How to Calculate Percentage Increase and Decrease: Formula and Worked Examples

To calculate a percentage increase or decrease, divide the difference between the two values by the original value, then multiply by 100. The formula is ((new value − original value) ÷ original value) × 100. If the result is positive, you have an increase; if it is negative, you have a decrease. For example, going from 80 to 100 is a 25% increase, while going from 100 to 80 is a 20% decrease.

The key idea to hold onto is that the change is always measured against the original value, not the new one. That single detail is responsible for most of the wrong answers people get. This guide walks through the formula, three common real-world examples, and the mistakes worth avoiding. If you just want the number, the percentage change calculator on Quialo does it instantly in your browser.

The Percentage Change Formula

Whether the value goes up or down, you use the same formula:

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

Work it in three steps:

1. Find the difference. Subtract the original value from the new value.
2. Divide by the original. This turns the raw difference into a proportion of where you started.
3. Multiply by 100. This converts the proportion into a percentage.

A positive answer is an increase, a negative answer is a decrease. You can drop the minus sign and simply call it a decrease in plain language.

Worked Example: A Price Increase

Suppose a monthly subscription rises from 80 to 100.

• Difference = 100 − 80 = 20
• Divide by original = 20 ÷ 80 = 0.25
• Multiply by 100 = 0.25 × 100 = 25%

So the price went up by 25%. Notice that the difference of 20 is compared against the starting price of 80, which is why the answer is 25% and not 20%.

Worked Example: A Price Decrease

Now reverse it: the price falls from 100 back to 80.

• Difference = 80 − 100 = −20
• Divide by original = −20 ÷ 100 = −0.20
• Multiply by 100 = −20%

The price dropped by 20%. This is the part that surprises people. A move from 80 to 100 and a move from 100 to 80 are the same 20 units in size, but they are different percentages (25% versus 20%) because the original value is different each time. Increases and decreases are not symmetric, which is exactly why a 50% drop needs a 100% rise to recover.

Worked Example: A Test Score

Percentage change is useful for tracking progress, not just money. Say a student scored 45 on a first test and 54 on the next.

• Difference = 54 − 45 = 9
• Divide by original = 9 ÷ 45 = 0.20
• Multiply by 100 = 20%

The score improved by 20%. If you instead want to express a single score as a percentage of the total marks available (for example 54 out of 60), that is a different calculation, and the percentage calculator handles those "what percent of" questions directly.

Worked Example: Growth Over Time

For business or population figures the method is identical. If monthly active users grow from 1,250 to 1,500:

• Difference = 1,500 − 1,250 = 250
• Divide by original = 250 ÷ 1,250 = 0.20
• Multiply by 100 = 20%

That is 20% growth. When you need to compare several periods, the percentage change calculator lets you plug in each pair of values without redoing the arithmetic by hand.

Working Backwards From a Percentage

Sometimes you know the percentage and one value, and want the other. To apply a known increase, multiply the original by (1 + the rate as a decimal). To apply a decrease, multiply by (1 − the rate).

• Increase 80 by 25%: 80 × 1.25 = 100
• Decrease 100 by 20%: 100 × 0.80 = 80

These mirror the examples above, which is a handy way to check your work. If applying the percentage does not return you to the value you started from, one of the steps is off.

Common Mistakes to Avoid

Dividing by the new value. Always divide by the original (starting) value. Dividing by the new value gives a different, incorrect percentage.

Forgetting the direction. A negative result means a decrease. Keep track of which value came first in time so up and down are not reversed.

Treating increases and decreases as symmetric. As shown above, a 25% rise and a 20% fall can connect the same two numbers. Recovering a percentage drop always needs a larger percentage rise.

Mixing percentage points with percent. If a rate moves from 4% to 6%, that is a 2 percentage point change but a 50% increase. They answer different questions, so state which one you mean.

FAQ

What is the formula for percentage increase and decrease?

Use ((new value − original value) ÷ original value) × 100. A positive result is an increase and a negative result is a decrease. The same formula covers both directions.

Why is 80 to 100 a 25% increase but 100 to 80 only a 20% decrease?

The change is measured against the original value, and the originals differ. From 80, a 20 unit rise is 20 ÷ 80 = 25%. From 100, a 20 unit fall is 20 ÷ 100 = 20%. Equal-sized moves give different percentages.

How do I reverse a percentage change?

Multiply the original value by (1 + rate) for an increase or (1 − rate) for a decrease, using the rate as a decimal. For example, 80 × 1.25 = 100, and 100 × 0.80 = 80.

What is the difference between percent and percentage points?

A percentage point is the plain difference between two percentages, while a percent change measures that difference relative to the starting percentage. Moving from 4% to 6% is 2 percentage points and a 50% increase.