Percentage Calculator

What does this percentage calculator compute?

A percentage expresses a number as a fraction of 100. This calculator handles the common phrases: what is P% of X; X is what % of Y; X is P% of what; change from A to B; increase or decrease by P%; and percentage difference between two values.

The published formula or method is Y=X·P/100; P=100·X/Y; Y=100·X/P; Δ%=100·(new−old)/|old|; diff%=100·|A−B|/((A+B)/2) for A≥0, B≥0, A+B≠0. The following references support the stated mathematics or method:

• NIST — SI Unit Rules and Style Conventions: The symbol % represents the number 0.01. Thus p% = p/100 and a part of p% of base b equals b×p/100; inverse percentage equations are algebraic rearrangements. CalculatorX’s negative-baseline signed-change convention is separately specified, not attributed to NIST. Mathematical reference only; not implementation validation or an endorsement of CalculatorX.

Which inputs and limits should you check?

Keep the part, base, and percentage distinct; percent means a ratio multiplied by 100. Each of the seven modes requires its two labeled fields. Use consistent units, finite decimal numbers or scientific notation, and at most512 characters per number. Aliases must agree; inactive and unknown fields are rejected. Percent change uses a nonzero |old| baseline; difference needs A,B≥0 and a nonzero sum.

Inputs round to IEEE-754 binary64 first. The engine evaluates each percentage formula exactly for those normalized inputs, then rounds each published numeric field once, ties to even. This is not exact decimal arithmetic or measurement uncertainty propagation. Explicit signed zero displays as 0. Nonzero inputs or outputs that round to zero, overflow, and unrepresentable change delta or difference average return NUMERIC_RANGE: rescale. Subnormal values are supported when the complete result remains representable. Near-zero denominators amplify input rounding; displayed digits use the shortest round-trip decimal.

The worked example uses 20% of 250 with 250 × 20/100. Compare it with the Example calculations and the complete result for the same inputs.

How can you verify and cite this result?

CalculatorX is responsible for this page. The mathematical references above explain the model; implementation checks and their scope are documented separately in the math.percentage v1.1.2 Evidence and capability contract. Read the displayed verification and production state together with the specification's numerical limits.

Use the clean calculator URL to cite the tool. A shared input link identifies a particular calculation. Content updates, numerical verification, and domain reviews have separate dates and scopes.

What is a percentage?

A percentage is a number expressed as a fraction of 100, written with %. It is a dimensionless way to compare a part to a whole (alongside ratios, fractions, and decimals).

Example: 25 of 50 students are male → 25/50 = 0.5 = 50%.

Core formulas

Y = (X · P)/100 P = (100 · X)/Y Y = (100 · X)/P

Algebraically these are the same relation P(decimal) × V₁ = V₂.

Percent change

% change = (new − old)/(|old|) × 100%

The absolute value in the denominator is a CalculatorX convention (shared with the Percentage Change calculator): a move from −100 to −50 is a +50% increase. Percent change is undefined when old = 0. Negative baselines can still be unintuitive in some domains — say so in the result interpretation.

Increase / decrease by P%

X increased by P% = X(1+P/100), X decreased by P% = X(1−P/100)

Percentage difference

% difference = (|A−B|)/((A+B)/2) × 100% (A ≥ 0, B ≥ 0, A+B ≠ 0)

This page does not extend percentage difference to negative values. A = −10, B = 10 would make the average zero; two negatives can make an unsigned relative-difference look signed. Use percent change when a signed starting value is the baseline.