Understanding Percentages
The word "percent" comes from the Latin per centum — "by the hundred." A percentage expresses a number as a fraction of 100. So 25% means 25 out of every 100, or 0.25 as a decimal. Percentages are used everywhere in everyday Australian life — tax rates, interest rates, discounts, statistical data, pay rises, property growth rates, and more.
The Four Core Percentage Calculations
Most percentage questions fall into one of four types:
- Finding a percentage of a number: 15% of $800 = 0.15 × 800 = $120
- Expressing one number as a percentage of another: 45 out of 180 = (45/180) × 100 = 25%
- Calculating percentage change: (New − Old) / Old × 100. If price went from $250 to $310: (310 − 250) / 250 × 100 = 24% increase
- Reverse percentage: Working backwards from a final value to find the original. If $600 is after a 20% increase: 600 / 1.20 = $500
Markup vs. Gross Margin: A Critical Difference
This is one of the most commonly confused percentage concepts in business. Both relate to the difference between cost and selling price, but they express it differently.
- Markup = (Profit / Cost Price) × 100. A product that costs $80 and sells for $120 has a markup of ($40 / $80) × 100 = 50%.
- Gross Margin = (Profit / Selling Price) × 100. The same product has a gross margin of ($40 / $120) × 100 = 33.3%.
The distinction matters enormously in pricing. A business owner who thinks they're operating at a "50% margin" but has actually calculated markup is significantly overestimating their profitability. GST adds another layer — our GST Calculator handles that calculation separately.
Percentage Change vs. Percentage Points
These are not the same thing — and confusing them is common in media reporting. If an interest rate rises from 4% to 5%, it has increased by 1 percentage point, but by 25% in relative terms (1/4 = 25%). When the RBA or government announces a change in rates or tax, it's always worth checking whether they mean percentage points or a relative percentage change.
Worked Example: Property Price Growth
A property purchased for $620,000 in 2019 is now valued at $875,000 in 2024. What is the percentage growth?
- Change: $875,000 − $620,000 = $255,000
- Percentage change: ($255,000 / $620,000) × 100 = 41.1%
- Annual growth rate (5 years): (875,000/620,000)^(1/5) − 1 = 7.15% per year
Worked Example: Understanding Discounts
A retailer advertises 30% off a $299 item. What do you actually pay?
- Discount: 30% × $299 = $89.70
- Sale price: $299 − $89.70 = $209.30
- Shortcut: multiply by (1 − 0.30) = $299 × 0.70 = $209.30
The shortcut — multiplying by (1 − discount rate) — is the fastest mental maths approach for discounts.
5 FAQs About Percentages
10% of any number is simply that number divided by 10 — move the decimal point one place to the left. 10% of $1,250 = $125. From there: 5% = half of that ($62.50); 20% = double it ($250); 15% = 10% + 5% ($125 + $62.50 = $187.50). This approach lets you estimate most tip, discount and tax calculations without a calculator.
To find X% of Y: type Y × X ÷ 100 = (or simply Y × 0.X). For percentage change: type (New Value − Old Value) ÷ Old Value × 100. Modern smartphones have a % key on the calculator that often automates this — but be careful, as different calculator apps handle the % key differently. When in doubt, use the manual formula.
Australia's GST is 10%. To add GST: multiply the pre-tax price by 1.10. To extract GST from a GST-inclusive price: divide by 11 (not by 10 — a common mistake). For example, GST in a $110 price = $110 / 11 = $10. See our GST Calculator for a full breakdown.
A percentage expresses one number as a fraction of another (25% = 25/100). A percentile is a position within a ranked distribution. If you scored in the 90th percentile on a test, you scored higher than 90% of test-takers. Percentiles are used in health data (growth charts, blood pressure), education results (ATAR, NAPLAN) and income data.
Yes. A percentage over 100% simply means the value is more than the reference value. If your investment returned 150% over five years, you now have 2.5 times what you started with. If a business grew revenue by 300%, it now earns four times its original revenue. Percentages are unbounded above 100 and can technically go below 0% for declines.