How to Calculate Percentage Change (Increase and Decrease) With Examples

Percentage change tells you how much something went up or down compared to where it started. You use it to understand price increases, sales, discounts, savings, test scores, and more.

The formula is simple:

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

It takes just three steps. If you would rather skip the math, our free percentage calculator does it for you and shows every step.

The percentage change formula, step by step

1. Subtract the old value from the new value.
2. Divide that answer by the old value.
3. Multiply by 100 to turn it into a percentage.

If the answer is positive, it is a percentage increase.

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

That is all there is to it. Let's try some examples.

Worked examples

Example 1: A price goes up

Your monthly phone bill goes from $40 to $46. What is the percentage change?

• Step 1: 46 − 40 = 6
• Step 2: 6 ÷ 40 = 0.15
• Step 3: 0.15 × 100 = 15%

Your bill went up by 15%.

Example 2: A price goes down

A jacket goes on sale. The price drops from $80 to $60.

• Step 1: 60 − 80 = −20
• Step 2: −20 ÷ 80 = −0.25
• Step 3: −0.25 × 100 = −25%

The price went down by 25%.

Example 3: Test scores

Your test score goes from 64 to 72.

• Step 1: 72 − 64 = 8
• Step 2: 8 ÷ 64 = 0.125
• Step 3: 0.125 × 100 = 12.5%

Your score went up by 12.5%.

Example 4: Money in savings

Your savings grow from $250 to $400.

• Step 1: 400 − 250 = 150
• Step 2: 150 ÷ 250 = 0.6
• Step 3: 0.6 × 100 = 60%

Your savings went up by 60%.

Example 5: Something more than doubles

A small business had 50 customers last month and 150 this month.

• Step 1: 150 − 50 = 100
• Step 2: 100 ÷ 50 = 2
• Step 3: 2 × 100 = 200%

That is a 200% increase. The number of customers tripled.

Percentage increase vs. percentage decrease

You use the same formula for both. The only difference is whether your answer is positive or negative.

Some people like to use two separate formulas:

• Percentage increase = (new − old) ÷ old × 100
• Percentage decrease = (old − new) ÷ old × 100

Both give you the same answers. The second one just gives you a positive number for a decrease.

Common mistakes to avoid

Mistake 1: Dividing by the wrong number

Always divide by the old value (where you started), not the new value.

For example, going from 80 to 60 is a 25% decrease. But going from 60 to 80 is a 33.3% increase. The difference is 20 both times, but 20 is a bigger part of 60 than it is of 80.

Mistake 2: Thinking percentages cancel out

A 50% increase and then a 50% decrease does not take you back to where you started.

• Start with 100.
• Increase by 50%: 100 + 50 = 150.
• Decrease by 50%: 150 − 75 = 75.

You end up at 75, not 100. That is because the second 50% was taken from 150, not from 100.

Mistake 3: Mixing up percent and percentage points

If an interest rate goes from 4% to 5%, it went up by 1 percentage point. But compared to where it started, it went up by 25% (1 ÷ 4 × 100).

News stories sometimes mix these up. Always check which one is meant.

Mistake 4: Starting from zero

You cannot find the percentage change from zero, because you cannot divide by zero. If something goes from 0 to 10, just say it went up by 10.

Mistake 5: Forgetting the negative sign

If your answer is negative, it is a decrease. Do not drop the minus sign unless you say the word "decrease."

Tips for estimating percentage change in your head

You do not always need an exact answer. These tricks help you get close fast.

• Find 10% first. Move the decimal point one place to the left. 10% of 80 is 8. If a price went up by about 8, it went up about 10%.
• Use halves and doubles. If the change is half of the old value, it is a 50% change. If the change is the same as the old value, it is a 100% change.
• Round the numbers. A change from 49 to 61 is close to a change from 50 to 60. That is a change of 10 on 50, or about 20%.
• Check if it doubled. If the new value is twice the old value, the increase is 100%. Three times the old value is a 200% increase.

Other useful percentage formulas

Percentage change is just one kind of percent math. Here are a few others you might need.

How to find a percentage of a number

To find 15% of 240:

• 15 ÷ 100 = 0.15
• 0.15 × 240 = 36

This is the same math you use to figure out a tip. Our guide on how to calculate a tip quickly shows easy tricks for doing it in your head.

