Percentage Change Calculator

Subtract the old value from the new, divide by the old value, then multiply by 100: (new − old) ÷ old × 100. Going from 200 to 250 is (250 − 200) ÷ 200 × 100 = +25%. A negative result is a decrease — 200 down to 150 is −25%. Everything rests on one choice: the denominator is the old value. Not the new one, not the average of the two. Swap that denominator and the same pair of numbers produces a different percentage, which is how two honest reports can disagree about the "same" change. A shortcut worth knowing: divide the new value by the old one and you get the growth factor directly. 250 ÷ 200 = 1.25, and a factor of 1.25 is +25%. Factors above 1 are increases, factors below 1 are decreases. Working in factors instead of percentages makes everything below much easier.

Add 10% and then take 10% off and you do not land back where you started. In factors, that is 1.10 × 0.90 = 0.99 — you finish 1% below the original, and the order makes no difference because multiplication commutes. The cause is simple: the second percentage is applied to a different base than the first. The bigger the swing, the worse the asymmetry. A 50% drop needs a 100% rise to recover; an 80% drop needs 400%. The general rule: after losing p percent, getting back to even takes a gain of p ÷ (100 − p) × 100 percent. Losing 20% needs +25%, losing 25% needs +33.3%. This is why a portfolio, a traffic chart or a sales figure that falls and then "recovers by the same percentage" is still down.

When the numbers themselves are percentages, two different things can be reported and they are not interchangeable. If an interest rate moves from 4% to 6%, that is a rise of 2 percentage points and a 50% percentage change. Both statements are true; they answer different questions. The gap gets dramatic when the base is small. A rate that goes from 2% to 3% is up 1 percentage point — but that is a 50% increase, and a headline is free to quote whichever number sounds bigger. Whenever a claim involves a percentage of a percentage, check which of the two is on the page. A good habit: reserve the phrase "percentage points" (often abbreviated pp) for the raw subtraction, and "percent change" for the relative one. This calculator reports the percent change of whatever two numbers you enter.

If the old value is zero, percentage change is undefined — the formula would divide by zero, and there is no sensible answer to "what percent of nothing is this". Going from 0 to 50 sales is not an infinite increase; it is a jump that percentages simply cannot describe. Report the absolute change instead. Negative starting values are the other trap. Going from −100 to −50 is an improvement, but the raw formula hands you a sign that reads backwards. This calculator divides by the absolute value of the old number, so an improvement still shows up as a positive change. When your figures cross zero — a profit that becomes a loss — percentages stop being informative altogether and you should quote the raw amounts.

Successive percentage changes multiply; they do not add. Two consecutive quarters of +10% and +20% come to 1.10 × 1.20 = 1.32, a total of +32%, not 30%. Three years of 10% growth are 1.10³ = 1.331, or +33.1%, not +30%. The same logic destroys the naive average. Suppose a value doubles (+100%) and then halves (−50%): the arithmetic average of +100% and −50% is +25%, and yet you are exactly back where you began. The honest average of a series of percentage changes is the geometric mean of the growth factors — √(2.00 × 0.50) = 1, a true average of 0%. So the working rule is: convert every change into a factor, multiply the factors, and convert back only at the end. Percentages are a display format; factors are what actually compose.