How to Calculate Discounts and Percentages (Formulas + Shortcuts)
A “40% off” sign, a 15% tip, a salary raise, an investment return — percentages run daily life, yet most people reach for a calculator with a vague sense of guilt. This guide gives you the four formulas that cover nearly everything, plus mental-math shortcuts that make the calculator optional.
On this page
- The 4 formulas you need
- Sale discounts, step by step
- Percentage points vs. percent
- Mental-math shortcuts
- FAQ
The 4 formulas you need
| Question | Formula | Example |
|---|---|---|
| What is X% of Y? | (X ÷ 100) × Y | 20% of 150 = 30 |
| X is what % of Y? | (X ÷ Y) × 100 | 30 is 20% of 150 |
| Percent change | ((New − Old) ÷ Old) × 100 | 80 → 100 = +25% |
| Price after X% off | Price × (1 − X ÷ 100) | $80 at 25% off = $60 |
That is genuinely the whole toolkit. Every percentage problem you meet — tips, taxes, grades, growth rates — is one of these four in disguise. Our free percentage calculator solves all four instantly, with an optional tax field for shopping.
Sale discounts, step by step
Take a $59.99 jacket at 30% off:
- Find the savings: 30% of $59.99 = 0.30 × 59.99 = $18.00.
- Subtract: $59.99 − $18.00 = $41.99 to pay.
Shortcut: compute what you pay directly — 100% − 30% = 70%, and 0.70 × 59.99 = $41.99. One step instead of two.
Stacked discounts (e.g. “20% off, plus an extra 10%”) do not add to 30%. They multiply: $100 → $80 after 20% → $72 after 10%, a total of 28% off. Retailers know this; now you do too.
Tax: in most places sales tax applies to the discounted price. $41.99 at 8% tax = $41.99 × 1.08 = $45.35 total.
Percentage points vs. percent — the classic trap
If a tax rate rises from 10% to 12%, headlines might call it a “2% increase” or a “20% increase” — and both phrases get used, confusingly, for different things:
- Percentage points: the plain difference — 12% − 10% = 2 points.
- Percent change: relative to the start — (12 − 10) ÷ 10 = 20% increase.
When someone quotes a change in percentages, always ask which one they mean. Politicians and marketers count on you not asking.
Mental-math shortcuts that actually work
- The 10% anchor: 10% of anything is just the decimal moved once ($48 → $4.80). Build from there: 20% is double, 5% is half, 15% = 10% + 5%.
- The flip trick: x% of y = y% of x. 8% of 50 feels hard; 50% of 8 is obviously 4.
- Round first: 18% of $79 ≈ 20% of $80 = $16 — close enough for shopping decisions.
- Doubling check: a 100% increase = double; a 200% increase = triple. (A “200% increase” is not double — the increase itself is twice the original, on top of the original.)
Put it into practice
The fastest way to get comfortable with percentages is to estimate before you calculate. Next time you see a sale sign, guess the final price using the 10% anchor, then check yourself with our percentage calculator. Within a week of doing this, the common figures — 10%, 15%, 20%, 25%, 50% — become instant. For anything trickier, like stacked discounts or tax-inclusive totals, let the calculator do the precise arithmetic while your estimate keeps you honest about the answer.
Frequently asked questions
How do I calculate “20% off” in my head?
Find 10% (move the decimal), double it for 20%, subtract from the price. $150 → $15 → $30 off → you pay $120.
Do two 10% discounts equal 20% off?
No — they compound to 19% off ($100 → $90 → $81). Each discount applies to the already-reduced price.
Is a 150% increase the same as 1.5×?
No — a 150% increase means the original plus 1.5× more, totaling 2.5×. “150% of” would be 1.5×. Wording matters.
How is tip calculated — before or after tax?
Custom varies, but standard etiquette is to tip on the pre-tax subtotal. 15–20% is customary in the US.
FH
The SomethingWebTools Team
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