Pie Charts

What a pie chart shows

A pie chart is a circle divided into slices, called sectors, that shows how a whole is split into parts. The bigger a sector, the larger that category's share of the total. Because the whole circle represents everything together, pie charts are ideal for answering questions about proportion: what fraction of the class walks to school, what share of a budget goes on food, what percentage of votes each candidate won.

The key idea is that a pie chart compares parts to the whole, not part to part by exact amount. A sector that fills half the circle means "half of everything", whatever that everything happens to be. This makes pie charts great for showing shares, but it also hides the actual totals — a point we will return to.

The circle is 360 degrees

A full circle contains 360°. That single fact unlocks every pie chart calculation, because the angle of a sector is simply its fraction of the whole scaled up to the full 360°.

Some friendly landmark sectors are worth memorising:

Fraction of data	Angle	Percentage
The whole	360°	100%
One half	180°	50%
One quarter	90°	25%
One third	120°	33.3%
One tenth	36°	10%

Notice that one tenth of the circle is 36°, because 360 ÷ 10 = 36. That makes percentages easy: each 1% is 3.6°, so a 25% sector is 25 × 3.6 = 90°.

Reading a pie chart

To read a pie chart, judge or measure how big each sector is compared with the whole. There are three things people commonly ask:

1. Which is biggest or smallest? The largest sector is the most common category. You can often see this at a glance, which is the chart's great strength.

2. What fraction or percentage is a sector? Compare its angle to 360°. A sector of 90° is 90/360 = 1/4 = 25%.

3. How many real items does a sector represent? This needs the total. Multiply the total by the sector's fraction.

Worked example 1: from angle to percentage

A sector in a pie chart has an angle of 72°. What percentage of the data does it represent?

1. Write the angle as a fraction of the whole: 72/360.
2. Simplify: 72/360 = 1/5.
3. As a percentage: 1/5 = 20%.

If you would like a refresher on swapping between these forms, see Converting Fractions, Decimals and Percentages.

Worked example 2: from a sector to a real quantity

In a survey of 90 students, the "reading" sector has an angle of 80°. How many students chose reading?

1. Fraction of the circle: 80/360 = 2/9.
2. Find that fraction of the total: 2/9 × 90 = 180/9 = 20 students.

Without the total of 90, we could only give the proportion, not the actual number — the total is essential for this kind of question.

Drawing your own pie chart

To turn raw data into a pie chart, you convert each category into an angle. The method is always the same:

1. Find the total of all the data.
2. For each category, work out (category ÷ total) × 360°. This is its angle.
3. Check the angles add up to 360°.
4. Draw a circle, mark the centre, and use a protractor to measure each angle in turn, starting each new sector from where the last one ended.
5. Label every sector and give the chart a title.

Worked example 3: building a pie chart from a table

A class of 24 students chose their favourite season:

Season	Students	Working	Angle
Spring	4	(4 ÷ 24) × 360	60°
Summer	10	(10 ÷ 24) × 360	150°
Autumn	6	(6 ÷ 24) × 360	90°
Winter	4	(4 ÷ 24) × 360	60°

Check: 60 + 150 + 90 + 60 = 360°. The angles add to a full circle, so the working is correct.

A neat shortcut: because 24 students share 360°, each student is worth 360 ÷ 24 = 15°. So Summer's 10 students give 10 × 15 = 150°, matching the table. Finding "degrees per item" once can save repeated division.

Pie charts hide the total: a warning

Here is the most important subtlety. A pie chart shows proportions only. Two pie charts can look almost identical yet describe completely different numbers.

Suppose School A surveys 20 pupils and School B surveys 200. Both find that 50% like cats, so both charts show a half-circle "cats" sector. But:

• School A: 50% of 20 = 10 pupils.
• School B: 50% of 200 = 100 pupils.

Equal-looking sectors, ten times the people. This is why you should never compare two pie charts by sector size alone unless you also know their totals. When the actual amounts matter, a bar chart is often the clearer choice, because the bar heights show real quantities directly.

Pie chart or bar chart?

Use a pie chart when…	Use a bar chart when…
Showing parts of one whole	Comparing separate categories
Proportion is the main message	Exact amounts matter
There are only a few categories	There are many categories
Sectors are clearly different sizes	Values are close and need precise comparison

Pie charts also become hard to read with many thin slices, or when two sectors are nearly the same size, because the eye struggles to judge small differences in angle.

Common mistakes to avoid

• Forgetting the angles must total 360°. Always check; if they do not, an angle is wrong.
• Reading a sector as a number instead of a share. A 90° sector is 25% of the total, not "90 of something".
• Comparing two charts without the totals. Equal sectors can hide very different counts.
• Confusing the fraction with the angle. A quarter of the data is a 90° sector, not a 25° one. Convert through 360°, not 100°, when you want an angle.

Why pie charts matter

So why slice data into a circle at all? Because the human eye is brilliant at comparing areas and angles within a single whole. A pie chart answers "how is this divided up?" faster than any table. Show someone a budget pie chart and they instantly see that housing dwarfs entertainment, without reading a single number. The trade-off is precision: pie charts sacrifice exact amounts for an immediate sense of proportion. Knowing when that trade-off is worth it — proportion over precision — is the real skill, and it is exactly the kind of judgement that good data handling is all about.

Activity: survey and chart

Carry out a small survey and present it as a pie chart.

1. Ask 20 people one multiple-choice question, such as their favourite type of film (action, comedy, drama, other). Twenty is a handy total because each person is worth 360 ÷ 20 = 18°.
2. Tally the results into a table.
3. For each category, work out the angle using (count ÷ 20) × 360°, or just count × 18°.
4. Check your angles add to 360°.
5. Draw the pie chart with a protractor, label each sector with its category and percentage, and add a title.
6. Write two conclusions, for example "Comedy was the most popular, with 40% of the vote."

Summary

A pie chart divides a circle into sectors to show how a whole is split into parts. Convert between data, angles and percentages through the fact that the whole circle is 360°: a sector's angle is its fraction of the total times 360°, and its percentage is that fraction times 100. To find a real quantity, multiply the total by the sector's fraction. Above all, remember that pie charts show proportion, not amount — so always know the total before drawing conclusions.