Percent Change Calculator divides the gap between two values by the original value, then multiplies by 100 to report a signed percent. The sign stays attached to the result, so a drop returns a negative percent and a gain returns a positive one.
Apply the percent change formula
The formula is P = ((New − Old) / Old) × 100. A savings account that grows from $1,200 to $1,350 gives (1350 − 1200) / 1200 × 100, which is 12.5 percent. A shipment count that falls from 900 units to 810 units gives (810 − 900) / 900 × 100, which is −10 percent.
Percent Change Calculator always divides by the old value, never the new one, because the old value is the reference point the change is measured against.
Work through a two-step calculation
Every percent change breaks into two arithmetic steps that the tool prints separately. First, subtract the old value from the new value to get the raw change. Second, divide that change by the old value and multiply by 100.
Keeping these steps visible catches the two places where manual work usually goes wrong: subtracting in the wrong order and dividing by the wrong value.
Use percent change to project a new value
Once a percent change rate is known, it can run forward to predict a new value from an old one. New = Old × (1 + P / 100). A population of 40,000 growing at 3 percent per period becomes 40,000 × 1.03, which is 41,200.
The same formula with a negative P models a decline: 40,000 at −3 percent becomes 40,000 × 0.97, which is 38,800.
Solve for the original value
When only the new value and the percent change are known, divide instead of multiplying. Old = New / (1 + P / 100). A retail price rose 8 percent to reach $64.80; dividing 64.80 by 1.08 recovers an $60.00 original price.
This mode is useful for reverse-engineering a pre-tax or pre-markup figure from a final price and a stated rate.
Avoid this common mistake
Swapping the numerator order is the most common slip. Computing (Old − New) / Old × 100 for a value that increased returns a negative number for what is actually a gain, and computing (New − Old) / New × 100 uses the wrong denominator entirely.
Percent change always subtracts old from new for the numerator, and always divides by old for the denominator, reversing either piece flips the sign or the magnitude of the answer.
Work through a stock price example
A stock opens the year at $48 and closes at $54. The percent change is (54 − 48) / 48 × 100, which is 12.5 percent.
If instead the stock had fallen from $54 to $48, the calculation would be (48 − 54) / 54 × 100, which is about −11.1 percent, a different magnitude than the 12.5 percent gain even though the raw dollar move is the same $6, because the two calculations divide by different starting values.
Apply percent change across multiple periods
Percent change compounds when applied across several periods in sequence rather than simply adding. A value growing 10 percent one year and then 10 percent the next does not end up 20 percent higher overall; it multiplies by 1.10 twice, reaching 1.21 times the original, a 21 percent total increase.
Percent Change Calculator computes each period's change independently, so chaining several results together requires applying the projection formula once per period rather than summing the percentages directly.
Frequently asked questions
How do you calculate percent change between two numbers?
To calculate percent change between two numbers, subtract the old value from the new value, divide that difference by the old value, and multiply by 100. Going from 50 to 65 gives (65 − 50) / 50 × 100, which is 30 percent.
Why can percent change be negative?
Percent change is negative whenever the new value is smaller than the old value, since the numerator (new minus old) comes out negative. A negative percent change reports a decrease, not an error in the calculation.
What is a 100 percent change?
A 100 percent change means the value doubled, since (New − Old) / Old equals 1 exactly when New is twice Old. Going from 30 to 60 is a 100 percent change: (60 − 30) / 30 × 100 = 100.
How is percent change different from percent difference?
Percent change assumes a direction from an old value to a new value and divides by the old value specifically, while percent difference is sometimes defined as symmetric, dividing by the average of the two values instead. This page uses the directional definition, matching how "before and after" comparisons are normally reported.
Can percent change be calculated for negative numbers?
Percent change can be calculated when the old or new value is negative, but the result needs care because dividing by a negative old value flips the usual sign convention. Percent Change Calculator computes the raw formula and reports the signed result exactly as the arithmetic produces it.
What percent change is a $10 raise on a $10 item?
A $10 raise on a $10 item is a 100 percent change, since the new value ($20) is twice the old value ($10): (20 − 10) / 10 × 100 = 100 percent.
Does a 10 percent increase followed by a 10 percent decrease return the original value?
A 10 percent increase followed by a 10 percent decrease does not return the original value; multiplying by 1.10 and then by 0.90 gives 0.99 times the original, a net 1 percent decrease, because the second percentage is taken from a larger base than the first.
Why does the same dollar change give a different percent change depending on direction?
The same dollar change gives a different percent change depending on direction because the formula always divides by the old (starting) value, and that starting value differs depending on whether the change is being measured forward or backward between the same two numbers.
Summary
Percent Change Calculator applies P = ((New − Old) / Old) × 100 to any pair of before-and-after values, returning a signed percent that stays positive for growth and negative for decline. The same tool runs the formula in reverse to project a new value from a known rate or to recover an original value from a new one.
The rule to keep straight: the denominator is always the old value.