Prices go up. Salaries change. Your savings grow, and the number on the scale moves. When you want to say how big a change was, a percentage is the clearest way. A change from 50 to 65 is easy to see, but a change from 4,380 to 4,715 is not. A percent change puts both on the same scale.

Our Percentage calculator can work out percent change for you. Here is how to do it yourself.

The percent change formula

Percent change = (new value − old value) ÷ old value × 100

• If the answer is positive, it is an increase.

• If the answer is negative, it is a decrease.

Always divide by the old value, the one you started with.

Example 1: a price goes up

A jacket costs $50 and goes up to $65.

• Change: 65 − 50 = 15

• 15 ÷ 50 = 0.30

• 0.30 × 100 = 30% increase

Example 2: a price goes down

A pair of shoes drops from $80 to $60.

• Change: 60 − 80 = −20

• −20 ÷ 80 = −0.25

• −0.25 × 100 = 25% decrease

Example 3: a pay rise

Your pay goes from $4,000 to $4,300 a month.

• Change: 300

• 300 ÷ 4,000 = 0.075

• 7.5% increase

Why up 25% and down 25% don't cancel out

This surprises many people. Start with $100. Go up 25% and you have $125. Now go down 25% from there. A quarter of $125 is $31.25, so you end up with $93.75, not $100.

The reason is that the second percentage is taken from a bigger number. This matters in investing. If an investment drops 50%, it needs to go up 100% to get back to where it was.

Percent change vs percentage points

These two are often confused. If an interest rate goes from 4% to 6%:

• It went up by 2 percentage points (6 − 4).

• It went up by 50 percent (2 ÷ 4).

News reports use both, so read carefully.

What if the old value is zero?

You can't calculate it. Dividing by zero has no answer. If something goes from 0 to 20, you can say it went up by 20, but a percent change is not defined.

Quick way to find a number after a change

You don't always need the formula. To add a percent, multiply by 1 plus the percent as a decimal. To take one off, multiply by 1 minus the percent.

• $200 plus 15%: 200 × 1.15 = $230

• $200 minus 15%: 200 × 0.85 = $170

Where it is useful

• Checking a price rise or a sale

• Tracking weight or fitness numbers

• Comparing sales or website traffic month to month

• Looking at how a stock or savings account changed

• School and science projects

How to use the calculator

1. Enter the old (starting) value.

2. Enter the new value.

3. Read the percent change, and whether it is an increase or a decrease.

Common questions

Which number goes first? The starting number goes first. If you swap them, you get a different answer.

Can a decrease be more than 100%? No. If something falls to zero, that is a 100% decrease. It can't fall below that for a normal quantity like a price. An increase can be over 100%, though.

What is the difference between percent change and percent difference? Percent change has a clear "before" and "after". Percent difference compares two values when neither is the starting point.

More tools

Our Advanced Calculator home page has all the tools in one place. For related ones, look at our math calculators.