Pie-Chart Data: Connect a Share, an Amount and an Angle
One circle represents one whole
A pie chart divides a whole into sectors. The full circle is 360°, just as the full amount is 100%. A sector's angle and its amount describe the same fraction of that whole.
A fictional study club plans a monthly budget of ₹24,000. These categories are separate and together account for the full budget. The table provides all sector data used in this lesson.
| Category | Amount | Share of the whole | Sector angle |
|---|---|---|---|
| Room rent | ₹9,000 | 37.5% | 135° |
| Books | ₹6,000 | 25% | 90° |
| Travel | ₹3,000 | 12.5% | 45° |
| Other expenses | ₹6,000 | 25% | 90° |
| Total | ₹24,000 | 100% | 360° |
Derive the relationship instead of memorising a shortcut
Books use 6,000/24,000 = 1/4 of the budget. Therefore books occupy 1/4 of the circle: (1/4) × 360° = 90°. The percentage is (1/4) × 100 = 25%.
For any sector in a pie representing this whole:
- Share as a fraction = category amount / total amount.
- Percentage = share × 100.
- Sector angle = share × 360°.
Rent gives 9,000/24,000 = 3/8 of the budget. So its angle is (3/8) × 360° = 135°, and its share is 37.5%.
The check is global: amounts add to ₹24,000, percentages to 100%, and angles to 360°. A discrepancy signals missing, overlapping or incorrectly calculated categories.
Reverse an angle into an amount
Suppose another pie for the same ₹24,000 total has a sector of 72°. That sector is 72/360 = 1/5 of the whole. Its amount is (1/5) × 24,000 = ₹4,800, and its share is 20%.
This 72° sector is a separate hypothetical case; it is not an extra category to add to the four-category table above.
Keep the whole fixed when comparing
Equal angles mean equal shares, not necessarily equal money across different pies. A 90° sector of ₹24,000 is ₹6,000, while a 90° sector of ₹40,000 is ₹10,000. Read each pie's total before comparing amounts. Do not treat a percentage as a rupee value or add a sector to its whole twice.
Check yourself
- Find the travel sector's fraction of the whole and its angle.
- In the separate ₹24,000 case, how much does a 72° sector represent? Show the fraction used.
- Combine books and travel in the original table. Find their amount, percentage share and combined angle.
Worked answers
- Travel's share = 3,000/24,000 = 1/8. Angle = (1/8) × 360° = 45°. Its percentage is 12.5%.
- Fraction = 72/360 = 1/5. Amount = 24,000/5 = ₹4,800. Check: 20% of ₹24,000 is ₹4,800 and 20% of 360° is 72°.
- Amount = 6,000 + 3,000 = ₹9,000. Share = 9,000/24,000 × 100 = 37.5%. Angle = 90° + 45° = 135°, also (3/8) × 360°. The combined category has the same amount and angle as rent, within this same whole.
The budget, sector data and practice questions are original mathematical examples, not attributed to an SSC paper.
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