Worked examples
Percentage calculation worked examples
Each example below shows the inputs, the formula, the working, and the result. Every numerical result has been checked. Use these as templates for your own calculations or as a learning reference.
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These examples cover the three most common percentage question types.
Example 1: What is 20% of 150?
Formula: (percentage / 100) × value. Working: (20 / 100) × 150 = 0.20 × 150 = 30. Result: 20% of 150 is 30.
Formula: (20 / 100) × 150 = 30
Example 2: 45 is what percent of 180?
Formula: (part / whole) × 100. Working: (45 / 180) × 100 = 0.25 × 100 = 25. Result: 45 is 25% of 180.
Formula: (45 / 180) × 100 = 25%
Example 3: What is 7.5% of 320?
Formula: (percentage / 100) × value. Working: (7.5 / 100) × 320 = 0.075 × 320 = 24. Result: 7.5% of 320 is 24.
Formula: (7.5 / 100) × 320 = 24
Percentage increase and decrease examples
In these examples, one value is clearly the starting point and the other follows after a change.
Example 4: Percentage increase from 80 to 100
Formula: ((new − original) / original) × 100. Working: ((100 − 80) / 80) × 100 = (20 / 80) × 100 = 25. Result: the value increased by 25%.
Formula: ((100 − 80) / 80) × 100 = 25%
Example 5: Percentage decrease from 200 to 170
Formula: ((original − new) / original) × 100. Working: ((200 − 170) / 200) × 100 = (30 / 200) × 100 = 15. Result: the value decreased by 15%.
Formula: ((200 − 170) / 200) × 100 = 15%
Example 6: Percentage difference between 95 and 105
Formula: |v1 − v2| / ((v1 + v2) / 2) × 100. Working: |95 − 105| / ((95 + 105) / 2) × 100 = 10 / 100 × 100 = 10. Result: the percentage difference is 10%.
Formula: |95 − 105| / 100 × 100 = 10%
Reverse percentage examples
These examples show how to find the original value before a percentage change was applied.
Example 7: Find the original after a 25% increase left £150
Formula: original = final / (1 + rate / 100). Working: £150 / (1 + 0.25) = £150 / 1.25 = £120. Result: the original value was £120.
Formula: 150 / 1.25 = 120
Example 8: Find the original after a 15% decrease left 85
Formula: original = final / (1 − rate / 100). Working: 85 / (1 − 0.15) = 85 / 0.85 = 100. Result: the original value was 100.
Formula: 85 / 0.85 = 100
Discount, VAT, and tax examples
These examples apply percentage maths to real pricing scenarios.
Example 9: 30% discount off £120
Saving = £120 × 0.30 = £36. Final price = £120 − £36 = £84. Alternatively: £120 × 0.70 = £84.
Formula: 120 × 0.70 = £84
Example 10: Add 20% VAT to £250 net
Formula: gross = net × (1 + rate / 100). Working: £250 × 1.20 = £300. VAT amount = £300 − £250 = £50.
Formula: 250 × 1.20 = £300
Example 11: Remove 20% VAT from £360 gross
Formula: net = gross / (1 + rate / 100). Working: £360 / 1.20 = £300 net. VAT portion = £360 − £300 = £60.
Formula: 360 / 1.20 = £300
Example 12: 8.5% sales tax on $60
Tax = $60 × 0.085 = $5.10. Total = $60 + $5.10 = $65.10.
Formula: 60 × 0.085 = $5.10; total = $65.10
Example 13: 15% tip on a $48 restaurant bill
Tip = $48 × 0.15 = $7.20. Total including tip = $48 + $7.20 = $55.20.
Formula: 48 × 0.15 = $7.20; total = $55.20
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