clock.
- Measure the first angle clockwise from that radius and draw the second radius.
- Measure each next angle from the last line you drew.
- Label every slice with its category and percentage.
Formula
Angle = (value ÷ total) × 360° · Angle from a percentage = p × 3.6° · Start angle of slice i = sum of the angles before it
Worked example
Inputs — Categories – one "label, value" per line: Walk, 12
Bus, 8
Car, 6
Bike, 4; The values are: Counts or amounts; Round to: Whole numbers; Order of slices: As entered.
Results — Slice angles = Walk 144° · Bus 96° · Car 72° · Bike 48°; Angles for drawing (clockwise from 12 o'clock) = Category Value Angle Starts at Ends at
──────────────────────────────────────────────
Walk 12 144° 0° 144°
Bus 8 96° 144° 240°
Car 6 72° 240° 312°
Bike 4 48° 312° 360°
Total 30 360° ; Total of the values = 30; Number of slices = 4; Largest slice = Walk (40%); Smallest slice = Bike (13.33%).
Key terms
- Central angle
- The angle a slice makes at the centre of the circle.
- Protractor
- A tool for measuring and drawing angles in degrees.
- Largest-remainder rounding
- Rounding down every value and handing the leftover units to the values with the largest remainders, so totals are preserved.
Frequently asked questions
How do I find the angle of a pie chart slice?
Divide the category's value by the total and multiply by 360°: 8 of 30 → 8 ÷ 30 × 360° = 96°.
How do I convert a percentage to an angle?
Multiply by 3.6. 15% → 54°, 40% → 144°, 62.5% → 225°.
How do I convert an angle back to a percentage?
Divide by 3.6 (or by 360 and multiply by 100). 54° → 15%.
Why don't my rounded angles add up to 360°?
Rounding each angle on its own can lose or gain a degree. This calculator uses the largest-remainder method so the rounded angles always total exactly 360°.
Where should the first slice start?
Conventionally at 12 o'clock (0°), going clockwise. The table gives each slice's start and end angle from that line.
How do I draw a pie chart with a protractor?
Draw a circle and a radius to 12 o'clock, place the protractor's centre on the circle's centre, mark the first angle, draw the next radius, and repeat from each new line.
What is the angle for one item out of n?
360° ÷ n. In a class of 30, each student is worth 12°.