Calculators
Everyday Percentage Formulas, With Worked Examples
The six percentage formulas behind almost every everyday question, worked examples for shopping, tips, raises and interest, and the mistakes people make most often.
By TooleemPublished Facts checked
Short answer
Almost every everyday percentage question is one of six formulas: x% of a number (number × x ÷ 100), what percent A is of B (A ÷ B × 100), add x% (number × (1 + x ÷ 100)), take off x% (number × (1 − x ÷ 100)), find the original before x% was added (total ÷ (1 + x ÷ 100)) and percentage change ((new − old) ÷ old × 100). The table below shows each one with a worked example, followed by the cases where people most often get them wrong.
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The six formulas
| Question | Formula | Example | Answer |
|---|---|---|---|
| What is 15% of 80? | number × 15 ÷ 100 | 80 × 0.15 | 12 |
| 24 is what percent of 60? | part ÷ whole × 100 | 24 ÷ 60 × 100 | 40% |
| Add 15% to 80 | number × 1.15 | 80 × 1.15 | 92 |
| Take 25% off 59.99 | number × 0.75 | 59.99 × 0.75 | 44.99 |
| 92 includes 15%: what was it before? | total ÷ 1.15 | 92 ÷ 1.15 | 80 |
| From 80 to 92 is what change? | (new − old) ÷ old × 100 | 12 ÷ 80 × 100 | +15% |
Turning a percentage into a multiplier is the shortcut behind all of them: 15% is 0.15, adding 15% is × 1.15, taking 15% off is × 0.85. Divide by the multiplier to go backwards.
Shopping: discounts and sales tax
- Two discounts in a row multiply, they do not add. 30% off, then a further 20% off: 0.70 × 0.80 = 0.56, a total discount of 44%, not 50%.
- A price that already includes tax: to find the price before 18% tax on a $53.10 total, divide by 1.18 to get $45.00. Subtracting 18% of $53.10 gives $43.54, which is wrong.
- “25% more” and “20% less” are the same gap. If A is 25% more than B, then B is 20% less than A (1 ÷ 1.25 = 0.8).
Money: tips, raises and interest
| Situation | Calculation | Result |
|---|---|---|
| 18% tip on a $45 bill | 45 × 0.18 | $8.10 tip, $53.10 total |
| 7.5% raise on $1,200 a week | 1,200 × 0.075 | $90 more, $1,290 a week |
| Pay after a 10% deduction is $3,150: gross pay? | 3,150 ÷ 0.90 | $3,500 |
| 3.5% interest for a year on $50,000 | 50,000 × 0.035 | $1,750 |
| Two years of 10% growth | 1.10 × 1.10 − 1 | +21%, not +20% |
Growth over several periods compounds, which is why two years at 10% give 21%. For longer horizons the compound interest calculator does the year-by-year work.
Five mistakes that come up again and again
- Using the wrong base. “What percent of the class passed?” divides by the class size; “by what percent did passes rise?” divides by last year’s passes.
- Subtracting a percentage to undo an increase. A 20% rise followed by a 20% cut leaves 96% of the start. Undo a 20% rise by dividing by 1.2, which is a 16.7% cut.
- Adding percentages of different things. 10% of one budget plus 10% of another is not 20% of anything unless the budgets are equal.
- Confusing percent with percentage points. A rate going from 2% to 5% rose by 3 points, which is a 150% increase.
- Percent of a percent. 20% of 20% is 4% (0.2 × 0.2), not 40%.
Splitting a restaurant bill with a tip is quicker with the tip calculator; scaling a recipe or a drawing is a job for the ratio calculator.
Do the calculation
Percentage Calculator
Pick the type of question, enter two numbers and get the answer with the formula used.