"Mortgage rates rose from 6.5% to 7%." One headline calls that a half-point increase. Another calls it a 7.7% jump. Both are correct, and the gap between them is the difference between percentage points and percent change.
Mixing the two up is one of the most common number mistakes in news, reports and slide decks. Here's how each one works, how to calculate it, and when to use which.
The difference in one example
Say an interest rate goes from 4% to 5%.
- Change in percentage points: 5 − 4 = 1 percentage point. You simply subtract the two percentages.
- Percent change: (5 − 4) ÷ 4 × 100 = 25%. You measure the change relative to where it started.
So "the rate rose 1 percentage point" and "the rate rose 25%" describe the same move. What you can't say is "the rate rose 1%," because that would mean it went from 4% to 4.04%.
Percent change: the formula
Percent change compares the new value with the old one:
percent change = (new − old) ÷ old × 100A positive result is an increase, a negative one a decrease. The U.S. Bureau of Labor Statistics uses exactly this calculation for the Consumer Price Index. In its guide to CPI math, the index moves from 239.261 to 240.236. That's a change of 0.975 index points, which divided by 239.261 and multiplied by 100 gives a 0.4% increase. BLS notes that it reports percent changes rather than index point changes "because index point changes are affected by the level of the index," while percent changes are not.
The "Percentage change" card in our Percentage Calculator does this calculation and shows the formula under the answer. A few results:
| From | To | Percent change |
|---|---|---|
| 80 | 100 | +25% |
| 100 | 80 | −20% |
| 6.5 | 7 | +7.692308% |
| 0.5 | 1 | +100% |
The first two rows show something that trips people up: going up 25% and then down 20% gets you back to where you started. Each percentage is taken from a different starting value.
Percentage points: when the numbers are already percentages
Percentage points only make sense when the values you're comparing are themselves percentages: interest rates, tax rates, unemployment rates, market shares, poll results, conversion rates. The change in percentage points is the plain difference:
change in points = new % − old %The Federal Reserve uses this language in its policy statements. In December 2024, for example, it announced that it would "lower the target range for the federal funds rate by 1/4 percentage point." It didn't say 1/4 percent, which would mean something very different.
Basis points
Finance often uses basis points, which are hundredths of a percentage point. 1 percentage point = 100 basis points, so the Fed's 1/4 point cut is 25 basis points. Basis points avoid the "percent or points?" ambiguity entirely, which is why bond and loan markets prefer them. To see what a quarter-point move means in dollars, run a loan at both rates through the Loan Calculator and compare the monthly payments.
Why the two can tell very different stories
Because percent change divides by the starting value, a small starting value makes any change look huge:
| Rate moves from | Percentage points | Percent change |
|---|---|---|
| 4% → 5% | +1 | +25% |
| 2% → 3% | +1 | +50% |
| 0.5% → 1% | +0.5 | +100% |
| 25% → 20% | −5 | −20% |
| 6.5% → 7% | +0.5 | +7.7% |
A risk that goes from 0.5% to 1% has "doubled," which sounds alarming, but in absolute terms it rose by half a percentage point. Both facts are true. Good reporting gives both, or at least the starting value, so readers can judge for themselves.
This works in the other direction too. A conversion rate that moves from 2% to 3% is "only one point," but it means 50% more customers from the same traffic. Which number matters depends on the question you're asking.
Common mistakes
Saying "percent" when you mean "points"
"Unemployment rose 2% to 6%" is ambiguous. Did it go from 4% to 6% (2 points), or from about 5.9% to 6% (2 percent)? Write "rose 2 percentage points to 6%" and the problem disappears.
Adding percentage changes together
Two 10% raises don't add up to 20%. The second raise applies to the already raised salary: 1.10 × 1.10 = 1.21, a 21% total increase. The same applies to growth rates over several periods. BLS makes the same point about inflation: the change over a year "is not equal to the sum of the over-the-month changes."
Reversing a change with the same percentage
A price cut by 20% needs a 25% increase to get back to the original. If something drops from 100 to 80, a 20% increase only takes it to 96.
Percent change from zero
There's no percent change from zero. The formula divides by the starting value, and dividing by zero has no answer, which is why the Percentage Calculator shows "Not defined" for it. Report the absolute change instead, such as "from 0 to 40 sign-ups."
Confusing percent change with percent difference
Percent change has a direction: from an old value to a new one. Percent difference compares two values with no "before" and "after," such as prices at two stores. It divides the gap by the average of both values. For 40 and 50, the percent difference is 22.22%, while the percent change from 40 to 50 is 25%. The calculator has a separate card for each.
Which one to use
- Comparing two percentages (rates, shares, proportions): give the change in percentage points. Add the percent change if the relative size matters.
- Comparing two amounts (prices, revenue, visitors, weights): use percent change. Percentage points don't apply.
- Comparing two things with no time order: use percent difference, or simply state both values.
- Writing about interest rates in finance: percentage points or basis points.
Writing it clearly
A few sentence patterns that leave no room for misreading:
- "The rate rose from 4% to 5%, an increase of 1 percentage point."
- "Revenue grew 12%, from $250,000 to $280,000."
- "Turnout fell 3 points to 58%, a 4.9% drop from the previous election."
Giving the starting and ending values, as in all three, lets readers check the math and compute whichever measure they care about. In the last example, 3 ÷ 61 × 100 = 4.9%.
Quick formulas for a spreadsheet
Percent change: =(B2-A2)/ABS(A2)
Percentage points: =B2-A2 (with both cells holding percentages)
Percent difference: =ABS(A2-B2)/AVERAGE(A2,B2)Format the first and third results as percentages. Using the absolute value of the old number in the percent change formula keeps the sign meaningful when the starting value is negative, which is also how the calculator handles it.
FAQ
Is a percentage point the same as a percent?
No. A percentage point is a unit for the difference between two percentages. A percent is a fraction of some amount. Going from 10% to 12% is 2 percentage points, or a 20% increase.
How do I convert percentage points to percent change?
Divide the point change by the starting percentage and multiply by 100. A 1.5-point rise from 3% is 1.5 ÷ 3 × 100 = 50%.
What is a basis point?
One hundredth of a percentage point. 25 basis points is 0.25 percentage point.
Can percent change be more than 100%?
Yes, for increases. Going from 50 to 150 is a 200% increase. A decrease can't be more than 100% unless the value turns negative.
