Maths⏱ 5 min read

How to Calculate Percentage Increase and Decrease (With Examples)

Percentage change is one of the most useful everyday maths skills. Here's the exact formula, common mistakes to avoid, and worked examples for every situation.

Whether you're working out a price rise, a salary increase, a weight loss percentage, or a drop in sales, the formula is always the same — and it's simpler than most people think.

The Percentage Change Formula

Percentage Change = ((New Value − Old Value) ÷ Old Value) × 100 Positive result = increase Negative result = decrease

Worked Examples

Example 1: Price increase. A coffee costs £2.80 in January and £3.20 in December. What's the percentage increase?

((3.20 − 2.80) ÷ 2.80) × 100 = (0.40 ÷ 2.80) × 100 = 14.3% increase

Example 2: Weight loss. Someone goes from 92kg to 84kg. What percentage of their bodyweight did they lose?

((84 − 92) ÷ 92) × 100 = (−8 ÷ 92) × 100 = −8.7% (an 8.7% decrease)

Example 3: Salary raise. Going from £28,000 to £31,500 a year.

((31,500 − 28,000) ÷ 28,000) × 100 = (3,500 ÷ 28,000) × 100 = 12.5% raise

Finding the New Value After a Percentage Change

If you know the original value and the percentage change, you can find the new value directly:

New Value = Old Value × (1 + Percentage ÷ 100) For a decrease: New Value = Old Value × (1 − Percentage ÷ 100)

Example: A £450 jacket is 30% off.

450 × (1 − 0.30) = 450 × 0.70 = £315

Finding the Original Value (Reverse Percentage)

This is where people get confused. If a price is already £78 after a 20% increase, what was the original price?

The mistake is to subtract 20% from £78 (which gives £62.40 — wrong). The correct method:

Original = New Value ÷ (1 + Percentage ÷ 100) 78 ÷ 1.20 = £65

This matters a lot for VAT calculations — if a price includes 20% VAT, the pre-VAT price is the total divided by 1.20, not the total minus 20%.

Percentage of a Number

A slightly different calculation that often gets conflated with percentage change:

X% of Y = (X ÷ 100) × Y 15% of 240 = (15 ÷ 100) × 240 = 36

Percentage Point vs Percentage Change

These are not the same thing and are frequently confused in news reporting.

ScenarioPercentage PointsPercentage Change
Interest rate: 2% → 3%+1 percentage point+50% increase
Tax rate: 20% → 22%+2 percentage points+10% increase

Saying a rate "went up by 50%" sounds alarming. Saying it "rose by 1 percentage point" sounds modest. They're describing the same change. Always check which one is being used when reading statistics.

Quick Mental Maths Tricks

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