Percentage increase formula
Percentage increase tells you how much a value has grown relative to where it started. Subtract the original value from the new value, divide by the original value, then multiply by 100.
If a price rises from $80 to $96, the increase is $16. Divide $16 by the original $80 to get 0.20, then multiply by 100. The result is a 20% increase.
Percentage decrease formula
For a decrease, subtract the new value from the original value and again divide by the original value.
If a monthly expense falls from $250 to $200, the decrease is $50. Dividing $50 by $250 gives 0.20, so the expense decreased by 20%.
One formula for percentage change
You can use one general formula for both directions: ((New − Original) ÷ Original) × 100. A positive result means an increase and a negative result means a decrease. This form is useful in spreadsheets and repeated business calculations.
How to increase a number by a percentage
When you already know the percentage and want the new value, convert the percentage to a decimal and multiply by a growth factor.
To increase $120 by 15%, multiply $120 by 1.15. The result is $138. The amount added is $18.
How to decrease a number by a percentage
To reduce $200 by 25%, multiply $200 by 0.75. The result is $150.
How to find the original value
Reverse percentage calculations are common when a final price or salary is known but the starting figure is missing. If a value increased by 20% and the current value is $120, divide by 1.20 to recover the original $100.
For a decrease, divide the final value by 1 − rate. If a sale price of $75 reflects a 25% reduction, divide $75 by 0.75 to get an original price of $100.
Percentage change versus percentage difference
These are not the same question. Percentage change has a clear original value and measures movement away from it. Percentage difference compares two values when neither is naturally the starting point, so the denominator is often the average of the two values. Before calculating, decide which relationship you actually want to measure.
Common percentage mistakes
- Dividing by the new value: percentage change normally uses the original value.
- Confusing percentage points with percent change: a rate moving from 20% to 25% rises by 5 percentage points, which is a 25% relative increase.
- Assuming equal increases and decreases cancel: a 50% increase followed by a 50% decrease does not return to the starting value because the second percentage uses a different base.
- Forgetting the ×100 step: 0.15 is the decimal form of 15%.
Worked examples
| Original | New | Change | Result |
|---|---|---|---|
| 100 | 125 | +25 | 25% increase |
| 200 | 150 | −50 | 25% decrease |
| 40 | 50 | +10 | 25% increase |
Frequently asked questions
What if the original value is zero?
Standard percentage change is undefined when the original value is zero because the formula requires division by the original value.
What is the fastest way to add 10%?
Multiply the original number by 1.10. To subtract 10%, multiply by 0.90.
Why does a 20% increase followed by a 20% decrease give a loss?
The decrease is applied to the larger, increased value. For example, 100 becomes 120, then a 20% decrease removes 24, leaving 96.
Enter your own values, review the result, then use the guide above to understand the formula and assumptions.