The key relation
A pie chart shows parts of a whole. A full circle is 360° and 100%, so
1% = 3.6°, and a sector's amount = (angle ÷ 360) × total = (percentage ÷ 100) × total.
Percentage pie charts
Monthly budget of a family, total ₹60,000:
Item | Share |
|---|---|
Food | 30% |
Rent | 25% |
Savings | 20% |
Education | 15% |
Transport | 10% |
Rent: 25% of 60,000 = ₹15,000.
Central angle for food: 30 × 3.6 = 108°.
Savings exceed transport by 10% of the total = ₹6,000.
Degree pie charts
720 employees by department, with central angles HR 40°, Sales 120°, Engineering 150°, Finance 50° (total 360°).
Engineering: 150/360 × 720 = 300 employees.
Sales as a percentage: 120/360 = 33.3%.
Each degree here represents 720/360 = 2 employees, so the HR slice of 40° is 80 people.
Comparing slices
You don't need the total to compare two slices: the ratio of their angles (or percentages) is the ratio of their amounts. Finance : HR = 50 : 40 = 5 : 4.
Shortcuts and tricks
The standard way is the proportion amount = angle ÷ 360 × total. Two shortcuts avoid the division.
Amount per degree (or per 1%)
Example: a chart of 1,080 people; how many are in a 50° slice?
Standard way: 50 ÷ 360 × 1,080 = 150.
Shortcut: 1,080 ÷ 360 = 3 people per degree, so 50° is 150. Work this out once and reuse it for every slice.
Benchmark angles
Example: 72° of a ₹1,500 budget.
Standard way: 72 ÷ 360 × 1,500 = ₹300.
Shortcut: 72° is 20% (one fifth of the circle), and 20% of 1,500 is ₹300. Others to know: 36° = 10%, 90° = 25%, 120° = 33⅓%, 180° = 50%.
Ratios straight from angles
Two slices are in the ratio of their angles or percentages. You don't need the total to answer a ratio question.
Exam tips
Check whether the chart is labelled in degrees or percentages.
Find "amount per degree" or "amount per 1%" once, then multiply.
If one item changes and the total changes too, recompute every share.