Percentages – multipliers and percentage points

Basic percentage calculations

Find a percentage of a number

When you know the percentage and the whole amount, think: «of» means multiply.

part = whole · p100

Example: 20% of SEK 800 is 800 · 0.20 = SEK 160.

Clue: The question asks «What is ...% of ...?» Write the percentage as a decimal: 20% = 0.20.

Find what percentage something is

When you know the part and the whole, think: part / whole.

percentage = partwhole · 100 %

Example: 30 of 120 students is 30120 · 100 % = 25 %.

Clue: The question asks «What percentage of the total?»

Percentage change and percentage points

Percentage change

First find the change including its sign: new value − old value. Then compare the change with what you started with:

percentage change = changeold value · 100 %

Example: The price goes from SEK 500 to SEK 600:

Find the change including its sign:new − old = 600 − 500 = +100 SEK

Divide by what you started with:100 / 500 · 100 % = 20 %

You divide by what you started with. A negative answer means a percentage decrease.

Percentage points

Percentage points are used when comparing two percentages.

change in percentage points = new percentage − old percentage

From 12% to 9%, the change is 9 − 12 = −3 percentage points, a decrease of 3 percentage points.

The percentage decrease, however, is:

9 − 1212 · 100 % = −25 %

Key difference: 12% → 9% is down 3 percentage points, but down 25 per cent.

Multipliers and a percentage change

Start with 100 % = 1. Add the percentage for an increase and subtract it for a decrease.

Increase by p%

1 + p100

5% increase → 1.05

Decrease by p%

1 − p100

7% decrease → 0.93

A multiplier above 1 means an increase. A multiplier below 1 means a decrease.

Reference table

Change	Multiplier	Calculation
+20 %	1.20	1 + 0.20
+5 %	1.05	1 + 0.05
+2 %	1.02	1 + 0.02
−2 %	0.98	1 − 0.02
−7 %	0.93	1 − 0.07
−20 %	0.80	1 − 0.20

Find the new value

new value = old value · multiplier

Example: SEK 800 increases by 10%: 800 · 1.10 = SEK 880.

Remember: Forwards = multiply.

Find the old value

old value = new valuemultiplier

Example: After a 20% increase, an item costs SEK 600:

Find the multiplier:1 + 0.20 = 1.20

Divide the new value by the multiplier:600 / 1.20 = 500 SEK

Remember: Backwards = divide.

Common mistake: Do not subtract 20% from 600. The 20 per cent was calculated from the old price.

Successive percentage changes

For several percentage changes, multiply the multipliers:

new value = old value · b₁ · b₂ · ...

Example: First +10%, then −10%:

1000 · 1.10 · 0.90 = 990

You do not return to 1000, because 1.10 · 0.90 = 0.99. This is an overall 1% decrease.

Percentage changes cannot usually be added. Use multipliers and multiply them.

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