From 4% to 5%: One Percentage Point, but a 25% Increase

A rate increasing from 4% to 5% has risen by one percentage point. Relative to its starting value of 4%, the rate has increased by 25%. Both descriptions are correct, but they answer different questions. Saying only “it rose by one percent” leaves the reader to guess which meaning was intended.

This is not a technicality reserved for economists. The distinction affects savings-rate comparisons, survey results, discount claims, and any report that describes a change in something already expressed as a percentage.

Subtract for percentage points

Percentage points are the arithmetic difference between two percentage values. Five minus four equals one, so the change from 4% to 5% is one percentage point. Eurostat uses this terminology to distinguish a rate difference from a relative percentage change.

For the relative change, divide the difference by the initial value: (5 − 4) ÷ 4 = 0.25, or 25%. The initial 4 is the denominator. Reversing the direction changes the denominator and therefore the relative result.

From 5% down to 4%, the decline is one percentage point but 20% of the starting rate. The upward and downward relative changes are not equal in magnitude because they start from different values.

Add a population to make the rates concrete

Imagine an invented survey of 1,000 people in each of two periods. In the first, 40 report a particular response, giving 4%. In the second, 50 do, giving 5%. There are ten additional responses, a one-percentage-point change, and a 25% relative increase in the rate.

Each description emphasizes a different scale. The relative figure sounds large because the starting rate is small. The percentage-point figure shows the difference across the full population. The count tells you the size of the observed change in this particular example.

Real surveys need uncertainty, sampling methods, and comparable populations considered as well. The arithmetic alone does not establish that a difference represents a reliable change in the wider population.

The denominator can change too

Now suppose 40 out of 1,000 people have a characteristic in one period, while 50 out of 2,000 have it in another. The count rises from 40 to 50, but the rate falls from 4% to 2.5%.

Reporting only the 25% increase in the count would conceal the expanded population. Reporting only the rate decline would omit that more individuals were counted. Neither number needs to be false for the presentation to be incomplete.

Whenever a claim moves between counts and rates, write the numerator and denominator for both periods. Population definitions, eligibility changes, and coverage differences may affect the comparison before any arithmetic is performed.

A rate change does not directly give a dollar change

Suppose a simplified one-year calculation applies 4% to $2,000, producing $80. Applying 5% to the same balance for the same period produces $100. The rate difference is one percentage point; the dollar difference is $20.

Changing the balance, time held, compounding, or fees changes the dollar result. A headline rate increase is therefore not a complete forecast of what a person will receive. This example isolates the relationship between a fixed base and two rates, rather than describing the full terms of a deposit product.

A compact translation table

If the initial value is zero, the usual relative percentage-change formula divides by zero and is undefined. Moving from 0% to 2% can still be described as a two-percentage-point increase. Calling it an infinite or ordinary percentage increase usually obscures the issue rather than helping.

The clearest wording supplies the old and new values and names the calculation. “The rate rose from 4% to 5%, a one-percentage-point increase” gives readers enough information to reconstruct the comparison and avoids making the size of the change depend on ambiguous phrasing.