Mathematics · percentages

Percentage Calculator

Twelve percentage questions, each with a diagram and the arithmetic written out.
per cent = per hundred

What do you need?

Also useful

Site search (/) takes the same phrases — try 15% of 84 or 84 plus 15%. For bills and gratuities see the Tip Calculator; for a percentage that repeats every year, the Compound Interest tool.

What is 15% of 84?

In proportion

Per cent means per hundred

Field notes

The percentage traps that cost people money

How it works

Every percentage is a multiplication

A percentage is a fraction with a fixed denominator: per cent is Latin for per hundred, so 15% is simply 15/100, or 0.15. Every calculation on this page is that fraction being multiplied or divided by something. Increases multiply by 1 + p, decreases by 1 − p, and reversing either one means dividing by the same factor rather than applying the opposite percentage — which is where most real mistakes happen, because subtracting feels like it ought to undo adding.

Worked example

A bill of 120 includes 20% tax. The tax is not 24. That total is 120% of the net price, so the net is 120 ÷ 1.2 = 100 and the tax is 20. Subtracting 20% would have given 96 and overstated the tax by a fifth. Check it the other way with A is what % of B: 20 is 16.67% of 120 — the tax is a fifth of the net, but only a sixth of the total.

How do I remove VAT or sales tax from a total?

Divide, do not subtract. A total of 120 including 20% tax is 120% of the net, so net = 120 ÷ 1.2 = 100 and the tax is 20. Subtracting 20% gives 96 and overstates the tax by a fifth. The Strip an included % mode does exactly this, and shows what subtracting would have given.

What is the difference between percent and percentage points?

A rate moving from 4% to 5% has risen one percentage point — but that is a 25% increase in the rate, because 1 is a quarter of 4. Both are true and they sound wildly different, which is why careful reporting says "up one point, from 4% to 5%".

Why is 20% off then 10% off not the same as 30% off?

The second discount applies to the already-reduced price: 0.8 × 0.9 = 0.72, so 28% off. The gap widens with bigger numbers — three stacked 30% codes give 65.7% off, not 90%.

What is the difference between markup and margin?

Markup measures profit against cost; margin measures the same profit against the selling price. A 50% markup on a cost of 100 gives a price of 150 — which is a 33.3% margin. They are never equal, and mixing them up systematically undercharges.

Does a 10% rise then a 10% fall return me to the start?

No — 100 becomes 110, then loses 11, finishing at 99. The fall is measured against the bigger number. Two equal and opposite moves of X% always leave you short by X²/100 percent: ±10% costs 1%, ±50% costs a quarter.

Percent and percentage points are not the same thing. A rate moving from 4% to 5% has risen one percentage point and twenty-five percent, and both are correct. Percentage changes also do not reverse: a 20% fall needs a 25% rise to get back to where it started, which is why a fund that loses a fifth and then gains a fifth is still down.
Version history · 1 release
  1. v0.742026-07-27Percentage Calculator rebuilt: 5 modes -> 12, diagrams, working shown (15kB -> 39kB)

Releases in which this page changed, newest last. Derived from the archived copy of every release, not from notes written afterwards — so it reflects what actually shipped. Site-wide passes are left out; they are in the full changelog.