A percentage-point change is the simple difference between two percentages. A percentage change compares that difference with the original percentage. They answer different questions, so they usually give different numbers.
This lesson sits between reversing a percentage and successive changes in percentages and changing bases, and it matters whenever a question quotes rates, shares or interest.
Why are there two kinds of change?
A percentage is already a ratio. When a rate itself changes, you can ask “by how many points?” or “by what percentage of where it started?”.
Imagine 20% of students in a school cycle to class. A year later it is 25%.
The rate moved 5 points along the scale. But compared with where it began, the rate grew by a quarter. Both statements are true, and they are not the same statement.
How do I find each one?
- Percentage-point change = new rate − old rate.
- Percentage change = (new rate − old rate) ÷ old rate × 100.
The word “points” (or the wording “by how many percentage points”) tells you step 1. The words “percentage increase” or “percent rise” tell you step 2.
Worked example
A savings account paid 4% interest per year last year. This year it pays 6%.
Step 1, percentage-point change: 6 − 4 = 2 percentage points.
Step 2, compare with the old rate: 2 ÷ 4 = 0.5.
Step 3, convert: 0.5 × 100 = 50.
So the rate rose by 2 percentage points, which is a 50% increase in the rate.
Check: a 50% increase in 4% means 4 × 1.5 = 6. ✓ The base here is the old rate of 4%, so that is what the percentage change is measured against.
The mistake to watch for
The usual slip is to report the point difference as if it were a percentage change.
Mistaken statement: “The rate rose from 20% to 25%, so it increased by 5%.”
The student gave the difference of 5 but labelled it as a percentage change.
The correction is to choose the right label.
The rate rose by 5 percentage points. As a percentage change it rose by 5 ÷ 20 = 0.25, which is 25%. Writing “5%” is wrong because 20% × 1.05 is 21%, not 25%.
A good habit is to ask, “Is the thing I am describing a rate, or a change in a rate?” If it is the second, name which kind of change you mean.
Check yourself
Try these without a calculator, then open each answer.
1. A rate falls from 8% to 6%. Give the change in percentage points and the percentage decrease.
Show answer
Points: 8 − 6 = 2 percentage points down. Percentage decrease: 2 ÷ 8 = 0.25, so 25% decrease.
Check: 8 × 0.75 = 6. ✓
2. Attendance rose from 80% to 84%. Give both changes.
Show answer
Points: 84 − 80 = 4 percentage points. Percentage increase: 4 ÷ 80 = 0.05, so 5% increase.
Check: 80 × 1.05 = 84. ✓
3. A report says unemployment rose from 3% to 4.5%. What is the change in percentage points, and what is the percentage increase?
Show answer
Points: 4.5 − 3 = 1.5 percentage points. Percentage increase: 1.5 ÷ 3 = 0.5, so 50% increase.
Check: 3 × 1.5 = 4.5. ✓
Where this leads next
Once the two kinds of change are separate in your mind, continue to successive increases and decreases. The percentage-base explorer lets you see which amount each percentage is taken from, and the percentages practice set mixes all the types together.
Students who lose marks here often know the method but read the question too quickly. A teacher in online one-to-one Mathematics tuition can slow that reading down with you and build a reliable checking habit.