Percent Increase Calculator

The formula this calculator uses

Percent Increase = (New Value - Original Value) / Original Value x 100

V0

Original value — where you began, and the divisor

Vn

New value — where you ended up

Vn - V0

Absolute increase, before conversion to a rate

Vn / V0

Growth multiple — 1.25 is the same fact as +25%

How to check the result by hand

1. 1

   Confirm that the movement really is upward

   Percent increase assumes the new value exceeds the original. When it does not, the arithmetic still works but the sign comes out negative and what you are describing is a decrease. From 80 to 100 the direction is upward, the gap is 20, and the answer has to be positive.

2. 2

   Subtract to get the absolute increase

   New minus original, always in that order. For 80 rising to 100 that is 20, and this figure is worth keeping separate from the percentage: it is the size of the change before any comparison has been made, and it is the number you should quote when the base is tiny or zero.

3. 3

   Divide by the original value, not the new one

   This is the step where errors happen, because both numbers are sitting there looking plausible. Divide the 20 by 80, the starting figure, giving 0.25. Dividing by 100 instead gives 0.20 and answers the reverse question — how far you would have to fall to get back.

4. 4

   Multiply by 100 and attach the unit

   0.25 x 100 = 25.00%. Writing the direction alongside the number matters, because a bare 25 is easily read further downstream as a quantity rather than as a rate. Round once, here, to a precision the inputs can support.

5. 5

   Verify by multiplying back

   Multiply the original by one plus the decimal form of the increase: 80 x 1.25 = 100. If the product does not return the new value, then either the denominator or the decimal conversion was wrong, and the check tells you so before anyone reads the number.