Percentage Change Calculator
Find the percentage increase or decrease from one number to another, or work backwards. Choose a calculation mode, fill in any two of the three fields (original value, new value, percent change), and get the missing number with a full step-by-step breakdown.
Formula
Worked example
From 80 to 100: (100 - 80) / 80 x 100 = 25% increase. Reverse: given 80 and +25%, new = 80 x 1.25 = 100. Find original: given new=100 and +25%, old = 100 / 1.25 = 80.
How percentage change works
Percentage change measures how much a value has grown or shrunk relative to where it started. You take the difference between the new and old values, divide by the absolute value of the original, and multiply by 100. A positive result means an increase; a negative result means a decrease. Using the absolute value of the original in the denominator ensures the formula works correctly even when the starting value is negative. Dividing by the original, and not the new value, is what makes it a true rate of change from the starting point.
Why increases and decreases are not symmetric
Going from 100 to 80 is a 20% decrease, but going back from 80 to 100 is a 25% increase, because the base value changed. This asymmetry trips people up constantly: a stock that falls 50% must rise 100% to break even. The recovery percentage you need is always larger than the loss percentage. Whenever you compare percentage changes, check what base each one is measured against. The change multiplier output (new / original) captures the full scaling factor in one number.
How to reverse-solve for the original or new value
When you know the percent change and one of the values, you can find the other. To find the new value: multiply the original by (1 + percent change / 100). Example: original 200 with a 15% increase gives 200 x 1.15 = 230. To find the original value: divide the new value by (1 + percent change / 100). Example: new value 230 with a 15% increase means the original was 230 / 1.15 = 200. Switch the calculator mode to use either reverse calculation.
Percentage change vs. percentage difference vs. percentage points
These three terms are often confused. Percentage change uses the original value as the base and can be positive or negative. Percentage difference (sometimes called relative difference) uses the average of both values as the base and is always reported as a positive number, making it useful when neither value is clearly the starting point. Percentage points are the plain arithmetic difference between two percentages: going from an interest rate of 2% to 3% is a 1 percentage-point increase but a 50% change in the rate itself. Always be clear about which concept you are using.
Common percentage change benchmarks
| Change magnitude | Finance example | Population example | Interpretation |
|---|---|---|---|
| 0% to 5% | Modest dividend growth | Slow-growing city | Small |
| 5% to 20% | Solid annual return | Normal city growth | Moderate |
| 20% to 50% | Strong bull market year | Rapidly expanding region | Large |
| 50% to 100% | Doubling investment | Boom-town growth | Very large |
| Over 100% | Startup 10x return | Explosive population surge | Exceptional |
| Negative (any) | Stock decline or loss | Population decline | Decrease |
Quick reference for interpreting the size of a percentage change in typical contexts.
Frequently asked questions
What is the difference between percentage change and percentage points?
Percentage change is relative to the starting value. Percentage points are the plain arithmetic difference between two percentages. A rise from 10% to 12% is a 2 percentage-point rise, but a 20% relative increase in the rate itself.
Why can't I calculate percentage change from zero?
Dividing by zero is undefined. Any increase from a starting value of zero is infinitely large as a percentage. When the original value is zero, only the absolute difference has meaning.
How do I find a percentage decrease?
Use the same formula. If the new value is smaller than the old one, the result will be negative, which represents the percentage decrease. For example, 100 to 75 gives (75-100)/100 x 100 = -25%.
How do I find the original value from the new value and percent change?
Divide the new value by (1 + percent change / 100). If a price is now 130 and it increased 30%, the original was 130 / 1.30 = 100. Use the "Original value" mode in this calculator to do that automatically.
What is the percentage change from a negative number?
The formula still works. Use the absolute value of the original in the denominator. Going from -10 to -25: (-25 - (-10)) / |-10| x 100 = -15 / 10 x 100 = -150%. Going from -10 to 25: (25 - (-10)) / 10 x 100 = +350%.
What is the multiplier and why is it useful?
The multiplier is the new value divided by the original value. A multiplier of 1.25 means the value grew to 125% of its original size (a 25% increase). A multiplier of 0.80 means the value shrank to 80% (a 20% decrease). Multipliers are easier to chain together than percentages: two 10% increases compound to 1.10 x 1.10 = 1.21, a 21% total increase, not 20%.