When comparing two percentages or describing a change (increase or decrease) in some percentage (such as interest rate or inflation), you can use either percentage points or percent. Their meaning is very different.
The difference between percentage points and percent is best explained on an example.
Let’s say country A has unemployment rate of 5%, while country B has unemployment rate of 20%.
What is the difference between the two unemployment rates?
Most people would immediately say “fifteen percent”, which is not entirely correct. The correct answer is any of the following.
Difference in Percentage Points
The difference between country A and country B unemployment rates is 15 percentage points.
Country B unemployment rate is by 15 percentage points greater than country A unemployment rate.
Country A unemployment rate is by 15 percentage points smaller than country B unemployment rate.
How did we get to that number?
20 – 5 = 15
Percentage points are about subtracting percentages. The definition of percentage point is a unit of arithmetic difference of two percentages.
We can also say the correct answer using the word “percent”. There are again different correct ways to say it, and notice the numbers are now different.
Difference in Percent
You can either express the difference in percent of country A unemployment rate or in percent of country B unemployment rate.
Difference in Percent of Country A Rate
Country B unemployment rate (20%) is four times greater than country A unemployment rate (5%). In other words, country B rate is 400% of country A rate. Country A rate is of course 100% of country A rate, as any quantity is 100% of itself. Therefore, the difference in percent of country A rate is the difference between 400 and 100 (percent of country A rate):
Country B unemployment rate is by 300 percent greater than country A unemployment rate.
The fastest way to get to this number is by dividing the two rates and subtracting 1:
20% / 5% = 4
4 – 1 = 3
3 = 300%
Difference in Percent of Country B Rate
Country A unemployment rate is four times smaller than country B rate. In other words, country A rate is 25 percent, or one fourth, of country B rate. Country B rate is 100% of country B rate. Therefore, the difference in percent of country B rate is the difference between 25 and 100 (percent of country B rate):
Country A unemployment rate is by 75 percent smaller than country A unemployment rate.
You could also say: Country A unemployment rate is by three fourths smaller than country A rate.
The calculation (same steps as above: first divide, then subtract 1):
5% / 20% = 1 / 4
1/4 – 1 = -3/4
-3/4 = -75%
The minus sign indicates that it is smaller than rather than greater than.
Percentage Points vs. Percent
Notice how with percentage points we always used the same number (15), regardless of the direction of the comparison, while with percent, the numbers were different, depending on the base of the comparison. One percent (one hundredth) of country A unemployment rate (0.05%) is a different number than one percent of country B unemployment rate (0.20%).
With percent, you always need to know of what. With percentage points, there is no of what. The expression “percentage point of something” makes no sense.
With percentage points, you are directly subtracting one rate from the other.
With percent, you must first divide one rate by the other (which is the same thing as expressing one rate as a percentage of the other rate). Then you subtract 1.
Percentage Change Example
Let’s say you have money in a savings account. The interest is 3%.
Now consider two scenarios:
- The bank increases the interest rate by one percentage point.
- The bank increases the interest rate by one percent.
What is the new interest rate in each scenario? Which is better?
When 3% increases by one percentage point, it gets to 4%.
When 3% increases by one percent, it gets to 3.03%, because one percent of 3% is 0.03 percentage points.
With percent you can say of what. In this case, the bank increases the interest rate by one percent of the original interest rate. Therefore, you must first multiply the percentage increase (1%) by the original interest rate (3%) to get the increase in percentage points (0.03). The second step is to add the increase in percentage points to the original rate to get the new rate of 3.03%.
With percentage points, there is no of what and no need to multiply. You simply add the fixed amount (1%) to the original rate (3%) to get the new rate (4%).
Percentage point is an absolute, fixed amount, literally the number 0.01. Percent is always relative to something (the of what), or the number 0.01 multiplied by that something.
Next time you hear on TV that inflation “increased by 0.5 percent from 2.1% to 2.6%”, you will know they are wrong and actually mean percentage points. When inflation of 2.1% increases by 0.5 percent, it only gets to 2.1105% (0.0105 percentage points higher).