Six tools that cover the percentage questions people actually ask — percent of a number, what percent one number is of another, reverse percentages, change over time, quick increase/decrease, and percentage difference. All update live as you type.
The classic — discounts, tips, commissions.
Test scores, market share, progress toward a goal.
Reverse percentages — work back to the original amount.
From an old value to a new value — prices, salaries, traffic.
Add VAT, apply a raise, take off a discount.
Compare two values with no "before" and "after" — measured against their average.
Everything the six tools above are doing, explained.
A percentage is just a fraction with 100 as the denominator — the word literally means "per hundred." Saying 25% is the same as saying 25 out of every 100, the fraction 1/4, or the decimal 0.25. That single idea powers every tool on this page; what changes between them is which piece of the puzzle you already know and which one you're solving for.
Multiply Y by X and divide by 100: X% of Y = Y × X ÷ 100. This is the workhorse of everyday life. A 20% tip on a $64 dinner in the US is 64 × 20 ÷ 100 = $12.80. A 15% discount on a €90 jacket is €13.50 off. GST at 18% on a ₹2,500 service is ₹450. Any time you know a rate and a base amount, this is the formula.
Divide the part by the whole and multiply by 100: (A ÷ B) × 100. Scoring 42 out of 60 on an exam is (42 ÷ 60) × 100 = 70%. If your team closed 30 deals out of 120 leads, that's a 25% conversion rate. The order matters — the number after "of" is always the denominator.
Divide the known result by the percent expressed as a decimal: original = Z ÷ (X ÷ 100). If a 15% deposit on a home came to $45,000, the home price was 45,000 ÷ 0.15 = $300,000. This mode also answers the very common "price before tax" question — if a receipt shows €121 including 21% VAT, the pre-tax price isn't 121 minus 21%; it's 121 ÷ 1.21 = €100. Working backwards through a percentage is the single most common place people get percentages wrong.
Subtract the old value from the new, divide by the old value, multiply by 100: (new − old) ÷ old × 100. A salary going from ₹8,00,000 to ₹9,20,000 is a 15% raise. Rent rising from $1,600 to $1,800 is a 12.5% increase. Note the asymmetry trap: a stock that falls from $100 to $80 has dropped 20%, but climbing back from $80 to $100 is a 25% gain — because the base changed. A 50% loss needs a 100% gain to break even. This is why "it went down X% then up X%" never returns you to the start.
Multiply by (1 + rate) to increase or (1 − rate) to decrease: 500 increased by 10% = 500 × 1.10 = 550; decreased, 500 × 0.90 = 450. Chaining matters here: two successive 10% increases aren't 20% — they're 1.10 × 1.10 = 21%. The same applies to inflation compounding year over year, or a price that's marked up 30% and then discounted 30% (you end up at 91% of the original, not 100%).
When neither value is the "original" — comparing prices at two shops, or output of two machines — percentage change is the wrong tool because there's no natural base. Percentage difference solves this by measuring against the average of the two values: |a − b| ÷ ((a + b) ÷ 2) × 100. Comparing 26 and 14: the gap is 12, the average is 20, so the percentage difference is 60%. It's symmetric — you get the same answer whichever number you enter first.
If a central bank rate moves from 5% to 7%, that's a rise of 2 percentage points, but a 40% relative increase in the rate itself (2 ÷ 5 × 100). Headlines routinely blur the two — "unemployment up 3%" could mean either, and the difference between 10% → 10.3% and 10% → 13% is enormous. When precision matters, say "points" for absolute changes in a rate and "percent" for relative ones.
Beyond the asymmetry and chaining traps above: percentages of different bases can't be added (a 10% discount on shoes plus a 10% discount on a jacket isn't "20% off the order"); an average of percentages is only valid when the underlying bases are equal; and "up to 70% off" legally means at least one item, somewhere, is 70% off. Finally, tiny bases produce dramatic-sounding percentages — going from 2 users to 4 is "100% growth," which is why early-stage statistics deserve a skeptical read of the absolute numbers behind them.
Mode 1 covers tips (US), VAT/GST additions (Europe, India), commissions, and interest for one period. Mode 2 covers exam marks, attendance, conversion rates, and body-fat or budget shares. Mode 3 covers back-calculating pre-tax prices, deposits, and "the sale price is $68 after 15% off — what was it originally?" Mode 4 covers salary changes, price and market moves, and year-over-year growth. Mode 5 covers markups, raises, shrinkage, and inflation adjustments. Mode 6 covers side-by-side comparisons with no before/after. If you're specifically working with sale prices, the Discount Calculator adds currency handling and reverse-price modes; for tax-inclusive pricing, the GST / VAT Calculator handles country-specific rates.
A laptop lists at $1,200 in a Black Friday sale at 25% off. Mode 1: the discount is 1,200 × 25 ÷ 100 = $300, so you pay $900. Sales tax of 8% applies at checkout — Mode 5: 900 × 1.08 = $972 out the door. A month later the same model is back at $1,200 — Mode 4 says the price rose (1,200 − 900) ÷ 900 × 100 = 33.3% from what you paid, even though the sale was "only" 25% off. Same dollars, different bases.
For general arithmetic rather than percentage questions, use the Basic Calculator. Deciding how many decimal places to keep? The Rounding Calculator covers significant figures and banker’s rounding. For proportions of images and screens rather than numbers, see the Aspect Ratio Calculator.