Percentage increase is one of the most practical calculations you'll encounter in everyday life — from checking a pay rise to comparing prices, analysing business growth or understanding inflation. In this guide, we'll cover the formula, step-by-step examples, and common mistakes to avoid.
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The Percentage Increase Formula
The formula for percentage increase is straightforward:
Breaking it down:
- New Value — the number after the change
- Original Value — the starting number (before the change)
- The result is a percentage — a positive number means an increase, a negative number means a decrease
Step-by-Step Example
Let's say a product cost £40 last year and now costs £52. What is the percentage increase?
- Find the difference: £52 − £40 = £12
- Divide by the original value: £12 ÷ £40 = 0.3
- Multiply by 100: 0.3 × 100 = 30%
The price increased by 30%.
More Worked Examples
Example 1: Salary increase
Your salary was £28,000 and you receive a pay rise to £30,800.
Percentage increase = ((£30,800 − £28,000) ÷ £28,000) × 100 = (£2,800 ÷ £28,000) × 100 = 10%
Example 2: Website traffic
Your website had 1,200 visitors last month and 1,560 this month.
Percentage increase = ((1,560 − 1,200) ÷ 1,200) × 100 = (360 ÷ 1,200) × 100 = 30%
Example 3: Temperature change
The temperature rose from 15°C to 21°C.
Percentage increase = ((21 − 15) ÷ 15) × 100 = (6 ÷ 15) × 100 = 40%
Percentage Increase vs Percentage Difference
These are related but different calculations:
- Percentage increase always uses the original (smaller) value as the denominator — it tells you by how much something grew relative to where it started.
- Percentage difference divides by the average of the two values — it's used when neither value is clearly the "original", such as when comparing two different products.
How to Calculate Percentage Decrease
The same formula works for decreases — you'll simply get a negative result. For example, if sales fell from 500 to 400:
Percentage change = ((400 − 500) ÷ 500) × 100 = (−100 ÷ 500) × 100 = −20%
That's a 20% decrease.
Common Mistakes
- Using the wrong denominator: Always divide by the original value, not the new value. A common error is dividing by the new value, which gives a different (incorrect) percentage.
- Confusing percentage points with percentages: If an interest rate rises from 2% to 3%, that's an increase of 1 percentage point, but a 50% increase in the rate itself.
- Reversing the direction: A 50% increase followed by a 50% decrease does not return you to the original number. (E.g., 100 → 150 → 75.)
Quick Reference: Percentage Increase Chart
| Original | New Value | % Increase |
|---|---|---|
| 100 | 110 | 10% |
| 200 | 250 | 25% |
| 50 | 75 | 50% |
| 1,000 | 1,200 | 20% |
| 40 | 52 | 30% |
Try the Percentage Calculator
Instead of doing the maths by hand, use our free Percentage Calculator. It handles percentage increase, decrease, what X% of Y is, and more — all instantly in your browser.
Summary
To calculate percentage increase:
- Subtract the original value from the new value
- Divide the result by the original value
- Multiply by 100
The formula is: ((New − Original) ÷ Original) × 100. A positive result means an increase; a negative result means a decrease.