How to Calculate Percentages: The Complete Guide (With Examples)

Percentages show up everywhere — sale tags, tax bills, exam scores, tips, interest rates, body-fat readouts. The math is simple once you see the pattern, but most people mix up which number goes on top. This guide walks through every percentage calculation you'll actually use, with worked examples and the calculators that do the arithmetic for you.

The core idea: a percentage is just a fraction with 100 on the bottom. 25% means 25/100, or 0.25. Every formula below is built on that one fact.

1. Percent of a number (the basic case)

Formula: part = (percent ÷ 100) × whole. Example: 18% of $240 = 0.18 × 240 = $43.20. That's the calculation behind tips, sales tax, and commission.

Shortcut for mental math: 10% is just the number with the decimal moved one place left. 10% of 240 is 24. Need 20%? Double it (48). Need 15%? Take 10% (24) plus half of it (12) = 36.

2. What percent is X of Y?

Formula: percent = (part ÷ whole) × 100. Example: you scored 34 out of 40 on a test. 34 ÷ 40 = 0.85, × 100 = 85%. The trap: people flip it. The total (40) always goes on the bottom.

3. Percent change (increase or decrease)

Formula: percent change = ((new − old) ÷ old) × 100. Example: a stock goes from $50 to $62. (62 − 50) ÷ 50 = 0.24 = 24% increase. If it dropped to $42 instead: (42 − 50) ÷ 50 = −0.16 = 16% decrease.

Critical rule: the old (original) value is always the denominator. A 50% gain followed by a 50% loss does NOT get you back to where you started — $100 → $150 → $75. Run the numbers; don't trust intuition here.

4. Percent off (discounts)

Formula: sale price = original × (1 − discount/100). Example: a $80 jacket at 30% off = 80 × 0.70 = $56. The shortcut is to think about what you're paying, not what you're saving: 30% off means you pay 70%.

Stacked discounts don't add. 20% off then an extra 10% off is NOT 30% off — it's 0.80 × 0.90 = 0.72, so 28% off. Retailers love this gap.

5. Reverse percentages (working backwards)

Formula: original = final ÷ (1 + percent/100) for an increase, or final ÷ (1 − percent/100) for a discount. Example: you paid $84 after 20% sales tax. The pre-tax price is 84 ÷ 1.20 = $70. Another: a shirt cost you $45 after a 25% discount. Original price = 45 ÷ 0.75 = $60.

6. Percentage points vs percent

If a rate goes from 4% to 6%, that's a 2 percentage point increase — but a 50% relative increase. News headlines mix these up constantly. Percentage points = absolute difference. Percent = relative change. Both are correct; they answer different questions.

7. Tips, tax, and the everyday cases

Tip: bill × (tip% ÷ 100). For 18% on a $54 dinner: 54 × 0.18 = $9.72. Sales tax works identically. To get the total bill in one step: 54 × 1.18 = $63.72.

Markup vs margin is the most-confused pair in retail. A 50% markup (over cost) is only a 33.33% margin (of price). They're not the same number — see our markup vs margin calculator for the conversion.

Common mistakes to avoid

• Using the new value as the denominator when calculating percent change (always use the original).
• Adding stacked percentages instead of multiplying them.
• Confusing percentage points with percent.
• Forgetting that a percentage increase and the matching decrease don't cancel out.
• Mixing up markup (over cost) and margin (over price).

Once you internalize the four building blocks — percent of a number, what percent of, percent change, and reverse percentages — you can solve every percentage problem you'll ever meet. The calculators below handle the arithmetic so you can focus on whether the answer makes sense.