Percent Change Formula

The formula

percent change = ((new value - old value) / |old value|) x 100

Three steps, always in this order:

1. Subtract. New value minus old value gives the absolute change, the raw difference in dollars, points, or units.
2. Divide. Divide that difference by the old value (the starting point). This scales the change relative to where you began, which is the entire point of a percentage.
3. Multiply by 100. This converts the decimal into a percentage. A result of 0.25 becomes 25 percent.

The absolute-value bars around the old value handle negative starting numbers, so the sign of the answer always points the right direction: positive means the value grew, negative means it shrank.

Why the starting value matters

The old value sits in the denominator, so the same dollar change can be a very different percentage depending on where you started. A $20 increase on an $80 price is 25 percent, but a $20 increase on a $400 price is only 5 percent. That is why percent change is useful: it tells you the size of a move relative to its context, not just its raw size.

This also explains why percentage losses and gains are not symmetric. A stock that falls 50 percent needs a 100 percent gain to get back to its starting price, because the second percentage is measured against the smaller number. The formula is honest about that; intuition often is not.

Worked examples

Example 1: a 25 percent increase. A price rises from $80 to $100. Subtract: 100 - 80 = 20. Divide: 20 / 80 = 0.25. Multiply by 100: 25 percent. The answer is positive, so it is an increase.

Example 2: a 20 percent decrease. A price falls from $100 to $80. Subtract: 80 - 100 = -20. Divide: -20 / 100 = -0.20. Multiply by 100: -20 percent. Notice the same $20 move is a smaller percentage here, because the starting value was larger.

Example 3: a salary raise. A salary goes from $50,000 to $56,000. Subtract: 56,000 - 50,000 = 6,000. Divide: 6,000 / 50,000 = 0.12. Multiply by 100: 12 percent. That is how a 12 percent raise is computed.

Formula variations you will actually use

Finding the new value. Rearrange the formula: new value = old value x (1 + percent change as a decimal). A $100 item with a 20 percent increase: 100 x 1.20 = $120. With a 20 percent decrease: 100 x 0.80 = $80.

Finding the original value. original value = new value / (1 + percent change as a decimal). A $120 item that already reflects a 20 percent increase came from 120 / 1.20 = $100. A $96 item after a 20 percent markdown came from 96 / 0.80 = $120.

Percent change in a spreadsheet. In Excel or Google Sheets, put the old value in A1 and the new value in B1, then enter =(B1-A1)/A1 and format the cell as a percentage. That is the entire formula in one cell.

Common mistakes

Dividing by the wrong value. The denominator is always the old (starting) value, never the new one. Dividing by the new value answers a different question: what share of the final number the change represents.

Zero or near-zero starting values. Percent change is undefined when the old value is zero, because you cannot divide by zero. It is also misleading near zero: going from 1 sale to 5 sales is a 400 percent increase that tells you almost nothing.

Mixing up percent and percentage points. Going from 10 percent to 15 percent is a 5 percentage point move but a 50 percent change relative to the starting 10 percent. They answer different questions. Our percentage points vs percent guide walks through the difference.