how do you calculate percentage change

What is percentage change?

Percentage change tells you how much something has increased or decreased compared with where it started. It is one of the most useful math tools in personal finance, business, school, and everyday life. You can use it to track stock returns, salary growth, price drops, exam score improvements, and much more.

Instead of just saying “the value changed by 20,” percentage change answers the more helpful question: “20 out of what?” A $20 increase on a $100 item is very different from a $20 increase on a $1,000 item.

The percentage change formula

The standard formula is:

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

In words:

• Find the difference between the new value and the original value.
• Divide that difference by the original value.
• Multiply by 100 to convert to a percent.

Step-by-step example

Example: A product rises from $50 to $65

• Original value: 50
• New value: 65
• Difference: 65 − 50 = 15
• Divide by original: 15 ÷ 50 = 0.30
• Convert to percent: 0.30 × 100 = 30%

Result: The value increased by 30%.

How to interpret the result

• If the percentage change is positive, it is an increase.
• If it is negative, it is a decrease.
• If it is 0%, there was no change.

For example, if your calculation gives -12%, that means the value dropped by 12% from the starting point.

Percentage increase vs. percentage decrease

Increase

If the new value is larger than the old value, you have a percentage increase. Example: from 200 to 260 is a 30% increase.

Decrease

If the new value is smaller than the old value, you have a percentage decrease. Example: from 200 to 150 is a 25% decrease.

Common mistakes to avoid

• Using the new value in the denominator: Always divide by the original value (starting point).
• Forgetting to multiply by 100: If you stop early, you get a decimal, not a percent.
• Mixing up percentage points and percent change: These are not the same thing.
• Ignoring signs: A negative value means decrease.

Special cases

What if the original value is zero?

Percentage change is not defined when the original value is zero because division by zero is impossible. If something goes from 0 to a positive number, you can describe it as a jump from zero, but not a standard finite percentage change.

What about negative starting values?

Negative values can appear in finance and science (for example, losses or temperatures). This calculator uses the absolute value of the starting number in the denominator so the direction (increase/decrease) is easier to interpret for everyday use.

Real-world uses of percentage change

• Comparing monthly expenses
• Tracking business revenue growth
• Measuring investment performance
• Evaluating test score improvements
• Monitoring website traffic trends

Quick recap

To calculate percentage change:

1. Subtract old value from new value.
2. Divide by old value.
3. Multiply by 100.

That’s it. Use the calculator above whenever you want a fast, accurate answer.