Percentage Change Calculator
Find the percentage increase or decrease between two numbers, with the exact change, the direction, and the multiplier — and see why a rise then an equal fall doesn't return you home.
Comment utiliser cette calculatrice
- 1Enter the original (starting) value.
- 2Enter the new (ending) value.
- 3Read the percentage change — positive for an increase, negative for a decrease.
- 4Check the multiplier and absolute change to sense-check the result.
Comment ça marche
Percentage change
percentage change = (new − old) ÷ |old| × 100 positive result = increase, negative = decrease multiplier = new ÷ old the base is always the original value
Percentage change expresses the difference between two values relative to the starting value. Subtract the old value from the new, divide by the absolute value of the old, and multiply by 100. The sign tells you the direction: positive is an increase, negative a decrease. The crucial subtlety is that the denominator is always the original value, which makes percentage change asymmetric — a rise of x% followed by a fall of x% does not return you to where you started, because the second percentage is taken from a different, larger base. This single fact explains a surprising amount of real-world confusion, from investment returns to discount stacking.
Exemple détaillé
Going from 50 to 75 is a change of +25 on a base of 50, which is (75 − 50) ÷ 50 × 100 = 50% increase. Reversing it, from 75 back to 50, is a change of −25 on a base of 75, which is only −33.3% — a smaller percentage for the same absolute move, because the base is larger.
Percentage Change Calculator : le guide complet
Increase and decrease are not symmetric
The most common mistake with percentage change is assuming it works both ways. If a price rises from $100 to $150, that is a 50% increase. But if it then falls from $150 back to $100, that is only a 33% decrease — not 50%. The reason is that percentage change is always calculated against the starting value, and the starting value is different in each direction. The $50 move is measured against $100 going up but against $150 coming down.
This asymmetry has real consequences. An investment that loses 50% of its value must then gain 100%, not 50%, to recover, because the gain is measured against the smaller post-loss base. A 20% pay cut followed by a 20% pay rise leaves you earning less than before. Whenever you see two percentages compared, check whether they share the same base — if they don't, they cannot simply be added or cancelled.
Percentage change versus percentage points
A frequent source of confusion is mixing percentage change with percentage points, which are not the same thing. If an interest rate moves from 4% to 6%, it has risen by 2 percentage points — but that is a 50% increase in the rate itself, because 2 is half of the original 4. Reporters and advertisers sometimes blur the two, and the difference can be enormous.
The rule is simple: percentage points describe the arithmetic difference between two percentages, while percentage change describes the relative difference. Use points when you are talking about a change in something that is itself a percentage (rates, shares, probabilities), and use percentage change when you want to express how large a move is relative to where it started. Being precise about which one you mean prevents a lot of misleading claims.
Where percentage change shows up
Percentage change is one of the most widely used calculations in everyday life and business. It underlies growth rates for populations, revenue, and web traffic; inflation, which is the percentage change in a price index; investment returns; and the markups and markdowns that move through retail. Any time two measurements of the same quantity at different times are compared, percentage change is the natural way to express how much it moved.
Its popularity is exactly why the base-value pitfall matters so much. A headline that says sales 'grew 200%' means they tripled, while 'grew by 200 percentage points' would be meaningless for a raw sales figure. And because the effect compounds, a series of percentage changes must be multiplied together, not added — three consecutive 10% gains produce a 33.1% total increase, not 30%. Keeping the original-value base and the compounding rule in mind turns percentage change from a source of errors into a reliable tool.
Questions fréquentes
How do I calculate percentage change?
Subtract the original value from the new value, divide by the absolute value of the original, and multiply by 100. A positive result is an increase and a negative result a decrease. Going from 50 to 75 gives (75 − 50) ÷ 50 × 100 = 50%.
Why isn't a 50% rise cancelled by a 50% fall?
Because each percentage is measured against a different base. A rise from 100 to 150 is +50% on a base of 100, but the fall from 150 back to 100 is −33% on a base of 150. The larger base makes the same absolute move a smaller percentage, so the two don't cancel.
What is the difference between percent change and percentage points?
Percentage points are the plain arithmetic difference between two percentages; percentage change is the relative difference. A rate moving from 4% to 6% is up 2 percentage points but a 50% increase. Use points for changes in a quantity that is itself a percentage.
What if the original value is zero?
Percentage change is undefined when the original value is zero, because you would be dividing by zero — there is no baseline to compare against. Any move away from zero is, in a sense, an infinite percentage increase. Use the absolute change instead in that case.