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How Our Percentage Calculations Work

This page describes the formulas used on Real Percentage Calculator, how results are displayed, and the cases we treat as errors rather than numbers. It is here so you can check our work.

Where the math runs

Calculations are performed in your browser. We do not send your inputs to our server to compute a result. If JavaScript is turned off, the calculators will not run.

Core formulas

  • Percentage of a number: (P ÷ 100) × N.
  • X is what percent of Y: (X ÷ Y) × 100.
  • X is P% of what number: X ÷ (P ÷ 100).
  • Percentage change or increase: ((New − Original) ÷ Original) × 100.
  • Percentage decrease: ((Original − New) ÷ Original) × 100.
  • Original after a decrease or discount: Current ÷ (1 − P ÷ 100).
  • Original after an increase: Current ÷ (1 + P ÷ 100).
  • Percentage difference: (|A − B| ÷ ((|A| + |B|) ÷ 2)) × 100.
  • Fraction to percentage: (Numerator ÷ Denominator) × 100.
  • Discount: amount = Original × (P ÷ 100); final price = Original − amount.
  • Marks percentage: (Obtained ÷ Total) × 100.
  • Profit percentage: ((Selling − Cost) ÷ Cost) × 100.

Cases we will not display as a number

If a formula would divide by zero, or if the original value cannot be recovered, the calculator shows an error message. It will not print Infinity or NaN. That includes:

  • Percentage change, increase, decrease, or profit percentage when the base (original value or cost) is 0.
  • “What percent” or percentage difference when both values are 0.
  • A fraction or marks calculation with a denominator or total of 0.
  • Reverse percentage after a 100% (or greater) reduction, including when the current value is already 0.
  • Marks obtained that exceed the total, or negative marks, on the marks calculator.
  • Empty or non-numeric input.

Rounding and large numbers

Ordinary results are shown with up to six decimal places, and trailing zeros are removed. If a number is so small that six decimal places would show it as 0, extra digits (or scientific notation) are used so the value is not hidden. Very large or tiny magnitudes may use scientific notation. Rounding is applied to the displayed text only.

Like any tool that uses standard computer floating-point arithmetic, extremely large magnitudes can lose precision. If a result is not a finite number, it is reported as an error.

Percentage change with negative originals

We use the standard formula even when the original value is negative. For example, a move from −50 to −40 is ((−40 − (−50)) ÷ −50) × 100 = −20%. That can feel unintuitive, but it is the conventional definition and we do not replace it with a different rule.

Questions

If you think a result is wrong, email info@realpercentagecalculator.site with the calculator, the inputs, and the figure you expected.

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