Percentage Calculator
Work out a percentage of a number, what percentage one number is of another, or the change between two.
Answer
12
Three questions that all get called “percentage”
Most percentage mistakes are not arithmetic mistakes — they are answering a different question than the one being asked. “What is 15% of 80” is a multiplication and gives 12. “12 is what percent of 80” is a division and gives 15%. “From 80 to 92” is a comparison against a baseline and gives +15%. The three share a symbol and nothing else, which is why this calculator makes you pick the question first and then writes your numbers into the sentence.
Why a rise and the fall back are different percentages
Going from 80 to 92 is a 15% increase. Going from 92 back down to 80 is a 13.04% decrease, not a 15% one, even though it is the same twelve units. Percentage change is always measured against where you started, so moving the starting point changes the answer. This is what makes “it fell 50% then rose 50%” leave you at 75% of where you began rather than back where you were, and it is the single most exploited gap between a true percentage and a misleading one. When the starting value is negative — a loss, an overdraft, a temperature below zero — the change is measured against its absolute value, so going from −80 to −40 reads as a 50% increase and from −80 to −120 as a 50% decrease.
Percentage points are not percent
If a rate goes from 4% to 6%, it has risen by two percentage points and by 50 percent. Both statements are true and they sound like they contradict each other, which is why the difference matters whenever the quantity being measured is itself a percentage — interest rates, conversion rates, market share, tax bands. The change mode here gives you the relative figure, the 50%; type both values with a % sign and it adds the two-point difference as well.
Discounts, tips and VAT, and the reverse ones
A 20% discount off 60 is the “X% of Y” mode, giving 12 off and 48 to pay. Working backwards is where it gets awkward: a price of 120 that already includes 20% tax does not contain 24 of tax, because the 20% was added to 100, not to 120 — it contains 20. To recover a pre-tax figure, divide by 1.2 rather than subtracting 20%, and the change mode will confirm the gap.
Nothing is a percentage of zero
Two inputs have no honest answer and this calculator says so rather than showing a fabricated one. Asking what percent something is of zero has no result, since no multiplier turns zero into a non-zero number. Asking for the change from zero to anything has no result either — any increase from nothing is infinite in relative terms, which is why growth reported from a zero baseline is always quoted in absolute numbers instead.