Take a whole pie, cut it so each slice is exactly as big as its piece of the story, and you can read a whole survey in a single glance. Bigger slice, bigger share.
Start hereA pie chart takes one whole thing — all the votes, all the people, all the money — draws it as a full circle, then slices that circle so each slice's size shows its share of the whole. A bigger slice means a bigger share. That's the entire trick.
The magic number behind it is 360. A full turn around a circle is 360 degrees, and that whole circle stands for everything — 100% of your data. Hand a quarter of it to one group and you've handed them 90° and 25% at the same time. By the end of this page you'll be slicing pies yourself, turning plain counts into exact angles, and spotting the one situation where a pie chart quietly lies to you.
Imagine a real pizza on the table, and your whole class wants a piece. The pizza is the whole — every slice that exists comes out of this one pizza, and nothing comes from anywhere else. If a friend takes a big wedge, there's less left for everyone else, because the slices all have to add up to exactly one pizza. That "all the slices make one whole" rule is what a pie chart is built on.
A pie chart swaps the pizza for a circle and swaps hunger for data. Each wedge — its proper name is a sector — stands for one category, and the size of the wedge shows how big that category's share is. Favourite fruit in your class? One sector for strawberry, one for banana, one for apple, and so on. Add the sectors together and you're back to the full circle: everyone, accounted for, exactly once.
This is why a pie chart is the perfect tool for a "parts of a whole" question. It doesn't try to tell you the raw totals or how things change over time. It answers one question, beautifully: of the whole, how is it split up? Which slice is the giant, which is the sliver, and roughly what fraction does each one grab.
Every pie chart leans on one idea: the complete circle is the whole lot, and you can describe that whole in two languages at once. In degrees, all the way around is 360°. In percentages, the whole thing is 100%. Those are two names for the same circle — so they line up perfectly.
Once you see that, the slices become easy to translate. Cut the circle in half and each half is 180° and 50%. Cut it into quarters and each quarter is 90° and 25%. A tenth of the pie? That's 36° and 10%, because 360 ÷ 10 = 36. The fraction, the angle, and the percentage are just three outfits the same share puts on:
A slice's fraction of the whole × 360 gives its angle. The same fraction × 100 gives its percentage. One share, told three ways.
And here's the rule that keeps everything honest: because the slices are all the parts of one whole, they must add up to the whole. Every angle together makes 360°; every percentage together makes 100%. If your slices add up to something else, a slice has gone missing — or you're not really looking at parts of a single whole. Keep that in your back pocket; we'll come back to it.
Here's a class survey: "What's your favourite fruit?" Tap the + and − buttons to change how many votes each fruit gets, and the pie redraws instantly. The legend keeps the maths live for you — each slice's count, its share as a percentage, and its angle in degrees — and the running total proves they always make one whole.
Watch two things as you click. First, no matter what you do, the percentages always land on 100% and the degrees on 360° — that's the "one whole" rule doing its job. Second, give one fruit a landslide and its slice swallows the circle, while the losers shrink to thin splinters.
Notice you can never quite break it. Pile every vote onto strawberry and you get one full-circle slice: 100%, 360°, the whole pie. Spread the votes out evenly and you get five equal wedges of 72° each, because 360 ÷ 5 = 72. The pie is just doing arithmetic on your behalf, live, every single click.
So how did the pie know to give strawberry exactly that wedge? It used the one move that powers every pie chart: turn a count into a fraction of the whole, then dress that fraction up as an angle or a percentage. Here are the two formulas — and they're really the same formula wearing different numbers on the end:
angle = counttotal × 360° percentage = counttotal × 100
Let's walk one through with the survey's starting numbers. Strawberry got 7 votes out of a class of 20. First, find its fraction of the whole: 7 ÷ 20 = 0.35. That little decimal is the heart of everything — it says strawberry owns 0.35 of the pie. Now just dress it up both ways:
Do the same for every fruit and you've built the whole pie by hand: banana 5/20 → 90° and 25%, apple 4/20 → 72° and 20%, orange 3/20 → 54° and 15%, grape 1/20 → 18° and 5%. Add the angles: 126 + 90 + 72 + 54 + 18 = 360°. Add the percentages: 35 + 25 + 20 + 15 + 5 = 100%. They have to — every slice was a fraction of the same whole, so together they rebuild the whole exactly. If your angles don't reach 360, that's your signal to hunt for the arithmetic slip.
