Percentages quietly run a large part of daily life: sale discounts, restaurant tips, loan interest, tax, salary raises, exam scores. Yet they're also one of the most fumbled bits of everyday maths — partly because "percent" problems come in several disguises, and the method that works for one doesn't obviously work for another.
This guide covers the handful of percentage calculations you'll actually use, each with a worked example using real numbers, plus the traps that catch people out.
The one idea behind every percentage
"Percent" literally means "per hundred." So 25% is just another way of writing 25/100, or 0.25. Every percentage calculation is really a fraction calculation in disguise, and converting between the two is the master key:
- Percent → decimal: divide by 100 (move the decimal point two places left). 25% → 0.25, 7.5% → 0.075, 150% → 1.5.
- Decimal → percent: multiply by 100 (move the decimal point two places right). 0.25 → 25%.
Once you can flip between the two without thinking, every problem below becomes one line of arithmetic.
Finding a percentage of a number (discounts, tips, tax)
Method: convert the percent to a decimal, then multiply.
Example — discount: a jacket costs $80, on sale at 25% off. How much do you save?
25% → 0.25. 0.25 × 80 = $20 off, so you pay $60.
Example — tip: a restaurant bill is $47.50 and you want to leave 18%.
18% → 0.18. 0.18 × 47.50 = 8.55. Tip = $8.55, total $56.05.
Example — tax: a laptop is $1,200 with 8% sales tax.
0.08 × 1200 = $96 tax. You pay $1,296.
Quick mental-math shortcut for tips: 10% of any bill is just moving the decimal point (10% of $47.50 = $4.75). Double it for 20% ($9.50), or take 10% + half of 10% for 15% ($4.75 + $2.38 = $7.13).
Percentage increase and decrease
Increase: new value = old value × (1 + rate).
Example: your $2,400 monthly salary rises 6%.
1 + 0.06 = 1.06. 2400 × 1.06 = $2,544.
Decrease: new value = old value × (1 − rate).
Example: a $95 pair of shoes at 30% off.
1 − 0.30 = 0.70. 95 × 0.70 = $66.50.
The trap here: successive percentages don't add. A 20% discount followed by another 20% discount is not 40% off — it's 0.8 × 0.8 = 0.64, i.e. 36% off. Similarly, a 50% price rise followed by a 50% cut doesn't return to the original: $100 → $150 → $75. Each percentage applies to the new base, not the original.
What percentage is X of Y? (grades, stats, proportions)
Method: (X ÷ Y) × 100.
Example — exam score: you scored 42 out of 50.
42 ÷ 50 = 0.84 → 84%.
Example — market share: your shop made $3,200 of the $20,000 total weekend sales on your street.
3200 ÷ 20000 = 0.16 → 16%.
For everyday estimates, a percentage calculator handles all three of these problem types — part-of, increase/decrease, and reverse — without you rearranging formulas.
Percentage change (growth, inflation, investment returns)
Method: ((new − old) ÷ old) × 100.
Example: rent goes from $900 to $990 per month.
(990 − 900) ÷ 900 = 90 ÷ 900 = 0.10 → a 10% increase.
Example: a stock falls from $60 to $45.
(45 − 60) ÷ 60 = −15 ÷ 60 = −0.25 → a 25% decrease.
Note the asymmetry: rising from 50 to 75 is a 50% increase, but falling from 75 back to 50 is only a 33.3% decrease — because the base changed. This is why "down 50%, up 50%" doesn't get you back where you started.
Finding the original (reverse percentages)
Problem: you paid $66.50 after a 30% discount — what was the original price?
Method: original = final ÷ (1 − rate).
66.50 ÷ 0.70 = $95.
Problem: a bill with 15% tip added came to $69 — what was the pre-tip amount?
69 ÷ 1.15 = $60.
This "work backwards" form is the one people get wrong most often. The instinct is to subtract 30% of $66.50, which gives $46.55 — wrong, because the 30% applied to the original price, not the discounted one. Always divide by (1 ± rate).
Common mistakes to avoid
- Adding successive percentages (20% + 20% ≠ 40% — it's 36%).
- Confusing "percentage points" with "percent." Interest rising from 3% to 5% is a 2 percentage point rise, but a 66.7% relative increase. Politicians and headlines exploit this confusion constantly.
- Reversing the base: 10% of 50 equals 50% of 10 (both are 5) — commutativity is a handy mental shortcut, but make sure you're applying the percent to the right number in multi-step problems.
- Forgetting that 100%+ is possible. A 150% increase means 2.5× the original, not 1.5×. Growth figures above 100% trip people up regularly.
Frequently asked questions
How do I calculate 15% of something quickly in my head?
Take 10% (move the decimal point one place left), halve it for 5%, and add them. For $80: 10% is $8, 5% is $4, so 15% is $12. This 10%-and-half trick handles 15% and 20% (double the 10%) for most everyday tipping.
What's the difference between percent and percentage points?
Percent describes a relative change; percentage points describe an absolute difference between two percentages. Going from 20% to 25% is +5 percentage points, which is a 25% relative increase. Mixing them up makes small changes sound huge and huge changes sound small.
Why isn't a 50% loss followed by a 50% gain back to zero?
Because the base changes. Lose 50% of $100 → $50. Gain 50% of $50 → $75. To recover from a 50% loss you need a 100% gain. This asymmetry is why investors fear drawdowns: the deeper the fall, the disproportionately harder the recovery.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. Scored 17 out of 20? (17 ÷ 20) × 100 = 85%. This is the same formula behind market shares, completion rates, and grade calculations.