To find the percentage of an increase, subtract the original number from the new number, divide that difference by the original number, then multiply by 100. That three-step formula works for any situation: pay raises, price changes, investment returns, or population growth. Once you understand the logic, you can do it by hand, on a calculator, or in a spreadsheet in seconds.
The Formula
The percentage increase formula is:
Percentage Increase = ((New Value − Original Value) / Original Value) × 100
Each piece of this formula does something specific. Subtracting gives you the raw amount of increase. Dividing by the original value turns that raw amount into a proportion, showing the increase relative to where you started. Multiplying by 100 converts that proportion into a percentage you can read naturally.
Step-by-Step Example
Say your monthly rent went from $1,200 to $1,350. Here’s how to find the percentage increase:
- Step 1: Find the difference. $1,350 − $1,200 = $150.
- Step 2: Divide by the original value. $150 ÷ $1,200 = 0.125.
- Step 3: Multiply by 100. 0.125 × 100 = 12.5%.
Your rent increased by 12.5%. The key detail people sometimes get wrong: you always divide by the original value (where you started), not the new value. Dividing by the new number would give you a smaller, incorrect result.
Calculating a Pay Raise
One of the most common reasons people search for this formula is to figure out the percentage of a salary or wage increase. The math is identical.
If your annual salary goes from $50,000 to $55,000, the increase is $5,000. Divide $5,000 by $50,000 to get 0.10, then multiply by 100. That’s a 10% raise. For a physical therapist earning $45,000 who gets bumped to $46,350, the increase is $1,350 ÷ $45,000 = 0.03, or 3%.
The same approach works for hourly wages. If your hourly pay goes from $18 to $19.50, the increase is $1.50 ÷ $18 = 0.0833, or about 8.3%.
You can also run the formula in reverse to find a new salary from a known raise percentage. Multiply your current salary by the raise percentage (as a decimal), then add that to your current salary. A 4% raise on $60,000: $60,000 × 0.04 = $2,400, so the new salary is $62,400.
How to Do It in Excel or Google Sheets
If you’re working with a list of numbers, a spreadsheet can calculate percentage increases instantly. Suppose your original value is in cell A1 and your new value is in cell B1. In any blank cell, type:
=(B1-A1)/A1
Press Enter, and you’ll get a decimal like 0.0675. To display it as a percentage, select the cell and click the percent style button (the “%” icon on the toolbar). The cell will then show 6.75%. You can drag this formula down an entire column to calculate percentage increases for hundreds of rows at once.
If you want to increase a number by a known percentage, use a slightly different formula. To increase the value in A1 by 25%, type:
=A1*(1+0.25)
This multiplies the original by 1.25 in one step, giving you the new value directly. Replace 0.25 with whatever decimal matches your percentage.
Percentage Increase vs. Percentage Points
This distinction trips people up when the numbers involved are already percentages. Say an interest rate rises from 5% to 7%. You might hear this described two different ways, and they mean different things.
The rate increased by 2 percentage points, meaning the simple difference between 7 and 5. But the percentage increase is 40%, because 2 ÷ 5 × 100 = 40%. A 10% rate falling by 1 percentage point becomes 9%. A 10% rate falling by 1% (a percentage decrease) becomes 9.9%, because 1% of 10 is 0.1.
In everyday life, news headlines and financial reports sometimes blur this distinction. When someone says a tax rate “increased by 3%,” ask yourself whether they mean 3 percentage points (the rate went from, say, 20% to 23%) or an actual 3% increase (the rate went from 20% to 20.6%). The difference can be significant when you’re calculating real dollars.
Quick Reference for Common Increases
Here are a few examples you can use to check your own math:
- 100 to 125: (125 − 100) / 100 × 100 = 25%
- 80 to 100: (100 − 80) / 80 × 100 = 25%
- 200 to 250: (250 − 200) / 200 × 100 = 25%
- 75 to 90: (90 − 75) / 75 × 100 = 20%
- 1,000 to 1,500: (1,500 − 1,000) / 1,000 × 100 = 50%
Notice that 80 to 100 and 100 to 125 are both 25% increases, even though the raw dollar amounts differ. That’s the whole point of expressing change as a percentage: it tells you the size of the increase relative to the starting point, making it easy to compare changes across different scales.