In a real exam you'll usually start from a frequency table — a tidy list of how many votes each category got — and you'll have to work out each slice's angle yourself. Here's a survey of 30 students and their favourite fruit. Pick a row and I'll show every step of turning its count into degrees.
| Favourite fruit | Votes (frequency) |
|---|---|
| Apple | 12 |
| Banana | 9 |
| Orange | 6 |
| Grape | 3 |
| Total (the whole) | 30 |
Because the whole survey is 30 students, each single vote is worth 360 ÷ 30 = 12°. So you can even count in votes: Apple's 12 votes × 12° each = 144°. Same answer, two roads.
That last trick — 360 ÷ total gives the degrees for one vote — is a lovely shortcut when the total divides neatly. With 30 students, one vote is 12°. With 36 students it'd be 10°, with 60 it'd be 6°. Multiply by each category's count and you've got every angle, no decimals in sight. When the total doesn't divide nicely, just fall back to the (count ÷ total) × 360 formula and round sensibly.
Most of the time you won't be measuring angles with a protractor — you'll be reading a finished pie someone hands you. The good news: your eyes are already good at this, because you've shared enough food. Two questions answer almost everything.
Those landmarks are worth memorising, because they turn a glance into a number. Train your eye on the three most useful ones:
One last reading skill: a pie chart shows shares, not raw counts. A slice that looks like "about a third" is telling you 33% of the whole — but unless someone writes the total beside the chart, you don't know if that third is 3 students or 3 million people. The angles tell you how the whole was split; only the total tells you how big the whole was. Good pie charts always print that total somewhere.
A pie chart is brilliant at exactly one job and clumsy at most others. Reach for it when you're showing how a single whole splits into parts. Reach for something else — usually a bar chart — when you're not.
The "too many tiny slices" problem is the one you'll hit most. Once slices get thin, your eye can't tell which of two slivers is bigger, and the chart stops helping. The fix is either to use a bar chart instead, or to bundle the smallest categories into a single "Other" slice so the big players stay readable.
A pie chart only ever shows shares of its own whole. A slice's angle tells you its fraction of that pie — never how it compares to a slice in a different pie.
Here's the trap, drawn from real life. A tiny shop sells 10 drinks; 30% of them are lemonade — that's just 3 lemonades. A giant shop sells 1,000 drinks; only 20% are lemonade — but that's 200 lemonades. The first pie has the bigger lemonade slice, yet the second shop sold far more lemonade. Shares within a pie say nothing about totals across pies. To compare amounts, you need the actual counts, not the slice sizes.
And one more rule the trap leans on: a pie chart only makes sense when its slices add up to the whole — 360° and 100%. If your categories can overlap (someone likes two fruits and gets counted twice), or if they don't cover everyone, then the parts don't make a clean whole, and a pie chart will quietly mislead. Parts of one whole, counted once each: that's the contract. Break it, and you've drawn a pretty circle that means nothing.
Click the answer you think is right — you'll get an instant explanation either way. No pressure, no score: this is just to make the ideas stick.
Fraction first, then angle. Football's share of the whole is 10 ÷ 40 = 0.25 — a quarter of the class. A quarter of the circle is 0.25 × 360 = 90° (and 0.25 × 100 = 25%). The count on its own isn't the angle; you always turn it into a fraction of the total first.
Parts of one whole must rebuild the whole. 50 + 30 + 15 = 95%, so 5% of the data has vanished — there's a fourth category nobody drew. Every pie chart's percentages must total 100% (and its angles 360°), because the slices are all the parts of a single whole.
A slice is a share, not a count. 40% of a small café could be fewer cups than 25% of a huge one. Pie slices only compare shares within the same pie. To compare cups across two cafés you need the real totals — the slice sizes alone can't tell you.
The full circle is everything — 360° and 100%. Each slice is one category's share of it.
(count ÷ total) × 360 is the angle; × 100 is the percentage. Slices always make 360° and 100%.
A bigger slice means a bigger share of its own pie — never more than a slice in a different pie.