Calculadora de porcentagem

The one idea behind every percentage

A percentage is just a fraction with a fixed denominator of 100. "Percent" literally means "per hundred", so 20% is another way of writing the fraction 20/100, or the decimal 0.20. Every single calculation this tool performs reduces to that one relationship: part ÷ whole × 100 = percentage. Once you internalise that, the six modes below are simply that same equation rearranged to solve for whichever quantity you are missing. The reason people reach for a calculator is rarely that the maths is hard — it is that the wording ("of", "off", "increase", "points") quietly changes which number is the part and which is the whole.

The six calculations, with formulas

This tool exposes six distinct modes. Each one is a real, named formula:

A worked example: percentage change

Suppose a subscription rose from $150 to $180. The change formula is (180 − 150) ÷ 150 × 100. The difference is 30; divided by the original 150 gives 0.20; times 100 is a 20% increase. The detail that trips people up is the denominator: percentage change is always measured against the starting value, not the ending one. If the price later fell back from $180 to $150, that would be (150 − 180) ÷ 180 × 100 = −16.7%. A rise and the matching fall are not the same percentage, because the base changed. This asymmetry is why a stock that drops 50% must then gain 100% just to break even.

Percentage points versus percent — the mistake that costs money

The sixth mode exists because of one of the most common errors in news and finance. If an interest rate moves from 5% to 8%, it has risen by 3 percentage points, but by 60 percent in relative terms (3 ÷ 5 × 100). Both statements are true and they describe the same move, yet they are wildly different numbers. Saying "rates went up 3%" when they actually rose 3 points understates the change by a factor of twenty. Whenever you compare two values that are themselves percentages, decide deliberately whether you mean the absolute gap (points) or the proportional change (percent) — this tool shows you both at once so you cannot conflate them.

Real-world use cases

• Shopping. "30% off" uses the discount mode; the tool shows both the final price and the amount you save, so you can compare two offers quickly.
• Dining. The tip mode adds the gratuity to the bill and returns the grand total — no mental arithmetic at the table.
• Grades and scores. "I got 47 out of 60" is the "X is what % of Y" mode: 78.33%.
• Business metrics. Month-over-month growth, churn, and margin all reduce to percentage change.
• Statistics literacy. Reading a poll that moved "from 42% to 45%" correctly as 3 points, not 7%, keeps you from being misled.

Tips and pitfalls

• Discounts and tax do not commute in your head, but they do mathematically. Applying a 20% discount then 10% tax gives the same result as tax then discount, because both are multiplications. Stacking two discounts, however, is not the same as adding them: 20% off then 10% off is 0.8 × 0.9 = 0.72, a 28% total reduction, not 30%.
• A percentage of a percentage shrinks fast. 50% of 50% is 25%, not 100%. Multiply the decimals (0.5 × 0.5), do not add.
• Watch the base when reversing a discount. If a $60 item was 25% off, the original was 60 ÷ 0.75 = $80, not 60 × 1.25 = $75. You divide by (1 − rate), you do not add the rate back.
• Rounding accumulates. The tool rounds displayed money to two decimals; for a long chain of calculations, keep full precision until the final step.

All six calculations run instantly in your browser as you type — nothing is sent anywhere — so you can flip between modes and watch the result update live.