Percent vs Percentage Points: What Is the Difference?

Short answer: a percentage point measures the gap between two percentages by subtraction. A percent change measures that gap relative to the starting figure. If an interest rate rises from 4% to 5%, it rose by 1 percentage point and by 25 percent. Both statements are true, and they answer different questions.

What is a percentage point?

A percentage point is one unit on the percent scale. Going from 40% to 46% is a rise of 6 percentage points, because 46 minus 40 is 6. It does not say how big that move is compared with where you started.

Percentage points apply to quantities that are already percentages: interest rates, tax rates, unemployment rates, survey shares, exam pass rates. A percentage point is not defined for a price in dollars or a weight in kilograms.

What is percent change?

Percent change divides the difference by the starting value: (new - old) / old, times 100. Mathify's percentage calculator uses this formula in its "change" mode, and divides by the absolute value of the starting number so the sign shows the direction.

We computed these with the repository code:

• 4% to 5%: change of +25% (1 divided by 4), a rise of 1 percentage point.
• 40% to 46%: change of +15% (6 divided by 40), a rise of 6 percentage points.

The same percentage-point move can sound small or large depending on the start. One point on a 4% rate is a quarter of the rate. One point on a 40% rate is only 2.5% of it.

How do you say it correctly?

State the unit. "The rate rose 1 percentage point, from 4% to 5%" is exact. "The rate rose 1%" is ambiguous, because a reader could take it as 4% to 4.04%. When you quote a relative change, say "rose 25 percent" and give the starting and ending values too.

In finance, a basis point is one hundredth of a percentage point, so 100 basis points equal 1 percentage point. The basis point calculator converts between them. Writing "up 25 basis points" is a common way to avoid the ambiguity.

Why does up 50% then down 50% not get you back?

A percent change is always relative to the number you start from, and after the first step the starting number has changed. We worked this through:

1. Start at 100 and increase by 50%: 150.
2. Decrease 150 by 50%: 75, not 100.

Going from 150 back to 100 takes a fall of 33.33 percent, and going from 200 to 150 is a fall of 25 percent, while 150 to 200 is a rise of 33.33 percent. The gap between the two numbers is the same, 50, but the starting points differ.

Two same-direction steps do not simply add either. Increasing 100 by 20% twice gives 144, not 140. Decreasing 100 by 10% twice gives 81, not 80.

Percent change versus percentage difference

These are different calculations, and calculators use both names loosely:

• Percent change has a direction and a starting value. From 50 to 80 it is +60%. From 80 to 50 it is -37.5%.
• Percentage difference is symmetric. It divides the gap by the average of the two values, so 50 and 80 give 46.15% whichever you list first.

Use change when one value comes before the other (last year to this year). Use percentage difference when neither is the reference, such as comparing two products. Mathify's code treats them as separate calculations, so check which one a tool is using before comparing results.

Which percentage question are you asking?

Match the wording to the formula before you reach for a calculator:

• "What is 25% of 80?" is a part of a whole. The answer is 20.
• "20 is what percent of 250?" is a share. The answer is 8%.
• "From 50 to 80, what is the change?" is percent change. The answer is +60%.
• "How many points did the rate move?" is subtraction, with no division.

The percent converter switches between percent, decimal and fraction forms, which helps when a rate appears as 0.046 in one place and 4.6% in another. A longer set of examples is in the guide to percentage calculation methods.

Common mistakes

• Writing "up 1%" when you mean one percentage point.
• Averaging percent changes over several periods instead of compounding them.
• Reversing a percent change by applying the same percentage in the opposite direction.
• Using percent change when the starting value is zero. It is undefined, and Mathify's calculator rejects a zero starting value.
• Treating percentage difference and percent change as interchangeable.

Key takeaways

• Percentage points are a subtraction. Percent change is a ratio to the start.
• 4% to 5% is +1 percentage point and +25 percent.
• Up 50% then down 50% ends at 75% of the start, not 100%.
• Always say which one you mean, and give the start and end values.

FAQ

Is a 1% increase the same as 1 percentage point?

Only if the starting value is 100%. For a starting rate of 4%, a 1% increase gives 4.04%, while a 1 percentage point increase gives 5%.

How do I calculate a percentage point change?

Subtract the old percentage from the new one. From 40% to 46% the change is 46 - 40 = 6 percentage points.

How do I convert percentage points to basis points?

Multiply by 100. A change of 0.25 percentage points is 25 basis points.

What is the difference between percent increase and percent decrease for the same two numbers?

They use different starting values. From 150 to 200 is +33.33%. From 200 to 150 is -25%.

Why do news reports sometimes quote both?

The two numbers answer different questions. The point change tells you how far a rate moved. The percent change tells you how large that move is relative to the starting rate.