Editing numbers
The difference between percentage and percentage point
Something I often query in scientific reports is the difference between ‘percentage’ and ‘percentage point’. These two terms are fundamental to statistical analyses, so it is good to have a solid understanding of what they mean and how to calculate them. Understanding ‘percentage change’ is also helpful. In this post, I explain all three concepts using examples.
A quick note on spelling and grammar
The word ‘percentage’ is a noun: it is used to identify a rate or proportion. The words ‘percent’ and ‘per cent’ are usually classed as adverbs: they describe the amount out of each hundred. The term ‘per cent’ is the Australian spelling and ‘percent’ is the US preferred spelling.
Percentage
A percentage describes a part of a whole in the form of a number or ratio as a fraction of 100. For example, 25% means ‘25 out of 100’.
How to calculate a percentage
1. Divide the number you want to determine the percentage of by the total number.
2. Multiply by 100 to convert to a percentage.
Example: 400 students sat an exam but only 300 passed. What percentage of students passed?
1. 300 (the number we want to determine the percentage of) ÷ 400 (the total number of students) = 0.75
2. 0.75 × 100 = 75%
75% of the students passed the exam.
Percentage change
Percentage change describes the difference between an old value and a new value, as a percentage of the old value. For example, the percentage change from 6 to 9 is 50%.
How to calculate percentage change
1. Subtract the old value from the new value to get the difference.
2. Divide the difference by the old value.
3. Multiply by 100 to convert to a percentage.
Example: If the cost of a vaccine will increase from $50 a dose to $75 a dose, what is the percentage change?
1. 75 (the new value) – 50 (the old value) = 25 (the difference)
2. 25 ÷ 50 = 0.5
3. 0.5 × 100 = 50%
The cost of the vaccine increased by 50%.
The calculation rule stays the same even if you are going from a larger number to a smaller number.
Example: If the cost of a vaccine will decrease from $100 a dose to $75 a dose, what is the percentage change?
1. 75 (the new value) – 100 (the old value) = –25 (the difference)
2. –25 ÷ 100 = –0.25
3. –0.25 × 100 = –25%
The cost of the vaccine decreased by 25%.
How to calculate percentage change of two percentages
You can also calculate the percentage change of two percentages, using the same formula.
Example: If the effectiveness of a vaccine increased from 75% to 90%, what is the percentage change?
1. 90 (the new value) – 75 (the old value) = 15 (the difference)
2. 15 ÷ 75 = 0.2
3. 0.2 × 100 = 20%
The effectiveness of the vaccine increased by 20%.
Percentage point
A percentage point is the simple numerical difference between two percentages. For example, the difference between 5% and 25% is 20 percentage points.
How to calculate percentage point change
1. Subtract the the old value from the the new value.
Example: If the effectiveness of a vaccine increased from 75% to 90%, what is the percentage point change?
1. 90 (the new value) – 75 (the old value) = 15
There was a 15 percentage point increase in vaccine effectiveness.
The calculation rule stays the same even if you are going from a larger number to a smaller number.
Example: If the effectiveness of a vaccine decreased from 90% to 75%, what is the percentage point change?
1. 75 (the new value) – 90 (the old value) = –15
There was a 15 percentage point decrease in vaccine effectiveness.
Rule of thumb when writing about percentages
A good rule of thumb is to always express percentages with an accompanying absolute number. Why? Because revealing the absolute number allows the reader to discern context, relativity and validity of the percentage statistic.
For example, if a medical study cites that the percentage of patients with side effects had doubled, it makes a difference whether that statistic is associated with the percentages of 1% to 2%, or of 25% to 50%.
Similarly, if a result states that the volume of contaminated glass disposed of to landfill had doubled, knowing the extent of that doubling makes a difference. Is it from 1% to 2%, or from 20% to 40%? Is the total volume doubling from 1 kg to 2 kg, or from fifty tonnes to a hundred tonnes?
There are many websites that can help you calculate percentages and percentage change. These online calculators can help you to check your calculations are correct.
Remember, incorrect calculations can reduce the professionalism of your work. Mistakes could be perceived as sloppy at best and incompetent at worst. The old saying ‘measure twice, cut once’ also holds true for percentage calculations. By double-checking your calculations, you can prevent embarrassing and potentially serious mistakes.
