Percentages Made Easy: 6 Formulas You'll Use

Percentages show up everywhere: a 25% discount, an 18% tip, a 7% pay rise, a score of 38 out of 50. Most people can do the easy cases in their head and then get stuck on the rest. This guide covers the six formulas you'll actually use, with a worked example for each, and the traps that catch even careful people.

What a percentage really is

"Percent" means "per hundred". 15% is just 15 out of every 100, or 0.15 as a decimal. That one idea converts every percentage problem into simple multiplication or division: move the decimal point two places, then multiply or divide.

1. Find a percentage of a number

Formula: percentage ÷ 100 × number

What is 15% of 80? 15 ÷ 100 × 80 = 12.

This is the formula behind tips, commission and tax. A restaurant bill of 47.50 with an 18% tip is 0.18 × 47.50 = 8.55.

2. Find what percentage one number is of another

Formula: part ÷ whole × 100

You scored 38 out of 50. 38 ÷ 50 × 100 = 76%.

The order matters: always divide the part by the whole, not the other way round. This is the formula for test scores, completion rates and "what share of my budget is rent".

3. Percentage change (increase or decrease)

Formula: (new − old) ÷ old × 100

A price goes from 80 to 92. (92 − 80) ÷ 80 × 100 = +15%. If it goes from 250 to 200, the result is −20%, a decrease. The key point is that the change is always measured against the old value, the starting point.

4. Apply a discount

Formula: price × (1 − discount ÷ 100)

25% off a 60 jacket: 60 × 0.75 = 45. Multiplying by 0.75 does the subtraction and the percentage in one step, which is quicker and avoids slips.

5. Add a percentage on top

Formula: price × (1 + rate ÷ 100)

A 5% increase on 80: 80 × 1.05 = 84. This is the same move used to add a sales tax or a service charge. For tax in particular, see our guide to adding and removing VAT or GST.

6. Work backwards to the original

If you know the final price and the percentage that was added or removed, divide instead of multiplying:

• After a 25% discount a price is 45. Original = 45 ÷ 0.75 = 60.
• After 20% was added a price is 120. Original = 120 ÷ 1.20 = 100.

This is the formula people most often get wrong, because the instinct is to take 20% of 120. That gives 24, and 120 − 24 = 96, which is not the original price.

The traps

Percentages are not symmetrical. A 25% discount takes 60 down to 45. To get back from 45 to 60 you need a 33.3% increase, not 25%. The base changed, so the percentage changed with it.

Successive changes don't cancel. Add 10% and then take off 10%, and you don't return to the start: 100 × 1.10 × 0.90 = 99. Add 50% then remove 50% and you end at 75. Each percentage applies to a different base.

Percent and percentage points are different. If an interest rate rises from 4% to 5%, that's a rise of 1 percentage point, but a 25% increase in the rate itself. News stories mix these up constantly, and the difference matters.

"Of" versus "off". "30% of 200" is 60. "30% off 200" leaves you paying 140. Read the wording before you reach for the calculator.

Percentages in business

Two business measures are easy to confuse because both are percentages: margin and markup. They use different bases, and mixing them up is a common and expensive mistake. Our post on profit margin vs markup walks through it. Similarly, a loan's interest is a percentage applied again and again, as explained in how loan EMI works.

Quick mental shortcuts

• 10%: move the decimal point one place left (10% of 340 is 34).
• 5%: half of 10% (17 for 340).
• 1%: move it two places (3.4).
• 15%: 10% plus 5%.
• 25%: a quarter. 50%: half. 75%: three quarters.
• To flip a percentage: 8% of 50 is the same as 50% of 8, which is 4. Use whichever is easier.

Let a calculator do the checking

Mental shortcuts are fine for a rough answer, but for anything that matters, such as a quote, an invoice or a salary offer, check it. The Percentage Calculator handles the three common questions: what is X% of Y, what is the percentage change between two values, and what percentage one number is of another. If you're checking tax-inclusive prices, use the GST / VAT Calculator, and for a quick unit conversion alongside, the Unit Converter.

The short version

Turn the percentage into a decimal, pick the right formula, and remember that every percentage is measured against a specific base. Be careful with reverse calculations and successive changes, and you'll avoid nearly every common mistake.