How to calculate percentages

Percentages trip people up because there are five different questions they can answer, and the formula changes slightly for each one. “What’s 15% of 80?” is a different beast from “80 is what percent of 320?” or “if the sale price is $60 at 25% off, what was the original?” Here are the five formulas you actually need, each with a worked example and a mental-math shortcut.

1. X% of Y

Formula: (X / 100) × Y. The most common version. Example: 15% of 80 is 0.15 × 80 = 12.

Mental-math shortcut: get 10% by moving the decimal one place left (10% of 80 is 8), then scale. 15% is 10% plus half of 10% (8 + 4 = 12). 20% is double 10% (16). 5% is half of 10% (4). Almost any round percentage collapses to this pattern.

2. A is what % of B

Formula: (A / B) × 100. Example: 24 is what percent of 80? (24 / 80) × 100 = 30%.

The thing to remember: A goes on top, B on the bottom. “A of B” maps directly to “A over B.” If you’re ever unsure which number is the denominator, it’s the one after “of.”

3. Percent change

Formula: ((new - old) / old) × 100. Example: price went from $50 to $65. Change: ((65 - 50) / 50) × 100 = 30% increase. Price went from $50 to $40: ((40 - 50) / 50) × 100 = -20%, a 20% decrease.

The common mistake: dividing by the new value. Always divide by the original. A stock that drops 50% then rises 50% is not back to even — it’s still down 25%, because the 50% rise is off a smaller base.

4. Reverse percent (finding the original)

This one catches people. The shirt is $60 after a 25% discount — what was the original price? The wrong move: take $60 and add 25%, which gives you $75. That’s incorrect, because 25% of $80 is $20 (the actual discount), not $15. The right formula: original = discounted / (1 - discount %). So 60 / (1 - 0.25) = 60 / 0.75 = $80.

Same pattern works for tax. Receipt shows $107 total at 7% tax — the pre-tax price is 107 / 1.07 = $100.

5. Tip math shortcut

Restaurant math is just 10% plus half of 10%. Bill is $42? 10% is $4.20, half of that is $2.10, so 15% is $6.30, 20% is $8.40. For 18%, take 20% and trim a touch. No mental long division required.

For groups, our tip calculator does the split-by-person math including tax. For everything else — discounts, margins, grade averages — the percentage calculator handles all five formulas above.

When you can’t trust your head

Three situations where a calculator beats mental math every time: anything compounding (interest, investment growth, population), anything over long chains (a 10% discount plus a 20% discount is not 30% — it’s 28%, because the second discount applies to the already- reduced price), and anything where the answer ends up on paperwork. For a coffee tip, do it in your head. For a mortgage calculation, use the tool.

A sanity check that works every time

Before committing to any percentage answer, ask: is this roughly in the right neighborhood? 15% of 80 should be noticeably less than half (40). 30% change on 50 should be around 15. If your calculator spits out 150, you fat-fingered a decimal. This three-second gut check catches 90% of the errors that actually cost money.