In mathematics, a percentage is a number or ratio that represents a fraction of 100.
It is one of the ways to represent a dimensionless relationship between two numbers; other methods include ratios, fractions, and decimals.
Percentages are often denoted by the symbol "%" written after the number. They can also be denoted by writing "percent" or "pct" after the number.
For example, 35% is equivalent to the decimal 0.35, or the fractions.
Although the percentage formula can be written in different forms, it is essentially an algebraic equation involving three values:
P × V1 = V2
P is the percentage, V1 is the first value that the percentage will modify, and V2 is the result of the percentage operating on V1.
The calculator provided automatically converts the input percentage into a decimal to compute the solution.
However, if solving for the percentage, the value returned will be the actual percentage, not its decimal representation.
Example:
P = 1.5 / 30 = 0.05 × 100 = 5%
The percentage difference between two values is calculated by dividing the absolute value of the difference between two numbers by the average of those two numbers. Multiplying the result by 100 will yield the solution in percent, rather than decimal form.
Example:
Percentage Difference = |10 - 6| / (10 + 6)/2 × 100 = 0.5 = 50%
Percentage increase and decrease are calculated by computing the difference between two values and comparing that difference to the initial value.
Mathematically, this involves using the absolute value of the difference between two values then dividing the result by the initial value, essentially calculating how much the initial value has changed.
Example:
500 increased by 10% (0.1): 500 × (1 + 0.1) = 550
500 decreased by 10%: 500 × (1 – 0.1) = 450