Percentage Change Calculator

What the Percentage Change Calculator Does

This Percentage Change Calculator finds the percent difference between two numbers: an old (starting) value and a new (ending) value. Enter both figures and it returns the percentage change, telling you whether the value went up or down and by how much.

It's useful for anyone comparing two numbers over time. Students checking math homework, shoppers comparing sale prices, investors tracking a stock's movement, and analysts measuring month-over-month sales or website traffic all rely on the same calculation. The tool reports a percent increase as a positive number and a percent decrease as a negative number.

How Percentage Change Is Calculated (The Formula)

Percentage change measures the size of a change relative to the original value. The formula is:

change = (new - old) / abs(old) x 100%

First, subtract the old value from the new value to get the raw difference. Then divide that difference by the absolute value of the old value, which scales the change against where you started. Multiply by 100 to express the result as a percentage. Using the absolute value of the old number keeps the result correct even when the starting value is negative, so the sign of the answer reflects the actual direction of change.

Worked Example With Real Numbers

Suppose a product's price rose from 80 to 100. Plug the values into the formula:

change = (100 - 80) / abs(80) x 100% = 20 / 80 x 100% = 0.25 x 100% = 25%. The price increased by 25%.

Now reverse it. If the price falls from 100 back to 80: change = (80 - 100) / abs(100) x 100% = -20 / 100 x 100% = -20%. The price decreased by 20%. Notice the two percentages differ even though the gap is the same 20 units, because the starting value is different each time.

Common Mistakes and Factors That Affect the Result

A few errors trip people up most often. Keep these in mind:

• Swapping old and new: always subtract the old value from the new one, not the other way around, or the sign will be wrong.
• Assuming an increase and decrease cancel out: a 25% rise followed by a 20% fall returns you to the start, but the percentages are not equal because the base changes.
• Dividing by the new value: the denominator must be the original value, not the ending value.
• Confusing percentage change with percentage points: going from 5% to 8% is a 3 percentage-point rise but a 60% increase.
• Starting from zero: if the old value is 0, percentage change is undefined because you cannot divide by zero.

Practical Tips for Accurate Results

To read the output correctly, treat a positive result as a percent increase and a negative result as a percent decrease. For example, +12% means growth, while -12% means a decline of the same magnitude.

When you need the percentage difference between two values where neither is clearly 'before' or 'after' (for instance, comparing two stores' prices), divide the difference by the average of the two numbers instead of one value. Percentage change is the right tool only when there is a genuine starting point and ending point, such as a measurement at two different times.