Two questions, one calculator
Percentage questions come in two shapes. Mode A: “It was 100, now it is 125 — what is the percentage increase?” Mode B: “Increase 200 by 10%.” This page answers both, side by side, because they are mirror images: Mode A finds the percent that connects two values, and Mode B applies a known percent to a value. If your question is instead “how far apart are these two numbers, with neither as the starting point?”, that is a job for the Percentage Difference Calculator — a different formula that divides by the average.
Mode A always divides by the original value — that choice of base is what makes a rise from 100 to 125 a 25% increase, while the fall back from 125 to 100 is only a 20% decrease. The two directions are never the same percent, and this asymmetry surprises people more than any other fact about percentages.
Worked example
From 100 to 125: the difference is 25, divided by the original 100, times 100 = a 25% increase. In Mode B, increasing 200 by 10% gives 200 × 1.10 = 220 — the change itself is 20. And decreasing 200 by 10% gives 180; notice that a 10% decrease followed by a 10% increase lands on 198, not 200, because the second percent acts on a different base.
How to use this calculator
- For a change between two numbers, enter them in Mode A — order matters: original first, new second.
- Read the headline percent: positive means an increase, negative means a decrease.
- For Mode B, enter a starting value and a percent, and choose increase or decrease.
- Follow the step-by-step panel to see the difference, the division and the multiplication with your numbers.
- For everyday “what is X% of Y” questions, try the general Percentage Calculator.
Where this shows up in real life
Pay rises and rent hikes (Mode A, to check what you were really given), price markups and sale discounts (Mode B), investment returns, inflation adjustments, and exam-score changes. One warning from reporting: when the values are themselves percentages — an interest rate moving from 10% to 12% — the change is 2 percentage points but a 20% percentage increase. This calculator reports the percentage change; if you need points, just subtract.