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Percent and percentage points

Percentage points are the difference between two percentages, so we subtract. Percent compares the change with where we started. From 2% to 3% is an increase of 1 percentage point (3 − 2 = 1), but of 50 percent (1 ÷ 2 = 0.5).

Years 8–9 and upper secondary · Updated

Watch Fox work it out on the board

Fox works one step at a time. Press play.

Two ways to compare

  • Percentage points: how big is the difference? We subtract: new percentage − old percentage.
  • Percent: how big is the change compared with the start? We divide the difference by the old percentage.

An example with interest rates

The interest rate rises from 2% to 3%. We want to describe the rise in both ways.

Percentage points: we subtract the old rate from the new one.

3 − 2 = 1 percentage point

Percent: we compare the rise with the old rate, which is the whole.

1 ÷ 2 = 0.5 = 50%

Both are correct. Someone who saves 10 000 kr gets 200 kr in interest at 2% and 300 kr at 3%.

Example

Example 1: A party in an election

A party went from 8% to 10% of the votes. We want to know the increase in both ways.

  1. Percentage points: the new share minus the old one.

    10 − 8 = 2 percentage points

  2. Percent: we compare the increase with the old share, 8%.

    2 ÷ 8 = 0.25

  3. Support rose by 2 percentage points, which is 25%.

    0.25 = 25%

8 · 1.25 = 10, so 10%. That matches the new election result.

Example 2: Fewer pupils cycle

Out of 600 pupils, 40% cycled in the autumn and 30% in the winter. We want to describe the decrease in both ways.

  1. Percentage points: the new share minus the old one.

    30 − 40 = −10

  2. The decrease is 10 percentage points. We compare it with the old share, 40%.

    10 ÷ 40 = 0.25 = 25%

  3. In numbers of pupils: 40% and 30% of 600.

    0.4 · 600 = 240 and 0.3 · 600 = 180

  4. The number went down by 240 − 180 = 60, and 60 ÷ 240 = 0.25. That is 25% too.

40 · 0.75 = 30, so a decrease of 25% from 40% gives 30%. That is correct.

Example 3: The interest rate rises by 10 percent

The interest rate on a loan is 4% and rises by 10%. We want to know the new rate.

  1. It says percent, so we compare with the old rate. The change factor is 1.1.

    4 · 1.1 = 4.4

  2. The new rate is 4.4%, which is 0.4 percentage points higher.

    4.4 − 4 = 0.4

  3. With "10 percentage points", the rate would instead have become 4 + 10 = 14%.

0.4 ÷ 4 = 0.1 = 10%. That matches the rise.

Pitfalls

  • Saying that an interest rate that goes from 2% to 3% has increased by 1%.

    3 − 2 = 1 is 1 percentage point. As a percentage, the increase is 1 ÷ 2 = 50%.

  • Dividing by the new percentage, so that 8% to 10% becomes 2 ÷ 10 = 20%.

    Compare with where we started: 2 ÷ 8 = 0.25, so 25%.

  • Adding straight away, so that 4% raised by 10% becomes 14%.

    "Rises by 10%" means 10% of the old rate: 4 · 1.1 = 4.4%. We only add when it says percentage points.

Practise on your own

0 of 4 correct

  1. The share who voted in a school vote went from 60% to 66%. By how many percentage points did the share increase?

  2. The share who voted went from 60% to 66%. By what percentage did the share increase?

  3. The interest rate on a savings account is cut from 4% to 3%. By what percentage has the rate been cut?

  4. The interest rate on a loan is 2.5% and rises by 20%. What is the new rate in percent?

Common questions

What is a percentage point?

The difference between two percentages when we subtract them. From 5% to 7% is an increase of 2 percentage points.

How do you convert percentage points to percent?

Divide the percentage points by the old percentage. 2 percentage points from 5%: 2 ÷ 5 = 0.4, so an increase of 40%.

Why does the news say percentage points about interest rates and elections?

To show that the percentages have been subtracted. "Rose by 2 percent" would mean much less: 2% of the old share.

Can an increase of 1 percentage point be an increase of 100%?

Yes. From 1% to 2% is 1 percentage point, but the new percentage is twice as big. That is an increase of 100%.

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