How to Calculate Percentage Increase (With Examples)
Percentages are everywhere: price rises, pay rises, discounts, inflation, growth reports and exam results. Yet calculating a percentage increase correctly trips up a lot of people, mostly because of one detail: what you divide by. This guide shows the method step by step, with examples, the most common mistakes and a few shortcuts you can do in your head. If you just want the answer, use our free percentage increase calculator.
The formula in one line
Percentage increase = (new value − old value) ÷ old value × 100
In words: find how much the value changed, compare that change with where you started, and turn the result into a percentage.
Step by step: a price that went up
A monthly phone plan went from $40 to $46.
- Find the change: 46 − 40 = 6.
- Divide by the original value: 6 ÷ 40 = 0.15.
- Multiply by 100: 0.15 × 100 = 15%.
The plan became 15% more expensive.
Step by step: a value that went down
A laptop was $1,200 and is now on sale for $900.
- Change: 900 − 1,200 = −300.
- Divide by the original: −300 ÷ 1,200 = −0.25.
- Multiply by 100: −25%, which is a 25% decrease.
The same formula works for increases and decreases; the sign tells you which one it is.
Why you always divide by the original value
A percentage change answers the question “compared with where we started, how big was the change?”. If you divided by the new value instead, the answer would change depending on the direction. That is also why increases and decreases do not cancel out:
- $100 increased by 50% becomes $150.
- $150 decreased by 50% becomes $75, not $100.
To get back from $150 to $100 you need a decrease of 50 ÷ 150 = 33.3%. Retailers sometimes take advantage of this: a price raised by 25% and then “discounted” by 20% ends up exactly where it started.
Percent vs. percentage points
When the numbers are themselves percentages, two different measures are possible. If a savings rate goes from 3% to 4%:
- It increased by 1 percentage point (4 − 3).
- It increased by 33.3 percent ((4 − 3) ÷ 3 × 100).
Both statements are true, but they sound very different. News articles and marketing material often choose the one that sounds more impressive, so it is worth checking which is meant.
Increases over several periods
Growth over several years does not add up; it multiplies. If rent rises by 10% one year and by 10% the next, the total increase is 1.10 × 1.10 = 1.21, or 21%, not 20%. To find the average yearly growth over several years, use the compound annual growth rate (CAGR):
CAGR = (final value ÷ starting value)1 ÷ years − 1
Revenue that grew from $50,000 to $80,000 in 4 years grew by 60% in total, but the average yearly growth rate is (80,000 ÷ 50,000)1/4 − 1 ≈ 12.5% per year. The idea is the same one behind compound interest.
Working backwards from a percentage
- Find the new value: multiply by (1 + rate). $80 increased by 15% is 80 × 1.15 = $92.
- Find the original value after an increase: divide by (1 + rate). $92 after a 15% increase came from 92 ÷ 1.15 = $80.
- Find the original price before a discount: divide by (1 − rate). $68 after a 15% discount was 68 ÷ 0.85 = $80.
Mental shortcuts
- 10% of a number: move the decimal point one place left (10% of 240 is 24).
- 5% is half of 10%; 20% is double 10%; 25% is a quarter.
- To check an increase quickly, ask what 10% of the original is. A rise from 240 to 270 is 30, which is a bit more than 24, so the increase is a bit more than 10% (it is 12.5%).
Doing it in a spreadsheet
In Excel or Google Sheets, with the old value in A2 and the new value in B2, type =(B2-A2)/A2 and format the cell as a percentage. Copy the formula down to calculate a whole column of changes at once.
Summary
- Subtract the old value from the new value.
- Divide by the old value.
- Multiply by 100. A negative result is a decrease.
- Over several periods, multiply the growth factors instead of adding the percentages.
Want to skip the arithmetic? Try the percentage increase calculator, or browse all our free tools.