How to calculate percentages: three formulas, with real examples

The word "percent" comes from Latin per centum — for each hundred. Five hundred years after Italian merchants put it on commercial ledgers, most of us still pause when someone asks "what's 45 out of 180 as a percentage?" Almost every percentage question reduces to one of three formulas. Here they are, with the kind of examples you'll actually run into.

FOLIOKIT · MAY 2026

The three formulas

If you only remember three things from this article, make them these:

That's the entire toolkit. Every "percent off," "what's the markup," "did sales grow," "what's my exam grade" question collapses into one of those.

Worked examples

The discount question — formula 1

A jacket has a sticker price of $89, marked 30% off. The discount is 30% of 89 — that's (30 ÷ 100) × 89 = $26.70. The price you actually pay is 89 − 26.70 = $62.30. Notice the trap: people often want a single step ("89 minus 30 percent"). That works mathematically — 89 × (1 − 0.30) = 89 × 0.70 = $62.30 — and is faster, but you lose the discount amount unless you compute it separately.

The exam question — formula 2

You scored 73 out of 90 on a test. What percentage? (73 ÷ 90) × 100 = 81.1%. The same formula tells you what fraction of a poll said yes (votes ÷ total × 100), what your conversion rate is (purchases ÷ visitors × 100), and what share of your day was spent in meetings (meeting minutes ÷ 1,440 × 100).

The "did it grow" question — formula 3

Your rent went from $1,400 to $1,575. The change: ((1575 − 1400) ÷ 1400) × 100 = 12.5% increase. If the new number is smaller than the old one, you'll get a negative answer — that's a decrease, just drop the sign and add the word. Same formula handles "stock went from $84 to $76" (−9.5%, a decrease) and "subscriber count went from 240 to 380" (+58.3%).

Three traps that catch almost everyone

Where percentages quietly run your life

Once you start noticing them, percentages are the operating system of consumer life. Sales tax, tip on a restaurant bill, interest on a credit card, the APR on a mortgage, the down-payment ratio on a house, your 401(k) employer match, the markup at the grocery store, the protein percentage on the dog food, the discount on Black Friday, the markup on the Black Friday discount you're about to find out about, the polling margin in news stories, the change in a stock price, the engagement rate on a tweet — all percentages.

The reason "percent" beat alternatives like "per mille" (per thousand, ‰) and basis points (1/100 of a percent — used in finance) is that 1 to 100 sits in a comfortable cognitive range. Most adults can intuit the difference between 25% and 40%. They struggle with 250 versus 400 basis points, even though it's the same comparison.

The fast-mental-math shortcuts

A handful of shortcuts cover a lot of everyday calculations:

• 10% of anything = move the decimal one place left. 10% of 87 is 8.7. 10% of 1,250 is 125.
• 5% = half of 10%. So 5% of 87 is 4.35.
• 20% = double 10%. So 20% of 87 is 17.4. (This is your tip-calculation cheat.)
• 15% tip = 10% plus half of 10%. On a $48 bill: 4.80 + 2.40 = $7.20.
• Swap the operation: 4% of 75 equals 75% of 4. The latter is obviously 3. This is a real identity, not a trick: a × b ÷ 100 is symmetric.