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Percent Change vs Percentage Points: Why the Difference Matters

By Reeliy Editorial Team · · 2 min read

Headlines love percentages, and they often blur two different ideas: a change in percentage points and a percent change. Both are correct uses of the word, but they answer different questions, and mixing them up can make a small shift sound huge or a big one sound tiny.

This article separates the two, shows why percent changes do not simply add, and explains how to average growth over several periods. Every example uses numbers you can check yourself.

Percentage points versus percent

A percentage point is the plain arithmetic difference between two percentages. If an interest rate rises from 4% to 6%, it has gone up by 6 − 4 = 2 percentage points.

A percent change compares the size of the move with the starting value. The same rise is 2 ÷ 4 = 0.5, so the rate went up 50 percent in relative terms.

percent change = (new − old) ÷ old × 100Percentage points are just new − old, with no division.

Both statements are true of the same event. "Rates rose 2 points" is the clearer description of the absolute move, and "rates rose 50 percent" describes the relative one. Be suspicious of any report that gives only the larger-sounding figure.

Why percent changes do not add up

Percent change always uses the current value as its base, so a second change acts on a different number than the first.

Worked example: a price goes from 80 to 100. That is a rise of 20 ÷ 80 = 25%. If it then returns from 100 to 80, the fall is 20 ÷ 100 = 20%. The same 20 units is a 25% rise in one direction and a 20% fall in the other.

The same effect catches people who expect a 10% rise followed by a 10% fall to cancel out. Multiply the growth factors instead: 1.10 × 0.90 = 0.99, so you finish 1% below where you started.

To combine several percent changes, convert each to a growth factor (1 + change as a decimal), multiply them together, then subtract 1.

Averaging growth over several periods

Suppose an investment grows 10% in the first year and 20% in the second. Adding the two and halving suggests 15% a year, but that overstates it, because the second year's growth applies to a larger amount.

average growth per period = (f₁ × f₂ × … × fₙ)^(1/n) − 1f is each period's growth factor; this is the geometric mean.

Worked example: the factors are 1.10 and 1.20. Their product is 1.32, so the total growth is 32%, not 30%. The per-year average is the square root of 1.32 minus 1, which is about 14.89%. Growing 14.89% twice gives 1.1489 × 1.1489 ≈ 1.32, as it should.

Reading percentages in reports

  • Ask what the starting value was. A 200% rise from a tiny base can still be a tiny number.
  • Check whether a figure about a rate is in percentage points or percent. If it does not say, work it out from the raw numbers if they are given.
  • Be careful with percent change near zero: going from 0.5% to 1% is a 100% rise but only half a percentage point.

When you need a quick, correct answer, use the percentage calculator, which finds percent change and percentage difference from any two numbers.

Try the tools
  • Percentage Calculator: Pick the question you need answered, enter two numbers and get the result instantly. The guide below shows the formula behind each mode.
  • Percent Error Calculator: Type the value you measured and the value you expected, and the calculator returns the percent error. A positive result means the measurement came out too high, a negative one too low.

This article is general information, not professional advice. See our Disclaimer and Editorial Policy.

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