What This Calculator Does

"Percentage" questions actually come in a few distinct shapes, and mixing them up is a common source of mistakes. This tool covers three of them separately: finding X% of a number, working out what percent one number is of another, and finding the percentage change between an old value and a new one — each with its own dedicated mode so you plug in the right numbers for the question you're actually asking.

How to Use It

Pick a Calculation Mode first, since it determines which two fields appear below it. "What is X% of Y?" asks for a Percentage Rate and a Base Value. "X is what % of Y?" asks for a Part Value and a Whole Value. "Percentage Change from X to Y" asks for an Old Value and a New Value, and reports the result as either an increase or a decrease depending on the sign — a drop in value shows as a decrease rather than a negative percentage.

The Formula

"What is X% of Y?" computes (Y × X) ÷ 100. "X is what % of Y?" computes (X ÷ Y) × 100. "Percentage Change from X to Y" computes ((Y − X) ÷ X) × 100, then the calculator takes the absolute value for display and labels it an increase or decrease based on whether the raw result was positive or negative.

A Worked Example

In "What is X% of Y?" mode, 20% of 50 gives (50 × 20) ÷ 100 = 10. Switch to "X is what % of Y?" mode and ask what percent 30 is of 150: (30 ÷ 150) × 100 = 20% — the same numbers as the first example, but rearranged to answer a different question. In "Percentage Change" mode, going from 100 to 120 is ((120 − 100) ÷ 100) × 100 = 20%, and the calculator reports this as a 20% increase; going the other direction, from 200 down to 150, is ((150 − 200) ÷ 200) × 100 = −25%, which the calculator reports as a 25% decrease.

How to Calculate Percentages Manually

For "X% of Y," turn the percentage into a decimal by dividing by 100 (20% becomes 0.20), then multiply by Y (0.20 × 50 = 10). For "X is what % of Y," divide X by Y and multiply by 100 (30 ÷ 150 = 0.2, then 0.2 × 100 = 20%). For percentage change, subtract the old value from the new one, divide by the old value, and multiply by 100 — a positive result is an increase, a negative result is a decrease (for example, (120 − 100) ÷ 100 = 0.2, times 100 is a 20% increase).

Percentage Change vs. Percentage Point Difference

This is a genuinely common mix-up, and it shows up regularly even in mainstream news coverage of interest rates, tax rates, and survey results. Say an interest rate moves from 2% to 4%. The percentage change— exactly what this calculator's Percentage Change mode computes — is ((4 − 2) ÷ 2) × 100 = 100%: the rate doubled, a 100% relative increase. The percentage point difference is simply 4 − 2 = 2 percentage points: the straightforward, absolute gap between the two rates. Both descriptions are correct at the same time — "the rate rose 100%" and "the rate rose 2 percentage points" both describe the exact same change from 2% to 4% — but they communicate very different-sounding magnitudes, and mixing them up (or using one when you mean the other) is a real, frequent error.

The two numbers only ever match when the old value is 100, which is why they're easy to conflate in everyday examples like this calculator's own 100-to-120 worked example above: a change from 100 to 120 is both a 20% increase and a 20 percentage point increase, since 100 is the one starting value where relative and absolute change are numerically identical. That coincidence disappears as soon as the starting value isn't 100 — as the 2%-to-4% example shows, where the relative change (100%) and the absolute gap (2 points) look nothing alike. This calculator's Percentage Change mode always computes the relative version (percentage change), not percentage points — for a straightforward percentage point difference between two percentages, simply subtract one from the other directly.