Percentage Increase Calculator

What Is a Percentage Increase?

A percentage increase expresses how much a quantity has grown relative to where it started. Saying a rent rose by $150 tells you the amount, but saying it rose by 10% tells you how large that change is compared with the old rent, which makes it possible to compare changes of very different sizes. The same idea run in reverse gives a percentage decrease, and together they are called the percentage change.

Everything depends on choosing the right starting point. The original value is the base, and the change is always divided by it. That is why a rise from 80 to 100 is a 25% increase, while the fall from 100 back to 80 is only a 20% decrease: the same 20-unit gap is measured against a different base each time.

The Percentage Increase Formula

Subtract the original value from the new value, divide by the original value, and multiply by 100. With the default figures, (100 − 80) ÷ 80 = 0.25, and 0.25 × 100 = 25%, so going from 80 to 100 is a 25% increase. The multiplier, 100 ÷ 80 = 1.25, says the same thing in another form: the new value is 125% of the original.

The percent change formula gives a negative answer when the value falls. Going from 80 to 60 gives (60 − 80) ÷ 80 = −0.25, a 25% decrease. If the original value is zero the formula would divide by zero, so no percentage change can be stated; report the absolute change instead.

Percentage change = (New − Original) ÷ |Original| × 100

New

the later or final value

Original

the starting value that the change is measured against

A positive result is a percentage increase and a negative result is a percentage decrease. The percentage difference instead divides |A − B| by the average of the two values.

Percentage Change vs Percentage Difference

Use percentage change when there is a clear before and after, such as last year's sales and this year's. Use the percentage difference calculator when the two numbers are on an equal footing, such as the prices of the same item in two shops. The percentage difference divides the gap by the average of the two values, so swapping them gives the same answer.

For 80 and 100 the gap is 20 and the average is 90, so the percentage difference is 20 ÷ 90 × 100 ≈ 22.22%. That sits between the 25% increase and the 20% decrease you get by taking either number as the base.

Increasing or Decreasing a Number by a Percent

To add a percentage, multiply by one plus the rate as a decimal: 80 increased by 25% is 80 × 1.25 = 100. To remove a percentage, multiply by one minus the rate: 80 decreased by 25% is 80 × 0.75 = 60. Working backwards needs division, not subtraction. If a price is $100 after a 25% markup, the original was 100 ÷ 1.25 = $80, not 100 − 25 = $75.

Common Mistakes With Percentages

A few traps account for most errors when people work out percentage changes by hand:

• Dividing by the new value instead of the original. That gives the change back to the start, not the change from it.
• Adding successive percentage changes. A 10% rise followed by a 10% fall leaves you at 99% of the start, because 1.10 × 0.90 = 0.99.
• Confusing percent with percentage points. An interest rate moving from 4% to 5% is a rise of 1 percentage point but a 25% increase in the rate.
• Expecting increases and decreases to cancel. A 50% fall needs a 100% rise to recover.

Frequently asked questions