Percentage Math Made Easy: Discounts, Tax, Tips, and More

A “25% off” sign, an 8% tax rate, an “18% tip” — percentages are the everyday math of shopping, money, and school. And they’re deceptively easy to get wrong, especially when a discount and a tax both apply to the same price.

This guide breaks percentages into three core problems, then shows how the common real-world cases (discounts, taxes, tips) map onto them — so you can solve any of them without a spreadsheet.

The three core percentage problems

Almost every percentage question is one of three types:

1. Find the percentage of a number. What is 20% of 80? → 16. This is the most common.
2. Find what percentage one number is of another. 80 is what percent of 200? → 40%.
3. Find the whole from a percentage. 15 is 25% of what? → 60.

If you can tell which type you’re looking at, the math falls into place. A good calculator does all three, and the trap is usually mixing them up — solving for the wrong value.

Discounts: percentages you subtract

A discount is a percentage you take off the original price. The final price is:

Final price = Original price × (1 − discount% / 100)

So a $100 jacket at 25% off costs $100 × 0.75 = $75.

The trickiest cases are stacked discounts. If a jacket is 40% off and you have an extra 20% off, it is not 60% off. The first cut takes it to $60, then the second takes 20% of that — $12 — leaving $48, which is a real 52% discount. Coupons multiply, they don’t add.

Tax and tipping: percentages you add

Sales tax and tips are percentages you add on top. The total is:

Total = base price × (1 + rate% / 100)

So a $48 jacket at 8% tax costs $48 × 1.08 ≈ $51.84.

For tipping, the same math applies, but what you tip on is a cultural choice. In the US, 15–20% is standard for table service, and traditional etiquette tips on the pre-tax amount rather than the final total.

Percentages aren’t symmetric — the classic trap

Here’s a subtlety that trips people up: increasing by a percentage and then decreasing by the same percentage does not bring you back. A price that goes up 20% (from $100 to $120) and then drops 20% lands at $96, not $100. Percentages are relative to whatever number they’re applied to, and that number keeps changing.

The same reasoning applies to discounts: working out the original price from a sale price isn’t just adding the discount back. If you know the final price and the discount rate, you divide: Original = Final / (1 − discount% / 100).

Quick Reference

• Three core problems: percent of a number, what percent one is of another, and the whole from a percent.
• Discounts multiply — a 40% then 20% off stack is a real 52%, not 60%.
• Tax and tips add: total = base × (1 + rate%/100).
• Percentages aren’t symmetric — a 20% rise then a 20% fall lands at 96%, not 100%.
• Work out the original price backward with Original = Final / (1 − discount%/100).

Getting started

If you need a quick answer, the Percentage Calculator handles the three core problems and the reverse cases. To check what a sale item really costs before you buy, the Discount Calculator shows the amount saved alongside the price. For taxes, the Sales Tax Calculator handles US state rates or a custom rate. And the Tip Calculator splits a bill across a group and shows what everyone owes.