Percentage Points and Promille

Percentage points measure the arithmetic difference between percentages, while promille expresses a proportion per thousand. In brief: a rise from 20% to 25% is 5 percentage points but a 25% relative increase. The value 5‰ means 5 per thousand, equal to 0.5% or 0.005.

These terms answer different questions and should not be used interchangeably. Percentage points compare two percentage levels directly; percent change compares their difference with an initial level; promille provides another scale for writing a proportion. This guide explains each meaning, shows conversions and uses labelled examples to keep the reference quantities clear.

What is a percentage point?

One percentage point is a difference of one unit on a percentage scale. Moving from 12% to 15% is an increase of 3 percentage points because 15 − 12 = 3. The calculation subtracts the displayed percentage numbers without dividing by the original percentage.

A decrease from 40% to 34% is a decrease of 6 percentage points. It can also be written as a signed change of −6 percentage points. This language is useful whenever both starting and ending values are already percentages, such as proportions of a group meeting a condition.

Percentage points are not the same as a count of items. If a share rises by 3 percentage points in a fixed group of 200, the corresponding increase is 0.03 × 200 = 6 items. If the group size changes, that direct count conversion needs additional information about both totals.

How is percent change different from percentage-point change?

Relative percent change divides the difference by the initial value. From 20% to 25%, the difference is 5 percentage points, and the relative increase is 5/20 × 100% = 25%. The percent signs in the original values describe proportions, while the new 25% describes the relative change of that proportion.

From 40% to 50%, the percentage-point increase is 10, but the relative increase is again 25%. The same relative change can therefore correspond to different percentage-point changes depending on the starting level. Conversely, a fixed point change has a larger relative effect when the initial percentage is smaller.

A change from 2% to 3% is only 1 percentage point but a 50% relative increase. Both statements are mathematically correct, yet they emphasise different aspects of the change. Reporting the starting and ending percentages alongside the chosen measure makes the comparison less ambiguous.

How do you calculate both types of change?

Suppose a hypothetical completion share increases from 60% to 72%. First subtract the levels: 72 − 60 = 12 percentage points. Next divide that difference by the initial level: 12/60 = 0.2, or 20%. Thus the share increased by 12 percentage points and by 20% relative to its original level.

If the same fixed total contains 250 tasks, the completed count rises from 0.60 × 250 = 150 to 0.72 × 250 = 180. The increase is 30 tasks, and 30/150 = 20% confirms the relative increase in completed tasks. The point change times the fixed total also gives 0.12 × 250 = 30.

If the total number of tasks changed between observations, the share change would not by itself determine the change in completed count. A higher percentage of a smaller total can still represent fewer completed tasks. Distinguish the proportion being compared from the underlying count before interpreting the result.

1. Subtract the original percentage from the new percentage for a point change.
2. Divide that difference by the original percentage for a relative change.
3. Multiply the relative ratio by 100 to express it as percent.
4. State both measures with their correct labels and reference levels.

What does promille mean?

Promille, also called per mille, means per thousand and uses the symbol ‰. A value of p‰ represents p/1000 of the reference whole. Thus 8‰ = 8/1000 = 0.008. The extra zero in the symbol reflects the thousand-based scale rather than the hundred-based percent scale.

Since 1% equals 10/1000, it equals 10‰. Therefore 1‰ equals 0.1%. A value such as 25‰ is 2.5%, not 25%, and 0.5‰ is 0.05%. Carefully distinguishing the symbols prevents a factor-of-ten error.

Promille is another notation for a ratio, not a different kind of number. It can be converted to a fraction, decimal or percentage without changing the underlying proportion. Its usefulness comes from expressing relatively small shares on a scale that may be more convenient than a percentage with several decimal places.

How do you convert promille, percentages and decimals?

To convert promille to a decimal, divide the displayed number by 1000. To convert a decimal to promille, multiply by 1000 and attach ‰. For example, 12‰ = 0.012, while 0.0045 = 4.5‰. The numerical conversion and the symbol must be changed together.

To convert promille to percent, divide the promille number by 10. To convert percent to promille, multiply the percentage number by 10. Thus 7.5‰ = 0.75%, and 3.2% = 32‰. Writing both as fractions can confirm the relationship: 7.5/1000 equals 0.75/100.

Values above 1000‰ are possible when the compared quantity exceeds the reference whole. For example, 1500‰ = 150% = 1.5 times the reference. In a literal subset of a whole, the share is limited to 1000‰, just as it is limited to 100%, but broader ratio comparisons need not obey that subset restriction.

How do you calculate a promille amount?

Multiply the whole by the promille rate divided by 1000. If a hypothetical inspection finds a specified category at a rate of 6‰ in 2500 items, the corresponding amount is 2500 × 6/1000 = 15 items. This uses the same part-whole structure as percentages, with a different denominator.

To find the promille rate from a part and whole, calculate part/whole × 1000. A count of 9 out of 3000 gives 9/3000 × 1000 = 3‰. The equivalent percentage is 0.3%, and the decimal ratio is 0.003.

To recover the whole from a nonzero promille rate, divide the part by the decimal rate. If 18 units represent 4.5‰ of a total, the whole is 18 ÷ 0.0045 = 4000 units. Checking 4000 × 4.5/1000 returns 18 and confirms the scale.

Why do different ratio scales and change measures exist?

Percent and promille are normalisations to convenient reference totals. A raw fraction such as 3/1000 can be read as 0.3% or 3‰, depending on which notation makes the comparison clearer. Neither notation adds information; both preserve the same numerator-to-denominator relationship.

Percentage points solve a different communication problem: describing a difference between values that are already on a percentage scale. Without the word points, a statement such as the share rose by five percent can be ambiguous about whether it means a five-point addition or a relative increase of five percent.

The same care applies to small rate differences. A rise from 1.2% to 1.5% is 0.3 percentage point, equivalent to a change of 3‰ of the underlying whole, but its relative increase is 25%. Naming the scale and reference prevents those distinct numbers from being mistaken for competing answers.

What mistakes are common with percentage points and promille?

Do not attach a percent sign to a percentage-point difference without explaining the intended measure. From 30% to 36%, the difference is 6 percentage points and the relative increase is 20%. Saying only a 6% increase would normally mean multiplication by 1.06, producing 31.8% rather than 36%.

Do not confuse ‰ with %. The same displayed number represents one tenth as much in promille as in percent. A quick benchmark is 10‰ = 1%; if a conversion contradicts that relationship, the factor of ten has likely been applied in the wrong direction.

Finally, relative percent change is undefined from an initial level of zero because it requires division by that level. A move from 0% to 4% is clearly a four-percentage-point increase, but it has no finite ordinary percentage increase from zero. The point description remains meaningful where the relative-change formula does not.