Prices go up, salaries rise, populations grow — knowing how to calculate percentage increase tells you exactly how much something changed, in relative terms. Unlike a plain subtraction, a percentage increase puts the change in context by comparing it to the original value. This guide shows the formula, worked examples, and the common traps to avoid. For instant results, try the free percentage calculator.
What Is Percentage Increase?
Percentage increase measures how much a value has grown relative to its starting point, expressed as a percentage of that original value. If your phone plan rose from $50 to $60, the raw increase is $10, but the percentage increase is 20% — because $10 is 20% of the original $50. The original value (the “old” number) is always the baseline you divide by.
The Percentage Increase Formula
Percentage Increase = ((New Value − Original Value) ÷ Original Value) × 100
Three steps:
- Subtract the original value from the new value (this is the amount of the increase).
- Divide the result by the original value.
- Multiply by 100 to express it as a percentage.
If the result is negative, the value actually decreased — that is a percentage decrease.
Step-by-Step Examples
Example 1: Salary increase
Your salary rises from $52,000 to $56,500. What is the percentage increase?
- Difference: 56,500 − 52,000 = 4,500
- Divide by original: 4,500 ÷ 52,000 = 0.0865
- Multiply by 100: 8.65% increase
Example 2: Price increase
A grocery bill grows from $84 to $97.
- Difference: 97 − 84 = 13
- Divide by original: 13 ÷ 84 = 0.1548
- 15.5% increase (rounded)
Example 3: Website traffic
Monthly visits rise from 2,400 to 3,120.
- Difference: 3,120 − 2,400 = 720
- Divide by original: 720 ÷ 2,400 = 0.30
- 30% increase
Percentage Increase vs Percentage Decrease
The same formula handles both directions. When the new value is smaller, the numerator is negative and you get a percentage decrease. For example, a gym membership falling from $75 to $60 is a (60 − 75) ÷ 75 × 100 = 20% decrease. Always subtract old from new — never the reverse — so the sign tells you the direction automatically.
Percentage Increase vs Percentage Difference
These are NOT the same. Percentage increase is directional: it measures change from an original value to a new one, dividing by the original. Percentage difference compares two values without a direction, dividing by their average. Use increase/decrease when one value came first (time, before/after); use difference when comparing two simultaneous values (two product prices, two test scores).
Percentage Points vs Percentage Increase
If an interest rate climbs from 4% to 5%, that is a 1 percentage point rise, but a 25% increase in the rate ((5 − 4) ÷ 4 × 100). Financial news confuses these constantly — knowing which one you need prevents expensive misunderstandings.
Reverse Calculation: Finding the New Value
If you know the original value and the percentage increase, find the new value by multiplying:
New Value = Original × (1 + Percentage Increase ÷ 100)
A $200 item with a 15% markup costs 200 × 1.15 = $230. This is the same maths used for tips, tax, and compound growth.
Common Mistakes to Avoid
- Dividing by the new value instead of the original — the baseline is always the starting number.
- Forgetting to multiply by 100 and reporting a decimal like 0.0865 instead of 8.65%.
- Mixing up order — (new − old) ÷ old, not (old − new) ÷ new.
- Adding percentages of different originals — two consecutive 10% increases make a 21% total increase, not 20%.
Worked Table: Quick Reference
| Original | New | Increase | % Increase |
|---|---|---|---|
| 50 | 60 | 10 | 20% |
| 200 | 250 | 50 | 25% |
| 1,200 | 1,500 | 300 | 25% |
| 84 | 97 | 13 | 15.5% |
| 52,000 | 56,500 | 4,500 | 8.65% |
Percent Change Language: Percent vs Percentage
Search results, news articles, and calculators use “percent increase” and “percentage increase” interchangeably. Both mean the same calculation. The same applies to percent change and percentage change. Use whichever term your audience expects — the formula never changes: (new − original) ÷ original × 100.
More Practice Problems
Problem 1: Utility bill
Last month’s electricity bill was $132. This month it is $158. What is the percent increase?
- Difference: 158 − 132 = 26
- Divide: 26 ÷ 132 = 0.197
- 19.7% increase
Problem 2: Fuel price
Petrol rises from $1.84 to $2.07 per litre.
- Difference: 0.23
- Divide: 0.23 ÷ 1.84 = 0.125
- 12.5% increase
Problem 3: Video views
A channel’s views grow from 8,500 to 21,400 in a month.
- Difference: 12,900
- Divide: 12,900 ÷ 8,500 = 1.518
- 151.8% increase — more than doubling gives a result over 100%
Problem 4: Finding the final value after a percent increase
A $340 hotel rate increases by 12% for peak season. What is the final price?
- Increase: 0.12 × 340 = $40.80
- Final price: 340 + 40.80 = $380.80
Problem 5: Two-step calculations
A $99 fee increases 10% in year one and 10% in year two.
- After year one: 99 × 1.10 = $108.90
- After year two: 108.90 × 1.10 = $119.79
- Total percent increase: (119.79 − 99) ÷ 99 × 100 = 21%, not 20%
Where Percent Increase Calculations Are Used
- Finance: inflation rates, interest growth, salary raises, investment returns.
- Business: revenue growth, price increases, sales uplift after campaigns.
- Health: weight change, training-load increases.
- Analytics: traffic, conversion rates, user growth month over month.
Any time a value moves from a starting point to an ending point, the percent increase tells you the size of that move relative to where it began.
FAQ
How do I calculate percentage increase quickly?
Use the formula ((new − original) ÷ original) × 100, or enter both values into the free percentage calculator for an instant answer.
How do I calculate a 5% increase?
Multiply the original value by 1.05. For example, a 5% increase on $80 gives 80 × 1.05 = $84.
Why do two 10% increases not equal a 20% increase?
Each increase applies to a different base. After the first 10%, the second 10% is calculated on the larger amount, so the combined growth is (1.10 × 1.10 − 1) × 100 = 21%.
Can percentage increase be more than 100%?
Yes. If a value more than doubles, the percentage increase exceeds 100%. A change from 40 to 100 is a 150% increase.
What is the difference between percentage increase and percentage change?
Nothing — they are the same calculation. Percentage change is the general term; percentage increase simply means the change came out positive.