Percentage Calculator

Where percentages rule daily life

Percentages are the common currency of everyday math. A store advertises 30% off; a restaurant bill needs a 15–20% tip; your salary goes up 8%; a news report says inflation fell by half a percent; a exam paper is graded out of 100. Interest rates, tax rates, battery levels, download progress bars and election polls are all percentages in disguise.

Because the three question shapes — “how much is X% of Y?”, “X is what percent of Y?” and “what is the percent change from X to Y?” — look similar but use different formulas, it is easy to reach for the wrong one under time pressure. This calculator keeps all three on one page, each written as a plain sentence you fill in, so the right formula is always the one in front of you.

It is also built for the way these questions actually arrive: mid-conversation, mid-shop, mid-homework. The shortcut chips prefill the most common rates — 10%, 15%, 20%, 25% — so a tip or standard discount is two taps away. Results appear as you type rather than after a button press, because in a checkout line nobody wants to submit a form.

The formulas, written plainly

Mode 1 — percent of a number: multiply the number by the percent divided by 100. Fifteen percent of 80 is (15 ÷ 100) × 80 = 0.15 × 80 = 12.

Mode 2 — what percent one number is of another: divide the part by the whole and multiply by 100. Thirty out of 120 is (30 ÷ 120) × 100 = 25%.

Mode 3 — percentage change: subtract the old value from the new value, divide by the old value, multiply by 100. From 80 to 100 is (100 − 80) ÷ 80 × 100 = +25%. Toggle “Show working” under any result to see these formulas with your own numbers substituted — the fastest way to learn them, and to double-check homework.

Why percentage change direction matters

A percentage gain and the same percentage loss do not cancel out, because each applies to a different base. Start with 100, add 50% and you get 150. Now subtract 50% — but 50% of 150 is 75, so you land at 75, a net loss of 25%. Investors run into this constantly: a portfolio that drops 50% needs a 100% gain just to break even.

The same trap appears with successive discounts. A price cut of 20% followed by another 20% is not 40% off — it is 100 → 80 → 64, a total of 36% off. Whenever percentages compound, use mode 3 step by step rather than adding them.

Percentages in finance: tips, tax, discounts and raises

For a tip, use mode 1: 18% of a $64 bill is (18 ÷ 100) × 64 = $11.52. For sales tax the same mode gives the tax amount, which you add to the sticker price. Discounts work in reverse — 30% off $80 is a $24 reduction, so you pay $56; or paste the original and sale prices into mode 3 to verify the store’s advertised percentage is honest.

Raises and price hikes are mode 3 territory. A salary moving from $52,000 to $56,160 is an 8% raise. If your rent goes from $1,400 to $1,500, that is a 7.14% increase — worth knowing before you negotiate. And when a headline says a rate “rose from 2% to 3%”, remember that is one percentage point but a 50% relative jump; mode 3 tells you the second, and the mistakes section below explains the difference.