How to Calculate Percentage Change: Formula & Examples

Knowing how to calculate percentage change helps you measure how much a value has increased or decreased relative to where it started. The standard method is to subtract the original value from the new value, divide the difference by the original value, and multiply by 100.

The formula is:

Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100

A positive result means the value increased. A negative result means it decreased.

If you want to calculate the result instantly, you can use the CalcMax Percentage Calculator, part of CalcMax's broader collection of free UK calculation tools.

How to Calculate Percentage Change Step by Step

The percentage change formula compares a new value with an original or starting value.

Use these four steps:

1. Find the difference between the new value and the original value.

2. Divide that difference by the original value.

3. Multiply the result by 100.

4. Add the % symbol.

For example, suppose a price rises from £80 to £100.

First calculate the difference:

£100 − £80 = £20

Then divide the difference by the original value:

20 ÷ 80 = 0.25

Multiply by 100:

0.25 × 100 = 25%

So the percentage change is a 25% increase.

Percentage Change Formula

The standard percentage change formula is:

Percentage Change = ((New Value − Original Value) ÷ Original Value) × 100

The important part is that you divide by the original value, not the new value.

This is because percentage change measures the size of the change relative to the starting point.

What Each Part Means

Original value: the starting number.

New value: the number after the change.

Difference: how much the value changed.

Percentage change: the difference expressed as a percentage of the original amount.

If you regularly work with percentage problems, the Percentage Calculator can help you check calculations quickly.

Percentage Increase Example

Suppose a business's monthly sales increase from £4,000 to £5,000.

Step 1: Calculate the Difference

£5,000 − £4,000 = £1,000

Step 2: Divide by the Original Value

£1,000 ÷ £4,000 = 0.25

Step 3: Multiply by 100

0.25 × 100 = 25%

The business experienced a 25% increase in monthly sales.

This same method can be used for:

• salary increases

• product prices

• website traffic

• investment values

• business revenue

• exam scores

• population data

• household expenses

Percentage Decrease Example

The same formula works when a value decreases.

Suppose the price of an item drops from £250 to £200.

Calculate the difference:

£200 − £250 = −£50

Divide by the original value:

−£50 ÷ £250 = −0.20

Multiply by 100:

−0.20 × 100 = −20%

The result is a 20% decrease.

You can also describe the result without the negative sign by saying:

The price decreased by 20%.

Percentage Increase vs Percentage Decrease

Percentage increase and percentage decrease use the same core formula.

ChangeExampleResult£100 → £120Increase+20%£100 → £80Decrease−20%50 → 75Increase+50%50 → 25Decrease−50%

The sign tells you the direction:

• positive percentage = increase

• negative percentage = decrease

• 0% = no change

Why Do You Divide by the Original Value?

This is one of the most common sources of mistakes.

Consider a value increasing from 40 to 50.

The change is:

50 − 40 = 10

To find percentage change:

10 ÷ 40 × 100 = 25%

You divide by 40 because 40 was the starting point.

If you divide by 50 instead:

10 ÷ 50 × 100 = 20%

you are measuring the difference relative to the new value, which is not the standard percentage change calculation.

The denominator should normally be the original value.

How to Calculate Percentage Change Between Two Numbers

If you simply have two numbers, first identify which one represents the starting value and which one represents the later value.

For example:

Original value: 120
New value: 150

Then:

150 − 120 = 30

30 ÷ 120 = 0.25

0.25 × 100 = 25%

Therefore, the percentage change from 120 to 150 is 25%.

For faster calculations, use CalcMax's free percentage calculation tool.

How to Calculate Percentage Change in Price

Percentage change is commonly used to compare prices.

Suppose your monthly energy bill changes from £120 to £138.

Difference:

£138 − £120 = £18

Divide:

£18 ÷ £120 = 0.15

Multiply:

0.15 × 100 = 15%

Your bill increased by 15%.

The same calculation is useful when comparing:

• supermarket prices

• rent

• fuel costs

• subscriptions

• insurance premiums

• product prices

For broader mathematical calculations, CalcMax also provides a dedicated range of Maths calculators, including percentage, algebra, fractions and scientific calculation tools.

How to Calculate Percentage Change in Salary

Suppose your annual salary rises from £30,000 to £33,000.

Difference:

£33,000 − £30,000 = £3,000

Divide by original salary:

£3,000 ÷ £30,000 = 0.10

Multiply by 100:

10%

So your salary increased by 10%.

Percentage change can help you compare pay rises even when salaries are very different.

For example:

A £2,000 raise on £20,000 equals:

10%

A £2,000 raise on £40,000 equals:

5%

The cash increase is identical, but the percentage increase is not.

How to Calculate Percentage Change in Business Data

Percentage change is particularly useful when comparing performance over time.

Businesses may calculate changes in:

• revenue

• profit

• expenses

• sales

• customers

• conversions

• website traffic

• average order value

Suppose website traffic increases from 25,000 visitors to 30,000 visitors.

Difference:

30,000 − 25,000 = 5,000

Divide by the original value:

5,000 ÷ 25,000 = 0.20

Multiply by 100:

20%

Traffic increased by 20%.

