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Percentage Calculator

Calculate percentages, ratios, and percent changes — three common questions, one simple tool.

Find a percentage of a number

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Enter two numbers to see the result.

Percentages are the most used and most misused arithmetic in daily life. The same word covers three genuinely different questions — what is X% of Y, what percent of Y is X, and what is the change from A to B — and mixing them up produces confidently wrong answers. The errors are not academic: a 50% gain followed by a 50% loss leaves you down 25%, a price that rises 20% must fall only 16.7% to return to where it started, and the difference between percent and percentage points changes the meaning of every statistic in the news. This calculator handles all the standard forms and shows the working.

How the calculator works

Choose the question you are asking — percentage of a number, what percent one number is of another, or percentage change between two values — and enter the numbers. The calculator applies the matching formula and displays the result with the calculation spelled out. Keeping the three forms separate is deliberate: most percentage mistakes come from applying the right arithmetic to the wrong question.

The three forms

What is P% of X? result = X × (P ÷ 100) 20% of 150 = 150 × 0.20 = 30 X is what percent of Y? percent = (X ÷ Y) × 100 30 of 150 = (30 ÷ 150) × 100 = 20% Change from A to B? change = ((B − A) ÷ A) × 100 150 → 180 = (30 ÷ 150) × 100 = +20%

The third form hides the asymmetry that catches everyone: percentage change is measured against the starting value, so the same absolute move is a different percentage in each direction. From 100 to 150 is +50%, but from 150 back to 100 is −33.3%. This is why a stock that drops 50% must gain 100% to recover, and why sequential percentages never simply add — a 10% rise followed by another 10% rise is 21%, not 20%, because the second applies to a larger base.

What to know about percentages

  • 1Percentage changes are not symmetric. A 50% loss requires a 100% gain to break even, because the loss is measured from the high base and the recovery from the low one. Any time someone chains gains and losses as if they cancel, the arithmetic is wrong — multiply the factors instead: 0.5 × 2.0 = 1.0.
  • 2Percent and percentage points are different units. If a tax rate moves from 10% to 15%, it rose five percentage points but 50 percent. News reports and political claims routinely exploit the ambiguity, choosing whichever framing sounds larger or smaller. When the base is itself a percentage, always ask which is meant.
  • 3Reverse percentage problems trip everyone. If a price after 20% VAT is 120, the pre-tax price is 100 — found by dividing by 1.20, not by subtracting 20% of 120, which gives the wrong answer of 96. To undo a percentage increase, divide by the growth factor; subtracting the same percentage always lands below the original.
  • 4Sequential percentages multiply, never add. Three consecutive 10% increases give 1.1³ = 33.1%, not 30%. Over short chains the gap is small; over long chains it compounds into the entire difference between linear and exponential thinking — the same mechanism as compound interest.
  • 5A percentage without its base is a rhetorical device, not information. "Sales grew 200%" from 10 units means 30 units; a "50% increased risk" of something affecting 2 in 10,000 people means 3 in 10,000. Always recover the absolute numbers before reacting — relative change is where statistics mislead most efficiently.

Frequently asked questions

How do I calculate a percentage increase or decrease?

Subtract the old value from the new, divide by the old value, and multiply by 100: ((new − old) ÷ old) × 100. The division is always by the starting value — that is the part people forget. From 80 to 100 is +25%, while from 100 to 80 is −20%, even though the absolute change is the same 20 either way. The direction determines the base, and the base determines the answer.

Why doesn't a 50% loss cancel a 50% gain?

Because each percentage applies to a different base. Start with 100: a 50% gain reaches 150, then a 50% loss takes half of 150, landing at 75 — down 25% overall. The order does not matter; the result is the same. To combine sequential changes correctly, multiply the growth factors: 1.5 × 0.5 = 0.75. Adding the percentages is the single most common percentage error.

What is the difference between percent and percentage points?

Percentage points measure the absolute gap between two percentages; percent measures the relative change. An interest rate moving from 4% to 6% rose two percentage points, but 50 percent. Both statements are true and sound wildly different, which is why the ambiguity is exploited so often in headlines. Whenever the quantity being changed is itself a percentage, insist on knowing which unit is meant.

How do I find the original price before a percentage was added?

Divide by the growth factor, never subtract the percentage. If a 120 price includes 20% tax, the original is 120 ÷ 1.20 = 100. Subtracting 20% of 120 gives 96, which is wrong — the 20% was charged on the original 100, not on the final 120. The same applies in reverse for discounts: a price after 30% off is the original × 0.70, so divide by 0.70 to recover it.

How do percentages relate to fractions and decimals?

They are the same number in three notations: 25% = 0.25 = 1/4. "Percent" literally means "per hundred," so the % sign is shorthand for dividing by 100. To convert, move the decimal two places — 0.375 is 37.5%. All percentage arithmetic is ordinary multiplication and division on the decimal form; the % notation exists purely because humans find "25%" more intuitive than "0.25 of."