Percentage Calculator

What is a percentage?

A percentage expresses a number as a part of one hundred. Fifty percent (50%) means fifty out of every hundred, which is the same as the fraction 1/2 or the decimal 0.5. The word comes from the Latin per centum, "by the hundred".

Because a percentage is a ratio with a fixed denominator, it lets you compare quantities of very different sizes on one scale: a 5 dollar rise on a 50 dollar item and a 5 dollar rise on a 500 dollar item are 10% and 1% respectively.

How to calculate percent change

Percent change compares a new value with an old one, using the old value as the baseline. It is the right tool for growth in sales, a price that moved, or a measurement that changed between two dates.

percent change = (new − old) ÷ old × 100A positive result is an increase, a negative result is a decrease.

Example: revenue grew from 80 to 100. The change is 100 − 80 = 20, and 20 ÷ 80 = 0.25, so revenue rose by 25%. If it had fallen from 100 to 80 the result would be −20%: note that going up 25% and then down 20% brings you back, but going up 20% and down 20% does not.

How to increase or decrease a number by a percentage

To raise or lower a starting value by a given percentage, multiply it by the percentage as a decimal and add or subtract the result.

increased value = start × (1 + p ÷ 100)

decreased value = start × (1 − p ÷ 100)

Example: adding 15% to 200 gives 200 × 1.15 = 230; taking 15% off gives 200 × 0.85 = 170. In both cases the amount that changed is 30. The same arithmetic prices a discount or adds VAT to a net price.

X is what percent of Y?

Divide the part by the whole and multiply by 100.

percent = X ÷ Y × 100

Example: a student scores 30 marks out of 120. 30 ÷ 120 = 0.25, so the score is 25%. When the answer does not divide evenly, such as 1 out of 3, the calculator shows it to four decimal places (33.3333%).

What is P percent of Y?

Turn the percentage into a decimal by dividing by 100, then multiply by the whole.

result = P ÷ 100 × Y

Example: 15% of 200 is 0.15 × 200 = 30. This is how a tip, a commission or a sales tax is worked out. For tips there is a dedicated tip calculator.

X is Y percent of what number?

Here you know a part and the percentage it represents, and you want the whole. Divide the part by the percentage written as a decimal.

whole = X ÷ (Y ÷ 100)

Example: if 30 is 20% of a number, the number is 30 ÷ 0.20 = 150. This is useful for working back from a known deposit, discount amount or sample size to the original total.

Percentage difference between two numbers

Percent change needs an older and a newer value. When neither number is the baseline, such as comparing two products or two groups, use the percentage difference, which divides by the average of the two.

percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100

Example: comparing 80 and 100 gives 20 ÷ 90 × 100 = 22.22%. The result is the same whichever number you enter first, which is what makes it symmetric.

Percentage points versus percent

A rate that moves from 4% to 6% has risen by 2 percentage points, but by 50 percent in relative terms (2 ÷ 4). Reports often mix the two up, so check which one a figure means before drawing conclusions.

Percent changes do not add up. A 10% rise followed by a 10% fall leaves you 1% below where you started (1.10 × 0.90 = 0.99). To combine several changes, multiply their growth factors.

Everyday uses

• Prices and savings: sale discounts, markups, taxes and tips.
• Money: interest rates, investment returns and inflation, see the compound interest calculator.
• Study and work: test scores, completion rates and performance against target.
• Science and health: error margins, concentrations and changes in measurements.