Percent Change — The Complete Guide
Percent change expresses how much a value has grown or shrunk, relative to where it started. It's one of the most common calculations in everyday life — a price rising, a population growing, an investment's return — and also one of the most commonly miscalculated, usually because people divide by the wrong number.
The Formula, and the Mistake Most People Make
Percent change = (New value − Old value) ÷ |Old value| × 100. The denominator is always the old value — the number you started from — never the new one. This matters because the same absolute change produces a different percentage depending on which direction you're measuring: going from 50 to 100 is a 100% increase, but going from 100 back down to 50 is only a 50% decrease, even though the absolute change (50) is identical both times.
Worked Example, Fully Shown
Problem: A product's price rises from $40 to $52. Find the percent change.
Difference: 52 − 40 = 12
Percent change: 12 ÷ 40 × 100 = +30%
Percent Change vs. Percentage Points — a Common Mix-Up
These two terms get confused constantly in news reporting. If an interest rate moves from 4% to 6%, that's a 2 percentage point increase (a simple subtraction: 6 − 4) but a 50% percent change in the rate itself (2 ÷ 4 × 100). Both statements are correct — they're just answering different questions — but conflating them makes a change sound much larger or smaller than it actually is, which is why careful writing specifies which one is meant.
Real-World Uses
Finance: investment returns, inflation rates, and stock price movements are all reported as percent change — a $1,000 investment growing to $1,120 is a 12% return.
Retail & economics: year-over-year sales growth, discount percentages, and population growth rates all use the same formula.
Compounding over multiple periods: if a quantity changes by a different percentage each period (not a single one-time change), the average percent change per period isn't the simple average of the percentages — it's the geometric mean growth rate. See our geometric mean calculator for that case.