Percentage Change Calculator

Percentage change is directional: it has a clear old value and a new value, and the answer carries a sign. From 100 to 150 is +50%; from 150 to 100 is -33.33%. Percentage difference is symmetric: |a - b| / average, the same in either direction. Use percentage change when there is a real before-and-after (a stock price last quarter, a salary raise). Use percentage difference when neither value is privileged (two sensor readings, two lab measurements).

Because the denominator changes with direction. The standard formula divides the change by the absolute value of the old value, so going up from 100 the base is 100 and a 100-unit move is 100%. Coming back down from 200, the base is 200 and the same 100-unit move is only 50%. Both numbers are correct; they answer different questions. If you want a single number that is the same in either direction, switch to the symmetric formula this calculator also reports.

Use it when neither value is a baseline. Scientific data without a clear before-and-after, instrument calibrations where you compare two sensors, or anywhere a reader could swap the two values without changing the meaning of the comparison. The symmetric formula divides the change by the arithmetic mean of the two values, so 100 vs 200 gives +66.67% in one direction and -66.67% in the other, identical magnitudes. The standard formula does not.

The standard formula is undefined: any nonzero change divided by zero is infinite, and zero divided by zero is indeterminate. The calculator returns no result and asks you to pick a nonzero baseline. If you genuinely have a zero starting point, you have a new-occurrence event rather than a change; describe it in absolute terms ("went from 0 to 10 cases") instead of as a percentage.

It is a rough size cue based on the absolute standard percent change: small is below 10%, moderate 10 to 25%, large 25 to 50%, and huge 50% or more. These are loose anchors that match how most people informally describe percent moves; they are not statistical thresholds. For decision-making you still want to compare against domain context (a 5% stock move is large for a day, small over a year).