How to find what percent one number is of another

What percent is 18 of 60?

• 18 ÷ 60 = 0.3
• 0.3 × 100 = 30%

How to find the original price before a discount

Something costs $68 after a 15% discount. What was the original price?

• 1 − 0.15 = 0.85
• 68 ÷ 0.85 = $80

Watch out: Taking 15% of $68 and adding it back gives you the wrong answer ($78.20).

How to find the original price before an increase

Something costs $115 after a 15% price increase. What was the original price?

• 1 + 0.15 = 1.15
• 115 ÷ 1.15 = $100

Quick reference table

How to calculate percentage change on a calculator

Using a phone or basic calculator:

1. Type the new value.
2. Press − and type the old value.
3. Press =.
4. Press ÷ and type the old value again.
5. Press =.
6. Press × and type 100.
7. Press =.

For example, for a change from 40 to 46: 46 − 40 = 6, then 6 ÷ 40 = 0.15, then 0.15 × 100 = 15. That is a 15% increase.

How to calculate percentage change in Excel or Google Sheets

1. Put the old value in cell A2.
2. Put the new value in cell B2.
3. In cell C2, type: =(B2-A2)/A2
4. Press Enter.
5. Format cell C2 as a percentage by clicking the % button in the toolbar.

You can drag the formula down to work out the change for a whole list of numbers.

Percentage change vs. percentage difference

These two sound alike, but they are used in different ways.

Percentage change is used when there is a clear "before" and "after." For example, a price last year and a price this year. You always divide by the old value.

Percentage difference is used when you compare two numbers and neither one is the starting point. For example, the price of milk at two different stores. For this, you divide the difference by the average of the two numbers.

Percentage difference = difference ÷ average of the two numbers × 100

Example: Milk costs $4 at one store and $5 at another.

• Difference: 5 − 4 = 1
• Average: (4 + 5) ÷ 2 = 4.5
• 1 ÷ 4.5 × 100 = about 22.2%

If you just want to know how much more the second store charges than the first, use percentage change instead: 1 ÷ 4 × 100 = 25% more.

Real-life example: which sale is better?

Two stores are selling the same pair of sneakers.

• Store A: The price drops from $90 to $63.
• Store B: The price drops from $80 to $60.

Which one is the bigger sale?

Store A: (63 − 90) ÷ 90 × 100 = −27 ÷ 90 × 100 = 30% off

Store B: (60 − 80) ÷ 80 × 100 = −20 ÷ 80 × 100 = 25% off

Store A has the bigger percentage discount. But Store B still has the lower final price ($60 vs. $63). This shows why it is smart to look at both the percent off and the final price before you buy.

Practice problems (with answers)

Try these on your own. The answers are below.

1. A video game costs $50. The price goes up to $60. What is the percentage change?
2. A town had 2,000 people. Now it has 1,800. What is the percentage change?
3. You ran a mile in 10 minutes. Now you run it in 8 minutes. What is the percentage change in your time?
4. Your allowance goes from $20 a week to $25 a week. What is the percentage change?
5. A plant was 12 inches tall. Now it is 18 inches tall. What is the percentage change?

Answers:

1. (60 − 50) ÷ 50 × 100 = 20% increase
2. (1,800 − 2,000) ÷ 2,000 × 100 = 10% decrease
3. (8 − 10) ÷ 10 × 100 = 20% decrease (you got faster)
4. (25 − 20) ÷ 20 × 100 = 25% increase
5. (18 − 12) ÷ 12 × 100 = 50% increase

You can check your answers with our free percentage change calculator.

Where you will use percentage change

• Shopping: How much did the price go down in a sale?
• Bills: How much did your electric bill go up this year?
• Pay: How big is your raise?
• School: How much did your grade improve?
• Savings: How much did your savings grow?
• Business: How much did sales grow this month?
• Health: How much weight did you lose or gain?

The bottom line

To find percentage change, subtract the old value from the new value, divide by the old value, and multiply by 100. A positive answer is an increase, and a negative answer is a decrease. Always divide by the old value, and remember that percentages do not cancel out. For quick answers without the math, try the TimeToNote percentage change calculator, which shows the formula next to every result.