# Pie Chart Angle Calculator

URL: https://speedycalculator.com/calculators/statistics/pie-chart-angle/
Last updated: 2026-10-30

> The pie chart angle calculator gives the central angle of every slice from raw counts or from percentages, rounded so the angles add up to exactly 360°, plus the start and end angle of each slice so you can draw the chart by hand with a protractor.

## Inputs

- 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

## Results

- Slice angles
- Note
- Angles for drawing (clockwise from 12 o'clock)
- Pie chart
- Total of the values
- Number of slices
- Largest slice
- Smallest slice

## Formula

```
Angle = (value ÷ total) × 360° · Angle from a percentage = p × 3.6° · Start angle of slice i = sum of the angles before it
```

## Explanation

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.

## 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.

## FAQ

**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°.


## Sources

- [Khan Academy – Statistics and probability](https://www.khanacademy.org/math/statistics-probability)
- [OpenStax – Introductory Statistics 2e](https://openstax.org/details/books/introductory-statistics-2e)