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Percentage Calculator

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Percentage questions look like one thing but are really five: what a percentage of a number is, one number as a percent of another, the rate of change from A to B, the price after an increase or a discount, and how far apart two percentages are. Most calculators answer one of these at a time; this one answers every question a pair of numbers can support. Two traps are called out separately. The rate of change divides by the original value, so it is asymmetric: 100 to 120 is +20%, while 120 to 100 is −16.67%, not −20%. Percentage points and percentages are different things: 15% is 5 points below 20%, but it is 25% lower relative to 20 — the pair most often confused in the news. Questions in Chinese, English and Japanese are all understood, and a line that cannot be parsed raises an error naming the line instead of being skipped. Everything runs locally in your browser; nothing is uploaded.

Features

  • Every common question about the same pair of numbers: share, rate of change, price after a percentage, percentage-point comparison
  • The rate of change uses the original value as its denominator, and the reverse direction is given too (100→120 is +20%, 120→100 is −16.67%)
  • Percentage points and percentages are written on separate rows
  • Adding then subtracting the same percentage does not return to the start, which is shown with the shortfall
  • Discounts understand “percent off” as well as the Chinese zhe notation
  • Questions in Chinese, English and Japanese are recognised, one per line
  • A line that cannot be parsed raises an error naming it, never skipped silently
  • Adjustable decimal places
  • Everything runs locally in your browser; nothing is uploaded

How to use

  1. Put one question per line, such as “15% of 120”, “18 is what percent of 120”, “from 100 to 120”
  2. Adjust the decimal places if you need to
  3. The result appears as you type, and every row can be copied on its own

FAQ

Why is 120 to 100 not a 20% decrease?
Because the rate of change divides by the original value. Here the change is −20 and the original is 120, giving −16.67%; going the other way, +20 over an original of 100 gives +20%. The denominators differ, so the percentages are asymmetric — that is the definition, not an error.
What is the difference between “5 points lower” and “25% lower”?
They are different quantities. Percentage points are the result of subtracting one percentage from another (20% − 15% = 5 points). A percentage divides that difference by the reference value (5 ÷ 20 = 25%). News reports often give only one, so both rows are shown here.
Why is 100 plus 15% then minus 15% not 100?
Because the second 15% is taken from 115: 115 × 0.85 = 97.75, which is 2.25 short of 100. Adding and subtracting the same percentage do not cancel, and the shortfall is called out as its own row.

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