Percentages run modern life — taxes, tips, discounts, exam scores. Master the math behind them in five minutes.
Percentages are one of the few bits of school math everyone uses every single day. The word literally means "per hundred" — 25% is just shorthand for 25 out of every 100. Once you internalise that, every percentage question becomes a two-step calculation.
A percentage is a fraction with 100 on the bottom. 25% = 25/100 = 0.25 as a decimal. Whenever you see %, you can mentally replace it with × 0.01.
Find X% of a number: Number × (X / 100) _Example: 18% of $42 = 42 × 0.18 = $7.56_
What % is A of B? (A / B) × 100 _Example: 35 marks out of 50 = (35/50) × 100 = 70%_
Percentage increase / decrease: ((New − Old) / Old) × 100 _Example: salary up from $50,000 to $55,000 → (5,000 / 50,000) × 100 = 10% raise_
Memorise these three and you can answer 95% of percentage questions you will ever meet.
A 15% tip on a $46 bill: 46 × 0.15 = $6.90. Mental shortcut — 10% is $4.60, half of that is $2.30, add them = $6.90.
A jacket marked "30% off" with original price $120: discount = 120 × 0.30 = $36, you pay $84. Watch out: "30% off then extra 20% off" is *not* 50% off — it is 30% then 20% of what is left = 44% off total.
Pre-tax bill $200 with 8% sales tax: tax = 200 × 0.08 = $16, total = $216. Going the other way (price *includes* tax)? Divide the total by 1.08 to find the pre-tax price.
Scored 82 out of 95 on a test? (82 / 95) × 100 = 86.3%. Most grading scales then map percentages to letter grades (90+ = A in many systems).
A 7% annual return on $10,000 = $700 in year one. Over many years, that compounds (see our compound-interest article — the same simple percentage drives it).
Combine these: 37% = (3 × 10%) + 5% + (2 × 1%). For 480, that is 144 + 24 + 9.60 = 177.60.
How do I reverse a percentage? If the post-tax total is $216 at 8% tax, divide by 1.08 to find $200.
What is a basis point? 1/100 of a percent. A rate cut from 5.25% to 5.00% is "25 basis points."
Can a percentage be more than 100? Absolutely — a 150% return triples your money.
Use our Percentage Calculator for every variant — "X is Y% of what," tip splits, tax-inclusive prices, and percentage change.