What Is the Formula for Percentages?

formula-percentages Credit: Nicholas Prior/The Image Bank/Getty Images

The formula for finding percentages is to divide part of the whole quantity by the whole quantity and then multiply by 100 percent. A percentage change can be found by simply dividing the old quantity into the difference between the old quantity and the new quantity. This will produce some kind of decimal, integer or other kind of quotient value. To convert the value into a percentage, simply multiply it by 100.

For example, to find the percentage change from five to seven, the difference between the old and new quantities, which is two, should be divided by five, which is the old quantity. This will yield the quotient value of 0.4 or 0.40, which should then be multiplied by 100 percent to equal 40 percent. Therefore, the percentage change that occurs when five turns to seven is a 40 percent increase.

A percentage change can also be "reversed" back to the original new quantity. To do this, whether or not the percentage change was an increase or decrease must be taken into account. If the percentage change was a decrease, then the percent quantity must be divided by the quotient found from dividing 100 from one minus the percentage change quantity. This should look like: x/(1-x/100), where x equals the percentage change decrease. If the percentage change relates to an increase, however, then the formula is slightly different: x/(1+x/100).