To draw a pie chart, find the total frequency, then calculate each sector angle using angle = (frequency ÷ total) × 360°. Draw a circle, use a protractor to mark each angle from the centre, label every sector, and give the chart a title. Always check your angles sum to 360°.
Why do we use pie charts?
A pie chart shows how a whole quantity is divided into categories — each slice (sector) represents a fraction of the total. Pie charts are most useful when you want to compare the proportions of each category, not their exact values. They work well for discrete data with a small number of categories (typically three to six).
What is the angle formula for each sector?
Every full circle spans 360°. Each sector angle must be proportional to its frequency:
$$\text{sector angle} = \frac{\text{frequency}}{\text{total frequency}} \times 360°$$
You can also find how many degrees one item represents:
$$\text{degrees per item} = \frac{360°}{\text{total frequency}}$$
Then multiply by each frequency to find each sector angle.
Step-by-step method for drawing a pie chart
- Find the total frequency by adding all the frequencies together.
- Calculate the sector angle for each category using the formula above.
- Check: all sector angles must sum to exactly 360° (allow for rounding).
- Draw a circle with a compass, or trace around a circular object.
- Draw a radius (a straight line from the centre to the edge — this is your starting line).
- Measure the first sector angle from the starting line using a protractor centred at the middle of the circle. Draw a new radius at this angle.
- Measure the second sector angle from the new radius. Continue until all sectors are drawn.
- Label each sector with the category name (and optionally its percentage or angle).
- Add a title describing what the chart shows.
Worked example: favourite school subjects
A class of 30 pupils was asked to choose their favourite subject. Here are the results:
| Subject | Frequency | Sector angle |
|---|---|---|
| Maths | 9 | (9 ÷ 30) × 360° = 108° |
| English | 6 | (6 ÷ 30) × 360° = 72° |
| Science | 8 | (8 ÷ 30) × 360° = 96° |
| History | 7 | (7 ÷ 30) × 360° = 84° |
| Total | 30 | 360° ✓ |
To draw this:
- Draw a circle and a starting radius pointing straight up (12 o'clock position).
- Measure 108° clockwise from the start line for Maths.
- From that new line, measure 72° for English.
- Then 96° for Science.
- The remaining sector (84°) is History — no need to measure it, but verify it fits.
How do you deal with rounding errors?
When frequencies do not divide 360° exactly, angles may come out to one decimal place. Round each to the nearest whole degree, then adjust the last sector to make the total exactly 360°. In the exam, a tolerance of ±2° is usually accepted when checking a drawn pie chart with a protractor.
Example of rounding: If one sector calculates as 72.3°, round to 72°. If the running total of rounded angles reaches 358° with one sector left, make the final sector 2° larger to compensate.
What are the most common mistakes?
- Not starting each sector from the end of the previous one. Each new sector begins at the boundary of the last — not always from the starting radius.
- Measuring from the wrong scale on the protractor. Protractors have two scales (0°–180° reading clockwise and anticlockwise). Choose the scale where you start at 0° and increase in the direction you are measuring.
- Forgetting to check the total. If your angles do not sum to 360°, you have made a calculation error — find it before drawing.
- Omitting labels or the title. An unlabelled pie chart cannot be interpreted and will lose marks.
Frequently asked questions
How do I convert a pie chart sector angle back to a frequency?
Use the reverse formula: frequency = (sector angle ÷ 360°) × total frequency. For example, if a sector spans 90° in a chart with a total of 40 items, the frequency is (90 ÷ 360) × 40 = 0.25 × 40 = 10.
Can a pie chart have only two sectors?
Yes. A pie chart with two categories simply has two sectors that together span 360°. However, a bar chart or simple percentage statement often communicates two-category data more clearly. Use a pie chart when showing part-to-whole relationships with more visual impact.
How do I draw a pie chart accurately without a compass?
Trace around a circular lid, coin, or protractor base to draw the circle. Then use a ruler to mark the centre point and draw radii. The shape does not need to be perfect, but the angle measurements must be accurate — always use a protractor at the centre.
What is the difference between a pie chart and a frequency diagram?
A pie chart shows proportions (each sector's size is relative to the whole). A frequency diagram (bar chart or histogram) shows actual frequencies on a vertical axis. Use a pie chart when you want to highlight shares; use a frequency diagram when the actual counts matter.
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