Calculating change...
Enter two values to compare them, or choose an increase or decrease mode.
What Is Percentage Increase or Decrease?
Percentage increase and percentage decrease measure how much a value changed relative to its original value. The difference between the old and new values is divided by the magnitude of the original value, then multiplied by 100. A positive result indicates an increase, a negative result indicates a decrease, and zero means there was no change.
This calculation is useful for salary raises, price changes, discounts, exam scores, revenue growth, website traffic, and investment values. It answers a different question from finding a simple percentage of a number: percent change compares two values across time or conditions.
How Percentage Increase and Decrease Work
Each chart shows real proportional bars, exact values, and the formula used.
80 100
((100 - 80) / 80) x 100 = 25%
80 increases to 100, so the added 20 is 25% of the original 80.
100 80
((80 - 100) / 100) x 100 = -20%
100 decreases to 80, so the removed 20 is 20% of the original 100.
250 212.5
250 x (1 - 15 / 100) = 212.5
Reducing 250 by 15% subtracts 37.5 and gives 212.5.
How to Calculate Percentage Increase
Subtract the original value from the new value, divide the increase by the absolute original value, and multiply by 100. If a salary rises from 48,000 to 52,800, the increase is 4,800. Dividing 4,800 by 48,000 gives 0.1, so the salary increased by 10%.
The original value is the baseline. Switching the values changes both the sign and denominator, so it describes a different comparison. Always identify which value came first before calculating the rate.
How to Calculate Percentage Decrease
Subtract the original value from the new value using the same signed formula. A price falling from 120 to 90 has a change of -30. Dividing -30 by 120 and multiplying by 100 gives -25%, which is reported as a 25% decrease.
Keeping the signed change is useful because it preserves direction. The calculator displays the decrease as a positive-sized label for readability while also showing the signed percentage and signed absolute change in the result details.
How to Increase a Number by a Percentage
Convert the percentage to a decimal, multiply it by the starting value, and add the amount. Increasing 80 by 25% means 80 x 0.25 = 20, followed by 80 + 20 = 100. The shortcut formula is value x (1 + rate / 100).
This method applies to markups, raises, growth forecasts, and budget increases. Percentages greater than 100 are valid: increasing 50 by 120% adds 60 and produces 110.
How to Decrease a Number by a Percentage
Multiply the starting value by the decimal rate, then subtract that amount. Decreasing 250 by 15% gives a reduction of 37.5 and a new value of 212.5. The shortcut formula is value x (1 - rate / 100).
A 100% decrease produces zero. A decrease greater than 100% produces a negative result, which can be mathematically valid even when it may not make sense for a physical quantity such as inventory.
Percentage Change Formula and Examples
| Task | Formula | Example |
|---|---|---|
| Percentage increase | (new - original) / abs(original) x 100 | 80 to 100 = 25% increase |
| Percentage decrease | abs(new - original) / abs(original) x 100 | 100 to 80 = 20% decrease |
| Increase a value | value x (1 + rate / 100) | 80 increased by 25% = 100 |
| Decrease a value | value x (1 - rate / 100) | 250 decreased by 15% = 212.5 |
Percentage increase and decrease are not symmetric. An increase from 80 to 100 is 25%, but a decrease from 100 to 80 is 20%. The amount is 20 in both directions, yet each calculation divides by its own original value.
Percentage points are also different from percentage change. If an interest rate moves from 4% to 5%, it rose by 1 percentage point but increased by 25% relative to the original 4% rate.
Percentage change from zero is undefined because division by zero has no finite result. Changes involving a negative original value are mathematically calculated using the original magnitude, but the interpretation depends on context. Moving from -100 to -80 is a numerical increase of 20%, while financial loss language may describe it differently.
Common Uses for Percentage Change
In personal finance, percent change can compare a previous salary with a new offer, measure a household bill increase, or calculate the effect of a discount. For example, a salary moving from 60,000 to 63,000 rises by 5%, while a product discounted from 80 to 68 falls by 15%. The original amount must always be used as the denominator.
Businesses use the same method for revenue, costs, orders, conversion rates, and website traffic. A store that grows from 1,200 to 1,500 monthly orders records a 25% increase. When comparing percentages such as conversion rates, report both percentage points and relative percent change when the distinction matters.
For grades and measurements, confirm that the two values use the same scale and units before comparing them. Percent change between dollars and euros, or between scores from tests with different maximum marks, is not meaningful until the values are converted to a common basis.
Percentage Increase / Decrease Calculator FAQ
How do I calculate percentage increase?
Subtract the original value from the new value, divide by the absolute original value, and multiply by 100. A positive answer is the percentage increase.
How do I calculate percentage decrease?
Subtract the original value from the new value and divide by the absolute original value. A negative result identifies a decrease, and its magnitude is the percentage decrease.
What is the percent change from 80 to 100?
The change is 20, and 20 divided by the original 80 equals 0.25. Therefore, the result is a 25% increase.
How do I increase a number by 20 percent?
Multiply the number by 1.20, which combines the original 100% with the additional 20%. Equivalently, find 20% of the number and add it.
How do I decrease a number by 15 percent?
Multiply the number by 0.85 because 100% minus 15% leaves 85%. You can also calculate 15% of the number and subtract that amount.
Why is percentage change undefined from zero?
The percent-change formula divides by the original value. When the original is zero, that division is undefined, so no finite percentage change exists.
Why are percentage increase and decrease not reversible?
Each direction uses a different original value as its denominator. Increasing 80 to 100 uses 80, while decreasing 100 to 80 uses 100.
What is the difference between percentage change and percentage points?
Percentage change measures relative movement compared with an original value. Percentage points measure the direct difference between two percentages, such as 5% minus 4% equaling 1 point.
Learn More About Percent Change
For deeper lessons and applied examples, review OpenStax Prealgebra on understanding percents, Khan Academy percent word problems, and the U.S. Bureau of Labor Statistics CPI escalation guide.
Related Calculators
Use the general Percentage Calculator to solve percent-of-number and part-to-whole questions. You can also try the Fraction Calculator, Mean, Median, and Mode Calculator, Standard Deviation Calculator, or Significant Figures Calculator.