Percentage Increase / Decrease Formula

Use the percentage increase or decrease formula when you want to compare a change with the starting value. The standard formula is

$$\text{percentage change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\%$$

If the result is positive, you have a percentage increase. If the result is negative, you have a percentage decrease.

This formula is only defined when the original value is not $0$. In most school and everyday examples, the original value is also positive.

What Percentage Change Measures

The key idea is "change relative to where you started." First find how much the value changed. Then compare that change with the original value, not the new one.

A change of $20$ means something very different if you started at $80$ than if you started at $400$. That is why the denominator matters.

How To Calculate Percentage Increase Or Decrease

1. Find the change: $\text{new value} - \text{original value}$.
2. Divide by the original value.
3. Multiply by $100\%$.
4. Read the sign.

Positive means increase. Negative means decrease.

Worked Example: From $80$ To $100$

A jacket costs $80$ and then rises to $100$.

Start with the change:

$$100 - 80 = 20$$

Now compare that change with the original price:

$$\frac{20}{80} = 0.25$$

Convert to a percent:

$$0.25 \times 100\% = 25\%$$

So the price increased by $25\%$.

Now reverse the situation. Going from $100$ down to $80$ gives

$$\frac{80 - 100}{100} \times 100\% = -20\%$$

So returning from $100$ to $80$ is a $20\%$ decrease, not a $25\%$ decrease. The percentages are different because the starting values are different.

Common Mistakes

Using The Wrong Denominator

The denominator should be the original value. If you divide by the new value, you are measuring a different ratio.

Assuming The Reverse Percent Must Match

A $25\%$ increase does not reverse with a $25\%$ decrease. The starting value changes, so the percentages usually do not match.

Forgetting The $0$ Condition

If the original value is $0$, the standard percentage change formula is undefined because division by $0$ is not allowed.

When You Use This Formula

You will see percentage increase and decrease in prices, discounts, population changes, test scores, and simple business or science reports. It is useful whenever you want to compare changes fairly across different starting values.

Try A Similar Problem

Try your own version with a price dropping from $60$ to $45$. If you want to check each step after setting it up yourself, a math solver can help you confirm that you used the original value in the denominator.