Percentage change is one idea with four everyday disguises: how much did something grow, what will it be after a rise, what was it before the discount, and how big is one number compared with another. This calculator has a mode for each, and returns the absolute difference alongside the percentage so neither number can mislead you alone.
The Four Modes
| Mode | Question it answers | Formula | | --- | --- | --- | | Percentage change | From old to new, by what % did it move? | | | New value | What is a value after ±p%? | | | Original value | What was it before a ±p% change? | | | B as % of A | One number as a percentage of another | |
Two implementation details matter. Percentage change divides by the absolute value of the starting number, so a move from −50 to −25 reports +50% (an improvement halving a loss) rather than a sign-tangled result. And the original-value mode refuses a decrease of 100% or more — correctly, because a value reduced by 100% is zero, and zero carries no memory of what it was reduced from.
Worked Examples — Including the Famous Trap
Change mode: revenue from 100,000 → difference +$20,000, change = 20,000 ÷ 80,000 = +25%.
The asymmetry trap: a price rises 25% (80 → 100) and then "falls back" by 25% — but 25% of 100 is 25, landing at 75, not 80. To undo a 25% rise takes only a 20% fall (100 → 80), because the percentage is always relative to where you start. This single fact explains investment losses (a 50% loss needs a 100% gain to recover), discount stacking, and most "percentages don't add up" arguments.
New value mode: a 270**.
Original value mode: a jacket sells for 100** original price. (Enter the change as −20%.)
B as % of A: 45 correct answers out of 180 questions → 45 ÷ 180 = 25% — a share of a whole, not a change over time. Keep the distinction: change modes compare across time, this mode compares within a whole.
Percent vs Percentage Points
When a rate itself changes, report the change both ways and know which you mean: an interest rate moving from 4% to 5% rose by 1 percentage point, which is a 25% relative increase in the rate. Headlines exploit the ambiguity relentlessly ("risk up 50%!" — from 2 in a million to 3 in a million). The change mode of this calculator gives the relative figure; subtract the two rates yourself for the points figure. A related discipline: percentages of different bases never add. Two successive 10% discounts are a 19% total discount (0.9 × 0.9 = 0.81), not 20% — the new-value mode applied twice shows why.
Limitations
A starting value of zero has no percentage change (division by zero is rejected, with the single exception 0 → 0 = 0%): growth from nothing is described in absolute terms. Results are exact arithmetic on your inputs; the calculator cannot know whether the two values you compare were measured consistently, which in real statistics is where most percentage errors actually live.
Frequently Asked Questions
Why did my 50% loss need a 100% gain to recover?
Because percentages are relative to the current base. Losing 50% of 50; gaining 50% of 25. Recovery requires gaining 50 base — 100%. The asymmetry grows with the size of the move, which is why drawdowns are so costly in investing.
How do I calculate a markup on cost?
Use change mode: cost as the initial value, selling price as the final value. A 100 is a 66.7% markup. Do not confuse markup (relative to cost) with margin (relative to selling price — that same sale is a 40% margin); the profit margin calculator handles the margin family.
Can the percentage decrease be more than 100%?
For a change from a positive value to another value, no — a quantity cannot fall by more than its whole self without going negative, and going negative (debt, temperature anomalies) is exactly when percentage change stops being meaningful and absolute differences should be reported instead.