Percentage Calculator

What a percentage represents

A percentage is a fraction with a fixed denominator of 100 — the word comes from the Latin per centum, "per hundred." Writing 15% is exactly the same as writing 15/100 or 0.15. That fixed base is the whole point: it lets you compare proportions of very different quantities on one scale. Saying that 45 of 180 students passed and 210 of 840 employees enrolled is hard to compare directly; saying both are 25% makes the comparison instant.

Because a percentage is just a scaled fraction, every percentage problem is really a multiplication or division dressed up in convenient notation. The four calculator modes above cover the four arrangements that come up in practice.

How to calculate X% of Y

To find a percentage of a number, convert the percentage to its decimal form and multiply:

result = base × percentage ÷ 100

So 15% of 200 is 200 × 15 ÷ 100 = 30. This works unchanged for decimals and negatives: 7.5% of 640 is 48, and 15% of −200 is −30.

How to find what percent X is of Y

Divide the part by the whole, then multiply by 100 to move onto the percentage scale:

percentage = part ÷ whole × 100

30 out of 200 is 30 ÷ 200 × 100 = 15%. Note the constraint: the whole must not be zero. Asking "12 is what percent of 0?" has no answer, because no multiple of zero can ever produce 12 — the calculator reports this instead of showing a misleading number.

How percentage change works

Percentage change measures how much a value moved relative to where it started:

change = (new − original) ÷ |original| × 100

Going from 80 to 100 is a change of +20 on a base of 80, which is a 25% increase. Going from 250 down to 200 is a change of −50 on a base of 250: a 20% decrease. The sign of the result tells you the direction; the magnitude tells you the size relative to the starting value.

One case needs special care: a starting value of zero. Any nonzero change from 0 would be an "infinite percent" increase, which is not a meaningful number. The calculator reports the absolute difference and the direction, and states plainly that a percentage change from a zero baseline is not defined.

Percentage change vs. percentage points

This distinction causes more real-world confusion than any other percentage topic. When both quantities are themselves percentages — interest rates, poll numbers, conversion rates — the difference between them can be described two ways:

• Percentage points — the plain subtraction. From 4% to 5% is a rise of 1 percentage point.
• Percentage change — the relative move. From 4% to 5% is a 25% increase, because 1 is 25% of 4.

Headlines that say a rate "rose 25%" when it moved from 4% to 5% are technically describing relative change, but most readers picture 4% → 29%. When you communicate changes between percentages, name your units explicitly.

Increasing or decreasing a number by a percentage

To grow or shrink a value by a percentage, compute the adjustment first, then apply it:

adjustment = starting value × percentage ÷ 100

Increasing adds the adjustment; decreasing subtracts it. Adding 18% to 75 means an adjustment of 13.5, giving 88.5. Subtracting 20% from 150 removes 30, leaving 120.

A useful shortcut: increasing by p% is the same as multiplying by (1 + p/100). Adding 18% to 75 is 75 × 1.18. Likewise, decreasing by 20% is multiplying by 0.80.

Common percentage mistakes

• Reversing an increase with the same percentage. Up 20% then down 20% does not return to the start (see the worked example below). To undo a p% increase you must divide by (1 + p/100), not subtract p% again.
• Using the wrong base. Percentage change is always measured against the original value. "100 is 25% more than 80" and "80 is 20% less than 100" are both true — the base changed, so the percentage changed.
• Confusing points with percent when comparing two percentages, as covered above.
• Adding percentages of different bases. A 10% raise this year and 10% next year is a 21% total increase, not 20%, because the second raise applies to a larger salary.
• Dividing by the new value instead of the original. From 80 to 100, dividing 20 by 100 gives 20% — the correct answer is 20 ÷ 80 = 25%.

Rounding considerations

Percentages often produce long decimals — a third is 33.333…% forever. This calculator computes at full precision internally and rounds only for display, showing up to six decimal places. When you chain calculations by hand, round only at the final step: rounding intermediate values compounds the error. For money, follow the rounding convention of the currency and context (typically two decimals) — and note that this calculator deliberately shows plain numbers, since not every value is money.

Everyday and business uses

In daily life, percentages price the world: a 30% discount on a jacket, an 18% tip on dinner, sales tax on a receipt, interest on savings, battery levels, exam scores. A quick example: an 18% tip on a $64 bill is an adjustment of 11.52, bringing the total to 75.52.

In business, percentages carry the load in margins and markups, VAT and sales tax, revenue growth rates, conversion rates, churn, and discount policies. Expressing a change as a percentage makes results comparable across products or periods of very different sizes — exactly why quarterly reports lead with "revenue grew 12%" rather than raw totals. Sanity checks stay easy too: if marketing spend is 12 of a 60-unit budget, that is 20% — an instant read on proportions.

Worked examples

Frequently asked questions

Accuracy and limitations

The formulas behind this calculator are implemented as pure, typed functions covered by an automated test suite, and every example above is computed by that same code when the page is built — the numbers cannot silently drift from the engine. Read more on the methodology and accuracy page. As with any general-purpose calculator, verify results independently before relying on them for consequential financial, legal, tax, medical, or business decisions.