Percentage Calculator
Work out percentages in every direction: a percent of a number, what percent one number is of another, the percentage difference between two values, and percentage increase or decrease. Each answer comes with the steps used to reach it.
Percentage Calculator
Please provide any two values below and click the "Calculate" button to get the third value.
Percentage Calculator in Common Phrases
Percentage Difference Calculator
Percentage Change Calculator
Please provide any two values below and click the "Calculate" button to get the third value.
What is a percentage?
A percentage is a number or ratio that expresses a fraction of 100. It is a dimensionless way to compare two numbers — the same job done by ratios, fractions, and decimals. Percentages are written with the "%" sign (or the words "percent" or "pct"), so 35% is exactly the decimal 0.35 and the fraction 720. To find the percentage that one number represents of another, compute the ratio and multiply by 100. If 25 of the 50 students in a class are male, the ratio is 2550 = 0.5, and 0.5 × 100 = 50 — so males are 50% of the class.
Percentage formula
Almost every percentage question fits one algebraic equation with three values:
P × V1 = V2
P is the percentage (in decimal form), V1 is the value the percentage acts on, and V2 is the result. Given any two values, the third follows. For example, if P × 30 = 1.5, then P = 1.530 = 0.05, and multiplying by 100 converts that back to a percent: 5%. Working by hand, keep the percentage as a decimal inside the formula and convert at the end; the calculators above accept the percent directly, which is the same thing with the conversion done for you.
Percentage difference formula
The percentage difference between two values divides the absolute difference between them by their average, then multiplies by 100:
Percentage Difference = |V1 − V2|(V1 + V2)/2 × 100
Because it uses the average, neither value is treated as "the original," and swapping the two values changes nothing. Example: the difference between 10 and 6 is |10 − 6|(10 + 6)/2 = 48 = 0.5 = 50%.
Percentage change formula
Percentage change is directional: it compares the difference between two values with the initial value. To change a number by a percentage, convert the percent to a decimal and multiply the original number by (1 + decimal) for an increase or (1 − decimal) for a decrease:
500 increased by 10% → 500 × (1 + 0.1) = 550
500 decreased by 10% → 500 × (1 − 0.1) = 450
Going backwards — from the starting and ending values to the percent — divide the end value by the start value and subtract 1. That asymmetry is why going from 6 to 10 is a 66.67% increase but coming back from 10 to 6 is only a 40% decrease.
Frequently Asked Questions
How do I calculate a percentage of a number?
Convert the percentage to a decimal by dividing by 100, then multiply by the number. For example, 5% of 30 is 0.05 × 30 = 1.5. The first calculator on this page also works in reverse: give it any two of the percentage, the base value, and the result, and it finds the third.
What is the difference between percentage difference and percentage change?
Percentage difference treats the two values symmetrically: it divides the absolute difference by the average of the two values, so swapping them gives the same answer. Percentage change is directional: it divides the difference by the original (starting) value, so an increase from 6 to 10 is 66.67% while the decrease from 10 to 6 is 40%.
How do I calculate a percentage increase?
Divide the new value by the original value and subtract 1, then multiply by 100. Or directly: new value = original × (1 + percent/100). For example, 500 increased by 10% is 500 × 1.1 = 550. For a decrease, use (1 − percent/100): 500 decreased by 10% is 500 × 0.9 = 450.
How do I convert a percent to a decimal or a fraction?
Divide by 100: 35% = 0.35. As a fraction, write the percent over 100 and simplify: 35% = 35/100 = 7/20. To go the other way, multiply a decimal by 100 and add the % sign.