Percentages and Discounts: A Practical Guide

How to work with percentages, sale prices, and discounts. With examples and links to free calculators.

Published 2025-02-01

Why percentages matter

Percentages show a part of a whole as a fraction of 100. You see them in sales (25% off), tips (15–20%), interest rates, and statistics. A few basic ideas make them easy to use.

The main ideas: “X% of Y” means multiply Y by X/100. “X is what percent of Y?” means divide X by Y and multiply by 100. “Percent change” from old to new is ((new − old) / old) × 100.

Finding a percentage of a number

To find X% of a number, multiply the number by X/100. Example: 20% of 400 = 400 × 0.20 = 80. On a calculator you can enter 400 × 20 % if it has a percent key, or 400 × 0.2.

Real use: a 15% tip on a $60 bill is 60 × 0.15 = $9. Tax at 8% on a $50 item is 50 × 0.08 = $4.

  • 15% of 200 = 30
  • 8% of 1,500 = 120
  • 100% of any number = the number itself

What percent is X of Y?

Divide X by Y, then multiply by 100. Example: 25 is what percent of 200? 25 ÷ 200 = 0.125, 0.125 × 100 = 12.5%. So 25 is 12.5% of 200.

Use this when you have a part and a total: exam score (e.g. 42/50 = 84%), or “how much of my budget did I spend?”

Percent change (increase or decrease)

Percent change = ((new value − old value) / old value) × 100. If the result is positive, it’s an increase; if negative, a decrease.

Example: price goes from $80 to $100. Change = (100 − 80) / 80 = 0.25 = 25% increase. Example: salary goes from $60,000 to $57,000. Change = (57,000 − 60,000) / 60,000 = −5% (a 5% decrease).

Discounts: percent off vs amount off

“30% off $80” means the discount is 30% of 80 = $24; you pay $56. “$20 off $80” means you pay $60. Same original price, different final price depending on whether the discount is a percent or a fixed amount.

When you see “up to X% off,” the actual discount may be lower on some items. Always run the numbers for the specific price you care about.

Tools to use

Use our Percentage Calculator for “X% of Y,” “what percent,” and percent change. Use the Discount Calculator for sale price and savings with either a percent or a fixed amount off. Both run in your browser and need no sign-up.

FAQ

What’s the difference between percent and percentage points?
If something goes from 10% to 12%, that’s a 2 percentage point increase but a 20% relative increase (2/10 = 0.20). News often says “percentage points” when describing changes in rates.
How do I add a percentage (e.g. tax)?
Multiply the amount by (1 + rate/100). Example: $50 + 8% tax = 50 × 1.08 = $54.
Can I chain discounts?
Apply the first discount to the original price, then apply the second discount to that result. “20% off, then 10% off” is not 30% off the original.

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