Percentage Change Calculator
Find the percentage increase or decrease between two numbers, with the direction of change and the exact difference shown instantly.
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Percentage change measures how much a value has grown or shrunk relative to where it started. It is the standard way to express a price increase, a stock's move, a salary raise, a weight loss, or a traffic jump — anything where "how big is the change compared to the original?" is the real question.
How it's calculated
% change = (new − old) ÷ |old| × 100
difference = new − old
A positive result is an increase, a negative result is a decrease, and zero means no change. For example, going from 200 to 250 gives (250 − 200) ÷ 200 × 100 = +25%, while going from 250 to 200 gives (200 − 250) ÷ 250 × 100 = −20%. Note the asymmetry: the same $50 move is a different percentage depending on the starting point, which is why a 25% gain followed by a 25% loss leaves you below where you began.
Why the absolute value in the denominator? When the old value is negative — say a company's earnings move from −$50 to +$25 — dividing by the raw negative number flips the sign and makes a clear improvement look like a decline. Dividing by |old| keeps the direction intuitive: −50 → 25 reads as a +150% increase, which matches what actually happened. Some finance textbooks simply call percentage change "not meaningful" across sign flips, so treat those cases with care.
Assumptions and limitations: percentage change is undefined when the old value is 0, because you cannot divide by zero — there is no baseline to compare against (this calculator says so explicitly instead of returning an error). Also keep two cousins straight: percentage points measure the simple arithmetic gap between two percentages (4% → 6% is +2 points but a +50% change), and percentage difference compares two values symmetrically using their average as the base, with no "before" and "after."
Frequently asked questions
What is the formula for percentage change?
Percentage change = (new value − old value) ÷ |old value| × 100. Going from 200 to 250 is (250 − 200) ÷ 200 × 100 = +25%. A positive result means an increase; a negative result means a decrease.
Why is percentage change undefined when the old value is 0?
Because the formula divides by the old value, and division by zero has no defined result. Conceptually, there is no baseline: going from 0 to 50 is not "infinity percent" — it is simply an increase of 50 with no meaningful percentage. This calculator reports the difference and direction instead.
What is the difference between percentage change and percentage points?
Percentage points measure the raw gap between two percentages, while percentage change is relative to the starting value. If an interest rate moves from 4% to 6%, that is an increase of 2 percentage points — but a percentage change of +50%, because 2 is half of 4.
How does the calculator handle negative starting values?
It divides by the absolute value of the old number, so the sign of the result always matches the real direction of change. Moving from −50 to 25 shows as a +150% increase, which is intuitive — dividing by the raw −50 would wrongly flag it as a decrease.
Is percentage change the same as percentage difference?
No. Percentage change is directional — it compares a new value against an original baseline. Percentage difference is symmetric: it divides the gap by the average of the two values and has no notion of before and after. Use change for trends over time, difference for comparing two peers.
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