Percentage Calculator

How to calculate percentages

A percentage expresses a number as a fraction of 100, which makes it easy to compare shares, discounts, and changes. This percentage calculator covers seven everyday cases: finding X% of a number, finding what percent one value is of another, finding the whole from a known part, increasing or decreasing a value by a percentage, measuring the change between two values, working backwards to an original value (reverse percentage), and converting fractions to percentages. Every answer comes with a chart — a donut for shares of a whole, and a before/after comparison for changes.

Formulas

X% of Y = (X ÷ 100) × Y

Part as a percent = (part ÷ whole) × 100

Whole from a part = part ÷ (percent ÷ 100)

Increase / decrease = base × (1 ± percent ÷ 100)

Percent change = ((end − start) ÷ |start|) × 100

Original value = final ÷ (1 + rate ÷ 100)

Fraction to percent = (numerator ÷ denominator) × 100

Worked examples

• 15% of 200 — (15 ÷ 100) × 200 = 30. The remaining value is 170.
• 30 as a percent of 200 — (30 ÷ 200) × 100 = 15%.
• 30 is 15% of what? — 30 ÷ 0.15 = 200.
• Increase 100 by 20% — 100 × 1.20 = 120; decrease instead: 100 × 0.80 = 80.
• Change from 100 to 125 — (25 ÷ 100) × 100 = +25%.
• Reverse: 125 after a 25% increase — 125 ÷ 1.25 = 100 was the original value.
• 3/8 as a percentage — (3 ÷ 8) × 100 = 37.5% (decimal 0.375).

Everyday situations where percentages come up

• Shopping — a "25% off" tag, a "buy one get 50% off the second" deal, or comparing unit prices.
• Tips and tax — adding an 18% tip or working out how much of a receipt is sales tax.
• Grades and tests — turning 47 correct out of 60 into a score (78.3%).
• Work and finance — a 4% raise, a commission rate, or interest on savings.
• Statistics — expressing "312 of 1,450 respondents" as 21.5% to compare groups fairly.

Quick mental-math shortcuts

You rarely need a formula for round numbers. To find 10%, move the decimal one place left (10% of 240 is 24). 1% moves it two places (1% of 240 is 2.4). Build the rest from those blocks: 20% is double 10%, 5% is half of 10%, and 15% is 10% plus 5%. Percentages are also reversible — 8% of 50 equals 50% of 8 (both are 4), so flip the problem whenever one side is easier.

Fractions, decimals and percentages

The conversion itself is one division — numerator ÷ denominator × 100 — but the common ones are worth knowing by sight rather than working out each time.

Thirds, sixths and twelfths never terminate — 1/3 is 33.33…% and rounding it to 33% loses a third of a percentage point every time. Where three shares must add to a whole, give one of them the remainder rather than rounding all three, or you will be a point short.

Percent, per mille and basis points

The same quantity gets three names depending on how small it needs to be expressed, and the conversions are just factors of ten:

Basis points exist to remove an ambiguity, not to sound technical. If a rate moves from 4% to 5%, saying it "rose one percent" is wrong and "rose 25 percent" is confusing; saying it rose 100 basis points can only mean one thing. Anywhere small changes to an already-percentage figure matter — interest rates, fees, yields — the unit does real work.

Percentage points vs. percent change

These are easy to confuse. If an interest rate rises from 5% to 7%, that is a jump of 2 percentage points, but a 40% increase in the rate itself (2 ÷ 5). News headlines often mix the two, so check whether a figure describes the gap between two percentages or the change relative to the starting value.

Percentage between two numbers

"What percentage is one number of another" is a single division. The number after the word of goes on the bottom:

percentage = part ÷ whole × 100

30 out of 200 is 30 ÷ 200 = 15%. Swapping them answers a different question entirely — 200 out of 30 is 667%, which is correct arithmetic and almost never what was meant.

Percentages in Excel and Google Sheets

Averaging percentages is the trap. A plain AVERAGE treats every row as equally important. A class of 10 scoring 90% and a class of 40 scoring 60% does not average to 75% — weight by class size and the real figure is 66%. Use SUMPRODUCT whenever the rows represent different-sized groups.

Percentages in school and exam contexts

• Attendance — sessions attended ÷ sessions possible × 100. Most schools count half-day sessions, so one absent day is two missed sessions.
• Percentage achievement — target hit ÷ target set × 100. Above 100% is allowed here, unlike a test score.
• Percentage accuracy — correct ÷ attempted × 100. In measurement work it means something else: 100 − percentage error, where error is |measured − true| ÷ true × 100.
• Percentage by mass — mass of the element ÷ total mass of the compound × 100. Water is 11.2% hydrogen and 88.8% oxygen by mass, even though two of its three atoms are hydrogen.
• Percentage abundance of isotopes — the weighted average that gives an element its atomic mass. Chlorine is 75.77% Cl-35 and 24.23% Cl-37, and (35 × 0.7577) + (37 × 0.2423) = 35.48, the figure on the periodic table.
• Atom economy — mass of the desired product ÷ total mass of all reactants × 100. It measures how much of what you put in ends up as something you wanted, which is why it matters in green chemistry.

Estimating percentages in your head

Break awkward percentages into 10% and 5% pieces, both of which are trivial: 10% is one decimal place left, and 5% is half of that.

One more shortcut: percentages commute, so x% of y equals y% of x. 4% of 75 looks awkward, but 75% of 4 is obviously 3.

For tracking growth or decline over several periods, try the percentage increase/decrease calculator, and for sale prices see the discount calculator.