Guides/Percent off vs percent of

Percent off vs percent of vs percentage difference

These phrases sound alike but answer different questions. Mixing them up is how “20% off” turns into the wrong sale price.

Three formulas

• Percent of: X% of N = N × (X ÷ 100). Example: 20% of 50 = 10.
• Percent off (discount): sale = original × (1 − off% ÷ 100). Example: 20% off $50 = $40.
• Percentage difference / change:((new − old) ÷ old) × 100. Example: 40 vs 50 → −20% (a 20% decrease).

Worked examples

1. Percent of: “What is 15% of 200?” → 30. Guide: what is 20%?
2. Percent off: “25% off $80” → save $20, pay $60. Guide: decrease & discounts.
3. Difference: price fell $80 → $60 → (80−60)÷80 × 100 = 25% decrease(same rate as the discount in this case).
4. Trap: “$40 is 20% off what?” needs reverse math: 40 ÷ 0.80 = $50 —original before discount.

Common mistakes

• Treating “20% of the price” as the amount you pay after 20% off (you pay 80%).
• Using the new price as the denominator when measuring a decrease from the old price.
• Adding stacked “percent off” rates as if they share one base.

One calculator, multiple modes

The freePercentage Calculatorcovers percent of, increase/decrease, and discount tabs.