Percentage: how it works
- X% of Y = X ÷ 100 × Y. 15% of 200 = 30.
- X is what % of Y = X ÷ Y × 100. 30 is 25% of 120.
- Percentage change = (new − old) ÷ old × 100. From 80 to 100 is +25%.
Note that a 25% increase followed by a 25% decrease doesn't get you back to where you started: 80 → 100 → 75.
Everyday Australian examples
- Pay rise: a 3.5% rise on an $85,000 salary is $85,000 × 0.035 = $2,975, taking it to $87,975.
- Home deposit: a 20% deposit on a $750,000 home is $150,000. A 5% deposit is $37,500.
- GST inside a price: GST is 10% of the price before GST, which is one-eleventh (about 9.09%) of a GST-inclusive price. A $110 bill includes $10 of GST, not $11.
- Interest rates: a home loan rate moving from 6.00% to 6.25% rises 0.25 percentage points (25 basis points), which is a 4.17% increase in the rate itself.
- Stacked discounts: 30% off, then a further 20% off the sale price, is 44% off in total, not 50%: 0.7 × 0.8 = 0.56 of the original price.
Percentage FAQs
How do I add a percentage to a number?
Multiply by (1 + percent ÷ 100). To add 15% to 200: 200 × 1.15 = 230.
How do I take a percentage off a price?
Multiply by (1 − percent ÷ 100). 25% off $80 is $80 × 0.75 = $60.
How do I work out the original price before a percentage increase?
Divide by (1 + percent ÷ 100). If a price is $115 after a 15% increase, it was $115 ÷ 1.15 = $100. Taking 15% off $115 gives $97.75, which is wrong.
What's the difference between percent and percentage points?
If a rate goes from 5% to 6%, it rose by 1 percentage point, which is a 20% increase.