Percentage Change Calculator
With original value 120, new value 150, percentage change comes to 25.00 % — percentage change. It is reached in 3 steps, the last of which is 30 / abs(120) * 100, and each one is printed on the page with its numbers filled in. The formula is the one published by US Bureau of Labor Statistics, not an approximation fitted to it.
Percentage increase or decrease between two values, with the absolute difference and the multiplier.
Formula and sources checked · How we check
Original value 120, New value 150
25.00 %
Percentage change for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.
It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.
- Absolute difference
150 - 12030- Percentage change
30 / abs(120) * 10025 %- Multiplier
150 / 1201.25 ×
Worked example
120 to 150 is a 25% increase. Reversing it — 150 back to 120 — is a 20% decrease, not 25%: the denominator changes with the starting value, which is why sequential percentage moves never cancel out.
How to work it out yourself
- 1.Order matters: the old value is the denominator. Swapping them gives a different number, and it is the commonest error with percentages.
- 2.An increase and the decrease that undoes it are never the same percentage. Up 50% then down 50% leaves you at 75%, not back where you started.
- 3.Read the multiplier line when chaining changes. Multipliers multiply; percentages do not add.
The formula
- Absolute difference
150 - 120 - Percentage change
30 / abs(120) * 100 - Multiplier
150 / 120
Source: US Bureau of Labor Statistics — percent-change methodology, NIST Engineering Statistics Handbook
Questions people actually ask
- Why does a 50% drop need a 100% rise to recover?
- Percentages are relative to their starting point. 100 falling to 50 is −50% of 100; 50 returning to 100 is +50 on a base of 50, which is +100%. The same trap makes a −20% year followed by a +20% year end at 96, not 100.
- What is the difference between percentage change and percentage points?
- A rate moving from 4% to 5% is a 1 percentage point rise but a 25% relative increase. Interest rates, unemployment and margins are quoted in points precisely to avoid that ambiguity.
- How is percentage difference different?
- Percentage change has a defined "before" and divides by it. Percentage difference is symmetric and divides by the mean of the two values, which is the right choice when neither is the baseline.
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