Percentages Explained: How Discounts, Markups, and Tax Actually Work
One formula, four everyday situations — discounts, sales tax, markup, and VAT all use the same underlying percentage math.
The one formula behind almost every percentage question
Nearly every percentage question people actually run into — "what's 20% off this?", "how much tax is that?", "what markup am I charging?" — comes down to one relationship: part = whole × percentage. Once that clicks, the rest is just rearranging which piece you're solving for.
If you want the raw calculation without the explanation, the Percentage Calculator handles all three directions: finding a percentage of a number, finding what percentage one number is of another, and finding the original number from a percentage and a part.
Discounts: taking a percentage away
A discount subtracts a percentage from a price: final price = original price × (1 − discount%). A $50 item at 20% off becomes $50 × 0.8 = $40 — not $50 minus 20, a mistake that's easy to make when doing it in your head quickly. The Discount Calculator does this instantly and also shows the dollar amount saved.
Sales tax and VAT: adding a percentage on top
Tax works the opposite direction — it adds a percentage on top: final price = original price × (1 + tax%). Where people get tripped up is going backward: if a price already includes tax and you want to find the pre-tax amount, you can't just subtract the tax percentage — you have to divide by (1 + tax%). The Sales Tax Calculator and VAT Calculator both handle this correctly in either direction, which matters more than it sounds like it should.
Markup vs. margin: the pair everyone mixes up
These sound like the same idea and use similar-looking formulas, but they're genuinely different numbers. Markup is profit as a percentage of cost. Margin is profit as a percentage of selling price. A $40 cost item sold for $60 has a $20 profit — that's a 50% markup (20/40) but only a 33.3% margin (20/60). Mixing the two up when pricing a product can quietly eat into profit on every sale. The Profit Margin Calculator shows both from the same two numbers so the difference is obvious, and the Markup Calculator solves the reverse question — what price to charge for a target markup or margin.
The takeaway
Discounts subtract a percentage, tax and markup add one, and margin measures profit against price rather than cost. Different labels, same underlying arithmetic — once you know which direction you're moving in, the calculation is always the same three numbers rearranged.