How to Calculate Percentage Increase and Decrease

Step by step

1. Identify the original and new values

   Write down the starting value and the later value. Keep the order clear: percentage change is measured from the original to the new value.

2. Find the absolute difference

   Subtract the original value from the new value. A positive difference means the value rose; a negative difference means it fell.

3. Divide by the original magnitude

   Divide the difference by the absolute value of the original, then multiply by 100. Percentage change from an original value of zero is undefined because the formula divides by zero.

4. Check the sign and interpretation

   A positive result is an increase, a negative result is a decrease. Use the Percentage Calculator's Percentage change mode to enter the original and new values and see the result update.

The percentage-change formula

Percentage change = ((new value − original value) ÷ |original value|) × 100. The absolute value in the denominator treats the original magnitude as the reference, while the numerator's sign indicates direction.

For 100 to 125, the difference is 25 and 25 ÷ 100 × 100 = 25%, an increase. For 100 to 75, the difference is −25 and −25 ÷ 100 × 100 = −25%, a decrease. When the original value is negative, state the context carefully; a percentage change can be mathematically calculated but may not match every domain's convention.

Percentage increase and decrease

To increase a value by p percent, multiply it by 1 + p/100. To decrease it by p percent, multiply it by 1 − p/100. For example, increasing 200 by 15% gives 200 × 1.15 = 230; decreasing 200 by 15% gives 200 × 0.85 = 170.

An increase followed by the same percentage decrease does not generally return to the starting value, because the second percentage is calculated from the new, larger base. A decrease greater than 100% can produce a negative result in the calculator's adjustment mode; whether that has a meaningful interpretation depends on the context.

Percentage versus percentage points

A percentage describes a proportion out of 100. A percentage point is the arithmetic difference between two percentages. If a rate changes from 20% to 25%, it increased by 5 percentage points. Relative to the starting 20%, it increased by 25% because (25 − 20) ÷ 20 × 100 = 25%. These statements answer different questions, so name the one you mean.

Common mistakes to avoid

• Dividing by the new value instead of the original value.
• Reversing original and new values and changing the sign.
• Calling a difference between percentages a percent change without naming the reference.
• Trying to calculate percentage change from zero.

Helpful checks

• Label both values before calculating.
• Use percentage points for a simple difference between rates.
• For financial, scientific, or regulated reporting, verify the convention used in that domain.

Frequently asked questions