Percent Change Calculator
This calculator uses standard published formulas and is reviewed for calculation accuracy and clarity. The result is exact arithmetic, not an estimate.
This free calculator finds the percentage change from one value to another. Enter a starting (original) value and an ending (new) value — the calculator tells you whether the change is an increase or a decrease, and by what percentage. It is useful for tracking price changes, salary adjustments, investment returns, statistics, and any situation where you need to measure how much a value has changed relative to where it started.
How It Works
Percentage change measures how large the difference between two values is relative to the starting value. The absolute-value sign (|Old value|) handles cases where the original value is negative, so the sign of the result correctly reflects the direction of change.
A positive result means the value increased. A negative result means it decreased. A result of zero means no change. Because the starting value is the reference point, the same absolute difference produces a larger percentage when the starting value is small and a smaller percentage when it is large — which is why "up $5" can be a huge change or a trivial one depending on where you began.
Worked Examples
Example 1 — price increase. A product cost $50, now costs $65. Change = ((65 − 50) ÷ 50) × 100 = (15 ÷ 50) × 100 = +30% increase.
Example 2 — price decrease. Value fell from $200 to $150. Change = ((150 − 200) ÷ 200) × 100 = (−50 ÷ 200) × 100 = −25% decrease.
Example 3 — salary change. Salary was $72,000, now $78,500. Change = ((78,500 − 72,000) ÷ 72,000) × 100 = (6,500 ÷ 72,000) × 100 ≈ +9.03% increase.
What This Result Means
The result is the size of the change as a share of where you started, with the sign showing direction: positive is up, negative is down. Two cautions on reading it. First, percent changes are not symmetric — a value that drops 50% has to rise 100% to get back to where it began. Second, a large percentage off a tiny base can look dramatic while the dollar move is small, so pair the percentage with the absolute difference when the stakes matter.
When to Use This Calculator
Percent change is useful in many everyday situations:
- Comparing prices: How much did gas, groceries, or rent increase over the past year?
- Evaluating a raise: A $3,000 raise means something different on a $40,000 salary versus a $120,000 salary — percent change puts it in context.
- Tracking metrics: Website traffic, sales figures, and performance statistics are commonly expressed as percentage change from a prior period.
- Checking investment returns: How much did a portfolio or asset value change from purchase to current price?
Limitations
- Undefined when the original value is zero — there is no percentage change from nothing.
- Order matters: the old value is always the denominator. Swapping the inputs measures a different thing.
- Percent changes do not chain by addition — a +20% then −20% does not return to the start (it ends 4% lower).
- For a simple part-of-whole share rather than change over time, use the Percentage Calculator instead.
Frequently Asked Questions
What is the difference between percent change and percentage points?
Percent change is relative to the starting value. Percentage points measure the arithmetic difference between two percentages. For example, if an interest rate moves from 3% to 5%, that is a 2 percentage-point increase, but a 66.7% percent change relative to the original 3%.
Why does the order of the values matter?
The old (original) value is the denominator — it is the reference point. Swapping the values changes what you are measuring. Always put the starting value first and the ending value second.
What if the original value is zero?
Percent change is undefined when the original value is zero, because division by zero has no mathematical result. If your starting value is zero, percent change cannot be calculated.
Can percent change exceed 100%?
Yes. If a value doubles, that is a 100% increase. If it triples, that is a 200% increase. There is no upper limit on percent increase, though a decrease cannot exceed 100% (that would take the value below zero).
Why isn't a 20% rise cancelled by a 20% fall?
Because each percentage applies to a different base. Rising 20% from 100 gives 120; falling 20% from 120 gives 96 — a net 4% below the start. Percent changes compound, they do not add.