Percentage Increase Formula

Find the percent

((new − original) ÷ original) × 100

The subtraction finds how much the number moved. Dividing by the original turns that move into a share of the starting amount. Multiplying by 100 writes the share as a percent. From 4 to 5, the change is 1, and 1 / 4 is 25%.

Nothing in the formula forces the new number to be larger. From 5 to 4, the change is −1, and −1 / 5 is −20%. Call that a 20% decrease. The absolute value is useful when you are describing the size of a drop in a sentence, but the signed result is what the formula actually produces.

Division by the original is why a start of 0 is undefined. There is no share of zero that equals a later number. Do not replace that case with infinity.

Try 4 and 5 in the calculator.

Apply a percent

original × (1 + percent ÷ 100)

The “1” keeps the original amount. The fraction adds the extra share. Five percent of 1,850 is 92.50, and 1,850 × 1.05 is 1,942.50. A percent written as a whole number has to be divided by 100 before you fold it in. Confusing 5 with 0.05 is how a 5% tip becomes a 500% tip.

Add 5% to 1,850.

Recover the original

new ÷ (1 + percent ÷ 100)

This is the apply formula solved for the original. Thirteen divided by 1.30 is 10, so a value that became 13 after a 30% increase started at 10. When the percent is −100, the divisor is 0 and the original is undefined.

Reverse 13 after a 30% increase.