Percentage points calculator

A move from 30% to 40% is an increase of 10 percentage points and a relative increase of 33.3333%. Enter the old and new percentages to see both measures, with a positive sign for a rise and a negative sign for a fall.

What this calculator does

Percentage points measure the direct gap between two percentages. They are especially useful for comparing interest rates, poll results and exam pass rates because they describe the change on the original percentage scale. One percentage point means one unit on that scale, regardless of the starting rate.

Relative percent change answers a different question: how large is that gap compared with the old percentage? The calculator puts the point change first and shows the relative change in the breakdown. These are two descriptions of the same pair of rates, not two competing answers to one formula. Always name the measure when reporting a result.

Formula

Percentage points = new percentage − old percentage

Or in one step: Relative percent change = (new − old) ÷ old × 100

In plain English, subtract the old rate from the new rate to get the signed number of percentage points. For relative change, divide that difference by the old rate and multiply by 100. If the old rate is zero, the point change is still valid but the relative change is unavailable because its denominator would be zero.

Worked example

A pass rate moves from 30% to 40%. Subtract 30 from 40: the change is +10 percentage points. For relative change, divide 10 by 30 and multiply by 100: +33.3333%, or about a one-third increase in the rate.

Worked example: interest rates and basis points

An interest rate rises from 4% to 5%. The point change is 5 − 4 = +1 percentage point. Relative to the original rate, the increase is 1 ÷ 4 × 100 = 25%. Saying that the rate rose by 1% would therefore be ambiguous and could substantially understate the relative rise.

On a fixed balance of 1,000 for one year with simple interest, those rates correspond to interest of 40 and 50. The extra interest is 10, not 250. A 25% rise in the rate does not mean a 25% rise in the balance. Actual loan and savings calculations may also depend on compounding, fees and changing balances.

Worked example: polls and exam pass rates

Poll support increases from 42% to 45%. Subtracting gives +3 percentage points. Dividing that gap by the old rate gives 3 ÷ 42 × 100 = approximately +7.1429% relative change. Neither measure tells you whether the difference is statistically meaningful without information about how the polls were conducted.

For exam pass rates, compare cohorts and entry rules as well as the percentages. A fall from 80% to 75% is −5 percentage points and −6.25% relative change. It does not necessarily mean five fewer students passed: the number of students taking the exam may have changed between the two groups.

Percentage points in Excel and Google Sheets

If A1 contains 30 and B1 contains 40 as ordinary numbers, use =B1-A1 for the point change. Use =(B1-A1)/A1*100 for relative percent change as an ordinary number. Check that A1 is not zero before using the second formula, and label the output cells so the two results cannot be confused.

If the inputs are percentage-formatted cells containing 30% and 40%, use =(B1-A1)*100 for points and =(B1-A1)/A1 for relative change. Format the points result as a number and the relative result as a percentage. Spreadsheet percentage cells store fractions, so applying the ordinary-number formulas without adapting them introduces a factor-of-100 error.

Everyday examples

Example	Answer	Try it
Interest rate: 4% to 5%	+1 percentage points
Poll support: 42% to 45%	+3 percentage points
Exam pass rate: 80% to 75%	−5 percentage points
A new rate: 0% to 12%	+12 percentage points

Common mistakes

Calling a rise from 30% to 40% a 10% increase. It is 10 percentage points, but the relative increase is approximately 33.33%.
Multiplying a point difference by 100 again. If inputs are written as 30 and 40, their difference is already 10 points.
Assuming relative change is defined from a zero starting rate. You can subtract zero, but you cannot divide by it.
Confusing percentage points with basis points. One percentage point equals 100 basis points, so a 0.25-point move is 25 basis points.

Common questions

What is the difference between percent and percentage points?

Percentage points are the direct difference between percentages. Percent change measures that difference relative to a starting value. A rate rising from 20% to 25% rises by 5 percentage points, while 5 ÷ 20 × 100 gives a relative increase of 25%.

How many percentage points is a rise from 30% to 40%?

10 percentage points. Subtract the old percentage from the new: 40 − 30 = 10. The relative change is different: 10 ÷ 30 × 100 is approximately 33.3333%. Use the label that matches the calculation you are reporting.

Can percentage points be negative?

Yes. A change from 80% to 75% is −5 percentage points because 75 − 80 = −5. With a positive starting rate, the relative change also indicates a decrease: −5 ÷ 80 × 100 = −6.25%.

What happens when the old percentage is zero?

The point change remains available. From 0% to 12% is +12 percentage points. Relative percent change cannot be calculated because division by zero is undefined. The calculator shows a note instead of displaying infinity or treating the relative change as 12%.

Is one percentage point the same as one basis point?

No. One percentage point equals 100 basis points. Moving from 4% to 4.25% is a rise of 0.25 percentage points, or 25 basis points. The relative rise in the rate is 6.25%, which is a third, distinct measure.

Can I compare negative rates or rates above 100%?

Yes, the calculator accepts signed percentages without imposing a zero-to-100 limit. For negative starting rates, relative change uses the signed old rate, so its sign may not describe an ordinary increase or decrease. The point change remains the direct signed difference.

Does a change in poll support prove an opinion shift?

Not by itself. The calculator measures the arithmetic gap, not statistical significance. Sampling uncertainty, question wording, fieldwork dates and the populations surveyed can affect the comparison. A three-point movement may be smaller than the uncertainty in either poll.

Last reviewed 8 November 2026. Results use exact decimal arithmetic and are rounded once for display.