The same relationship, drawn — the shorter bar is the percentage of the taller one.
The best mental-math trick in this business: X% of Y always equals Y% of X. Stuck on 8% of 25? Flip it — 25% of 8 is 2, done. It works because both are just X × Y ÷ 100, and multiplication doesn't care about order. Once you know it, awkward percentages start volunteering to be easy ones.
Calculate what is X percent of Y, what percent X is of Y, and reverse percentages — X is Y percent of what number — with decimal and fraction forms and worked arithmetic steps.
Two bars, one story. The percentage always measures the jump relative to where you started — which is why the same gap reads differently in each direction.
The undo asymmetry — the most useful thing on this page: a +50% rise is not undone by a −50% fall; it takes only −33.3%. Lose 50% and you need +100% just to get home. Percent changes measure against a moving baseline, so up-then-down never cancels. Investors relearn this in every crash. And one more disambiguation for reading the news: going from 5% to 7% is a rise of 2 percentage points, but of 40 percent — two different claims that headlines love to swap.
Calculate percent increase and decrease between two values, the multiplier form, the exact percentage needed to undo a change, and the difference between percent and percentage points.
The price, taken apart.
Order never matters: tax-then-discount equals discount-then-tax, and tipping on a taxed total equals taxing a tipped one — percentage changes are multiplications, and multiplication doesn't care about sequence. (Whether you should tip on pre-tax or post-tax is etiquette, not arithmetic — convention says pre-tax, generosity says post.) All money figures here are computed in whole cents with exact integer arithmetic, so the pennies always reconcile.
Calculate sale prices and savings from discounts, tips with penny-perfect bill splitting between any number of people, and sales tax totals — all in exact cent arithmetic.
Each change applies to what's left, not to the original — the second discount bites a smaller number.
Why "extra 10% off" beats its own headline: a 20%-off sale with a further 10% coupon takes 28% off, not 30 — the coupon works on the already-reduced price. Same law, sneakier costume: +10% then −10% lands at −1%, never zero. Multipliers tell the truth that percent signs blur: ×0.8 × ×0.9 = ×0.72, no exceptions, and any sequence of changes can be summarized as one honest multiplier.
Calculate the combined effect of successive percentage changes — double discounts, raise-then-cut sequences — versus the naive sum, with step-by-step values and the single equivalent multiplier.
Margin = markup ÷ (1 + markup): they start together at zero and diverge forever — a 100% markup is only a 50% margin. The dot marks your numbers.
Why two numbers for one profit? Pricing looks forward from cost — "add 25%" — so buyers and merchandisers speak markup. Accounting looks backward from revenue — "we keep 20¢ of each dollar" — so financial statements speak margin. Neither is wrong; confusing them is. A business that wants a 25% margin but applies a 25% markup quietly gives away a fifth of its intended profit — the classic small-business pricing mistake. The break-even stat above shows how much discount erases the profit entirely: it always equals the margin.
Convert between profit margin and markup from cost and selling price, see profit and break-even discount, and understand why the two percentages measure the same money differently.