Percentage Change Calculator
Enter an old value and a new value to calculate the exact percentage change. The result shows whether the change is an increase or decrease.
Percentage Change Quick Reference
| Old Value (V1) | New Value (V2) | Change | Direction |
|---|
| 100 | 110 | +10% | Increase |
| 100 | 125 | +25% | Increase |
| 100 | 150 | +50% | Increase |
| 100 | 200 | +100% | Increase |
| 100 | 90 | −10% | Decrease |
| 100 | 75 | −25% | Decrease |
| 100 | 50 | −50% | Decrease |
| 50 | 75 | +50% | Increase |
| 200 | 150 | −25% | Decrease |
| 80 | 100 | +25% | Increase |
| 1000 | 800 | −20% | Decrease |
| 25 | 25 | 0% | No Change |
How to Calculate Percentage Change
Percentage change calculation measures how much a quantity has grown or shrunk relative to its original value. It is one of the most widely used formulas in business, science, and everyday math.
% Change = ((V2 − V1) / |V1|) × 100
V1 is the original or old value. V2 is the new or final value. The vertical bars around V1 mean the absolute value, which ensures the formula handles negative starting values correctly.
Reading the Result
A positive result means the value increased. A negative result means the value decreased. A result of zero means no change occurred. The number itself tells you by how many percentage points the value changed relative to the starting point.
Price rise
$40 to $50: +25% change
Price drop
$80 to $60: −25% change
No change
200 to 200: 0% change
Doubled
50 to 100: +100% change
Percentage Change With Negative Numbers
Percentage change with negative numbers requires the absolute value of V1 in the denominator. This prevents the sign of the starting value from flipping the direction of the result.
For example, going from negative 20 to positive 20: V2 minus V1 equals 40, divided by the absolute value of negative 20 which is 20, multiplied by 100 gives 200%. The value increased by 200%, which is correct. Without the absolute value, the sign would be wrong.
Common Percentage Change Mistakes
The most common mistake is dividing by V2 instead of V1. Always divide by the original value, not the new one. Another mistake is forgetting to multiply by 100, which gives the decimal form of the change rather than the percentage.
Frequently Asked Questions
What is the formula for percentage change?+
The percentage change formula is: ((New Value minus Old Value) divided by the absolute value of the Old Value) multiplied by 100. A positive result means an increase and a negative result means a decrease.
How do I calculate percentage change from 50 to 75?+
To calculate the percentage change from 50 to 75: subtract 50 from 75 to get 25, divide 25 by 50 to get 0.5, then multiply by 100 to get 50%. The value increased by 50%.
What is percentage change vs percentage difference?+
Percentage change is used when you have a clear old value and a new value, such as a price going from $40 to $50. Percentage difference is used when comparing two values without a defined starting point or direction of change.
Can percentage change be negative?+
Yes, percentage change can be negative. A negative percentage change means the value decreased. For example, going from 100 to 80 gives a percentage change of negative 20%, meaning the value fell by 20%.
Why use the absolute value of V1 in the formula?+
The absolute value of V1 is used in the denominator so the sign of the result correctly reflects the direction of change when the starting value is negative. Without it, going from negative 50 to positive 50 would give a misleading sign in the result.
What does 100% change mean?+
A 100% change means the value doubled. If the old value was 50 and the new value is 100, that is a 100% increase because the value grew by an amount equal to the original. A negative 100% change would mean the value dropped to zero.
How is percentage change used in real life?+
Percentage change is used in finance to measure stock returns, in economics to track inflation and GDP growth, in science to measure experimental changes, and in everyday life to calculate price increases, salary changes, and population growth.
