Percentage Increase Calculator

Quick answer

Percentage increase tells you how much a value has grown compared with where it started. Subtract the old value from the new value, divide by the old value and multiply by 100. For example, going from 80 to 100 is a 25 percent increase.

Use the calculator above for the four most common jobs: finding the percent increase between two numbers, adding a percent to a number, finding the original number before an increase, and working out repeated increases over several periods.

How to calculate percentage increase

Follow these three steps. Here the monthly electricity bill goes from 120 to 138.

1. Subtract the original value from the new value. 138 minus 120 is 18.
2. Divide that change by the original value. 18 divided by 120 is 0.15.
3. Multiply by 100 to turn it into a percentage. 0.15 times 100 is 15 percent.

The bill grew by 15 percent. Always divide by the original value, the one you started from. If you divide by the new value instead, you get a different and wrong answer.

Percentage increase formulas

The part in brackets, 1 plus the percent as a decimal, is called the multiplier. A 15 percent increase has a multiplier of 1.15, and a 5 percent increase has a multiplier of 1.05.

Percentage increase examples

Type any of these into the calculator to see the steps. The same method works for prices, wages, sales, subscribers, temperatures and anything else that can grow.

How to add a percentage to a number

To increase a number by a percent, multiply it by the multiplier. To add 15 percent to 250, multiply 250 by 1.15. The answer is 287.5. The increase is 37.5, which is 15 percent of 250.

This is the same method used for price rises, tax added to a price, a tip on a bill and a pay rise. Choose the Add a percent mode in the calculator to do it with steps.

How to find the original number before an increase

Sometimes you know the final value and the percentage increase, and you want the number you started with. Divide the final value by the multiplier.

A price is now 115 after a 15 percent increase. The multiplier is 1.15, so the original price was 115 divided by 1.15, which is 100.

A common mistake is to take 15 percent off 115. That gives 97.75, which is wrong, because the 15 percent was added to the original 100, and 15 percent of 115 is a larger amount than 15 percent of 100. Use the Find the original mode to avoid this.

Repeated percentage increases

When a value grows by the same percent in each period, such as savings that grow by 5 percent a year, each period increases the value that the last period produced. Multiply the start by the multiplier once for every period.

Starting with 1,000 and adding 5 percent three times gives 1,000 times 1.05 times 1.05 times 1.05, which is 1,157.63. The total increase is 15.76 percent, not 15 percent, because each year the 5 percent is applied to a bigger amount. The Repeat over time mode shows the value after every period in a table.

Percentage points and percentage decrease

Percentage points and percent are not the same thing. If an interest rate moves from 4 percent to 6 percent, it rises by 2 percentage points. That is a 50 percent increase in the rate, because 2 divided by 4 is 0.5.

Increases and decreases are also not mirror images. If 100 rises by 50 percent, it becomes 150. A 50 percent decrease from 150 gives 75, not 100. To get back from 125 to 100, you need a decrease of 20 percent, not 25 percent, because the decrease is measured against the larger number. For falling values, use our percentage decrease calculator.

Special cases

• The original value is 0. The percentage increase cannot be worked out, because the formula divides by 0.
• The new value is smaller. The answer is negative, which is a decrease. The calculator shows the size of the drop.
• The new value is more than double. The increase is above 100 percent. Going from 100 to 300 is a 200 percent increase.
• The original value is negative. The formula uses the size of the original value so that a move upward still shows as an increase. Read these results with care, because a percent change from a negative number can be confusing.
• The two values are the same. The increase is 0 percent.

Quick mental maths for percent increases

You can often add a percent in your head. Ten percent of a number is found by moving the decimal point one place to the left, so 10 percent of 80 is 8. Five percent is half of that, which is 4. Twenty percent is double the 10 percent amount, which is 16. Twenty five percent is a quarter of the number, which is 20. Add the amount you found to the original number to get the new value. For 80 plus 25 percent, add 20 to get 100.

To check a percent increase, ask whether the answer makes sense. If the new number is a little larger than the old one, the increase should be small. If the new number is about double, the increase should be close to 100 percent.

Where percentage increase is used

You will meet percentage increase in everyday money and in work. It is used for price rises and inflation, pay rises, rent changes, growth in sales or website visitors, population growth, grade improvements and investment returns. Seeing a change as a percentage makes it easier to compare, because a rise of 50 on a price of 100 is large, while a rise of 50 on a price of 10,000 is small.

Common mistakes

• Dividing by the new value instead of the original value.
• Mixing up percentage points and percent.
• Subtracting the percent from the final value to find the original number.
• Adding the percent twice in repeated increases, instead of multiplying.
• Rounding too early. Keep the full number until the last step.

Frequently asked questions

About this calculator

Written by Umar Khan. The calculator uses the standard formulas shown on this page and rounds results to four decimal places at most. It works with whole numbers and decimals, and it runs in your browser, so nothing you enter is stored or sent.

About the author

Umar Khan is a PhD student in engineering at NTNU. He writes and checks the maths on UtilMora.

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