Percentage change is useful because it gives context that raw numbers alone may not provide.

Percentage Change vs Percentage Difference

These two calculations are often confused.

Percentage Change

Use percentage change when comparing an old value with a new value.

Example:

January revenue → February revenue

The original value acts as the reference point.

Percentage Difference

Percentage difference is more commonly used when comparing two values where neither is clearly the starting value.

Instead of dividing by one original number, the calculation generally uses the average of the two values as the reference.

So if your question involves:

before vs after

or:

old vs new

percentage change is usually the appropriate calculation.

Percentage Change vs Percentage Points

Percentage change should also not be confused with percentage-point change.

Suppose an interest rate increases from 4% to 5%.

The percentage-point increase is:

5% − 4% = 1 percentage point

But the percentage change is:

(5 − 4) ÷ 4 × 100 = 25%

So the interest rate increased by:

• 1 percentage point

• or 25% relative to its original value

These mean different things.

What Happens If the Original Value Is Zero?

The standard percentage change formula cannot be used when the original value is zero because it would require division by zero.

For example:

Original value = 0
New value = 100

Trying to calculate:

(100 − 0) ÷ 0

is mathematically undefined.

You can say the value increased from zero to 100, but you should not describe it using the standard percentage change formula.

This is an important limitation to remember when working with data.

Can Percentage Change Be More Than 100%?

Yes.

Suppose a company's monthly orders increase from 100 to 250.

Difference:

250 − 100 = 150

Then:

150 ÷ 100 × 100 = 150%

The number of orders increased by 150%.

A percentage increase can exceed 100% whenever the increase is greater than the entire original value.

For example:

• 100 → 200 = 100% increase

• 100 → 250 = 150% increase

• 100 → 300 = 200% increase

Common Percentage Change Mistakes

Using the New Value as the Denominator

Wrong:

Change ÷ new value

Correct:

Change ÷ original value

Forgetting to Multiply by 100

A decimal such as:

0.15

becomes:

15%

after multiplying by 100.

Ignoring the Direction of Change

A negative result represents a decrease.

Confusing Percentage Change With Percentage Points

A change from 20% to 25% is:

5 percentage points

but:

25% percentage increase

because:

(25 − 20) ÷ 20 × 100 = 25%

Reversing the Starting and Final Values

Percentage change is directional.

Going from 50 to 100 is:

100% increase

Going from 100 to 50 is:

50% decrease

These are not opposites of equal magnitude because the starting values are different.

When Is Percentage Change Useful?

Percentage change is useful whenever you want to compare how a value has changed relative to its starting point.

Common applications include:

Finance

• investment returns

• savings growth

• price changes

• inflation

• interest rates

CalcMax's UK Inflation Calculator is an example of how percentage-based changes can help explain changes in purchasing power over time.

Education

Students may use percentage calculations for:

• test scores

• grade improvements

• statistics

• GCSE maths

• A-Level maths

The Fractions Calculator can also help when calculations involve fractions that need converting into decimals before applying percentage formulas.

Business

Businesses commonly track percentage changes in:

• revenue

• costs

• customers

• leads

• conversion rates

Everyday Life

You may calculate changes in:

• household bills

• shopping prices

• weight

• travel costs

• fuel consumption

How to Check a Percentage Change Calculation

A simple way to check your calculation is to convert the percentage back into an amount.

Suppose £200 increases by 15%.

Calculate 15% of £200:

£200 × 0.15 = £30

Add the increase:

£200 + £30 = £230

So if your original calculation showed that £200 → £230 represents a 15% increase, the result checks out.

You can also verify your answer with the CalcMax Percentage Calculator.

CalcMax provides free browser-based calculators across maths, finance, health, education and other categories, with results calculated directly from user inputs.

Frequently Asked Questions

How do you calculate percentage change?

Subtract the original value from the new value, divide the difference by the original value, and multiply by 100.

For example, changing from 50 to 60 gives:

(60 − 50) ÷ 50 × 100 = 20%

How do you calculate percentage increase?

Use the same percentage change formula. If the new value is larger than the original value, the result will be positive and represents a percentage increase.

How do you calculate percentage decrease?

Subtract the original value from the new value and divide by the original value. A negative result indicates a decrease. You can report the magnitude without the negative sign when saying that something “decreased by” a certain percentage.

Can percentage change be negative?

Yes. A negative percentage change means the new value is lower than the original value.

For example:

100 → 75 = −25%

or a 25% decrease.

What is the difference between percentage change and percentage difference?

Percentage change compares a new value against a clearly defined original value. Percentage difference generally compares two values without treating either one as the starting point.

Conclusion

Learning how to calculate percentage change is straightforward once you remember the correct reference point.

Use:

new value − original value → divide by original value → multiply by 100

A positive result indicates an increase, while a negative result indicates a decrease.

Percentage change is useful for comparing prices, salaries, sales, investments, grades, business data and many other values. Just remember that the standard formula cannot be used when the original value is zero and that percentage change is different from percentage-point change.

For a faster way to check your calculations, use the CalcMax Percentage Calculator. You can also explore CalcMax's free UK calculators for maths, finance, health, education and everyday calculations.