Practical guide
How to Calculate Percentage Increase and Decrease
Percentage change describes how large a change is compared with the starting value. It is useful for checking price changes, scores, measurements, and other comparisons, but the direction of the calculation matters. This guide shows the formula for increases and decreases, works through examples, and explains how to avoid mixing up a percentage amount with a final value.
By Ather Saud · Updated on November 1, 2026
The percentage-change formula
Subtract the original value from the new value. Divide that difference by the original value, then multiply by 100. In symbols: percentage change = ((new value − original value) ÷ original value) × 100. A positive answer represents an increase, a negative answer represents a decrease, and zero means the values are equal.
The original value belongs in the denominator because percentage change asks how large the change is relative to where you started. If the starting value is zero, division by zero is undefined, so there is no ordinary finite percentage-change result. A later value of zero can be used: changing from 40 to zero is a 100% decrease.
Worked examples
Increase: a score changes from 80 to 100. The difference is 100 − 80 = 20. Divide 20 by the starting value 80 and multiply by 100: 20 ÷ 80 × 100 = 25%. The score increased by 25% relative to its original value.
Decrease: a price changes from 240 to 204. The difference is 204 − 240 = −36. Then −36 ÷ 240 × 100 = −15%. This is a 15% decrease. The amount of the decrease is 36; the percentage decrease is 15%; the new price is 204. Those are three related but distinct values.
A percentage of a value is another operation. Fifteen percent of 240 is 240 × 15 ÷ 100 = 36. Subtracting that amount gives 204. The Percentage Calculator includes modes for finding a percentage, finding what percentage one number is of another, calculating change, and adding or subtracting a percentage.
Percent versus percentage points
Percent describes a relative amount, while percentage points describe the arithmetic gap between two percentages. If a rate rises from 10% to 12%, the difference is 2 percentage points. Relative to the starting 10%, the increase is 20% because 2 ÷ 10 × 100 = 20%. The two descriptions answer different questions.
When you read a report or compare a grade, check whether it asks for a percentage-point difference or percentage change. Avoid describing a move from 10% to 12% as simply a “2% increase,” because that phrase can be read in more than one way.
Common mistakes and things to check
The most common error is dividing by the new value instead of the original. Another is reversing the values: the formula’s first input is the starting amount and its second is the ending amount. Use consistent units, such as comparing kilograms with kilograms, and do not compare a gross figure with a net figure unless that is the question you intend to answer.
A 20% increase followed by a 20% decrease does not return to the original number. Starting at 100, a 20% increase gives 120; decreasing 120 by 20% gives 96 because the second change is calculated from 120. The base changes after each operation.
A quick workflow
Write the original and new values with labels before calculating. Decide whether you need the change amount, the percentage change, or the result after adding or subtracting a rate. Run the correct operation, then check the sign and units. If you are reporting the result, include the baseline so someone reading it can understand what the percentage compares.
For discounts, taxes, and fees, confirm what amount the rate applies to. A calculator can apply a percentage to an input, but it cannot know whether a shop, school, or service applies the rate before or after another charge. That rule comes from the situation, not the arithmetic.
Explain the baseline when sharing a result
A percentage is easier to interpret when the baseline is clear. Instead of writing only “up 25%,” say what changed and from which starting figure, such as “the score increased from 80 to 100, a 25% increase.” This makes the direction and denominator visible to another reader. It also prevents confusion between a percentage-point difference and a relative percentage change.
When values are rounded, calculate with the original values if you have them. Rounding the starting and ending numbers first can slightly change the final percentage. If you only have rounded data, state that the result is based on those displayed figures. The calculator returns up to four decimal places and removes trailing zeros, so a concise display does not mean the underlying comparison was exact to that many decimal places.
| Question | Calculation | Answer |
|---|---|---|
| 15% of 240 | 240 × 15 ÷ 100 | 36 |
| Change from 80 to 100 | (100 − 80) ÷ 80 × 100 | 25% increase |
| Change from 240 to 204 | (204 − 240) ÷ 240 × 100 | 15% decrease |
Key takeaways
- For percentage change, divide by the original value.
- A negative percentage change means a decrease.
- Percentage points and percent change are different comparisons.
Frequently asked questions
Can percentage change be negative?
Yes. When the new value is lower than the original, the formula returns a negative percentage, which represents a decrease.
Can I calculate a percentage change from zero?
No ordinary percentage-change result exists from a zero starting value because the formula divides by the original value.
Is a 2 percentage-point rise the same as a 2% increase?
No. Percentage points are the direct difference between two percentages. A percent increase compares that difference with the starting percentage.