The percent change formula calculates how much a value has increased or decreased relative to its original amount, expressed as a percentage. It's used everywhere from finance and retail to science and everyday comparisons.
You can also write it as:
Or in fraction notation: [(New − Old) / Old] × 100. All three are identical — the notation changes but the equation does not.
36,800 − 32,000 = 4,8004,800 ÷ 32,000 = 0.150.15 × 100 = 1584 − 120 = −36−36 ÷ 120 = −0.30−0.30 × 100 = −305.85 − 4.50 = 1.351.35 ÷ 4.50 = 0.300.30 × 100 = 30−5,000 − (−8,000) = 3,0003,000 ÷ −8,000 = −0.375−0.375 × 100 = −37.5The formula gives −37.5%, which is mathematically correct but counterintuitive — the loss actually shrank, which is an improvement. When working with negative baselines, always sense-check the result in context rather than relying on the sign alone.
The core equation stays the same, but it's written differently depending on context.
Same formula — used when the new value is higher than the old. Result is always positive.
Subtract in the opposite order to get a positive result for a decrease. Equivalent to the standard formula with the sign flipped.
P1 = original price, P2 = new price. Used for stock prices, retail prices, and cost tracking.
Compares equivalent periods 12 months apart. Removes seasonal noise from the comparison.
A1 = old value, B1 = new value. Format the cell as a number or percentage as needed.
Different equation — used when there is no clear "original" value. Symmetric: order doesn't matter. See our full comparison.
When the values being compared are themselves percentages — interest rates, conversion rates, tax rates. See our full guide with examples.
Same formula, different framing. Used in financial reporting to compare performance against a plan. See our percentage variance guide.
These two are often confused. The key difference is what you divide by.
(New − Old) ÷ Old × 100|A−B| ÷ ((A+B)÷2) × 100The old value is always the denominator. Dividing by the new value produces a different (incorrect) result. If a price goes from £50 to £75: correct is (75−50)÷50×100 = 50%. Using the new value gives (75−50)÷75×100 = 33.3% — wrong.
Without ×100 you get a decimal ratio (0.50), not a percentage (50%). Both are mathematically equivalent but percentage is the expected format in almost every real-world context.
A +50% increase followed by a −50% decrease does not return to the original. Starting at £100: +50% → £150, then −50% → £75. You need a +100% increase to reverse a −50% decrease.
Division by zero is undefined — the formula breaks down entirely. If the original value is zero, describe the change in absolute terms instead (e.g. "grew from 0 to 200 units").
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Use the free calculatorThe percent change formula is: (New Value − Old Value) ÷ Old Value × 100. A positive result means an increase; a negative result means a decrease. The old value is always the denominator.
Find how much the value changed (new minus old), then ask "what fraction of the original is that?" (divide by old), then convert to a percentage (multiply by 100). Three steps: difference, divide, scale.
Yes. If a value doubles, that is a 100% increase. If it triples, that is a 200% increase. There is no upper limit — very large percentage changes occur when starting values are small and ending values are large.
Percent change uses the original value as the denominator and is directional (positive or negative). Percent difference uses the average of both values and is always positive. Use percent change for before-and-after scenarios; use percent difference when comparing two independent measurements. See our full guide.
If your old value is in cell A1 and new value in B1, enter: =(B1-A1)/A1*100. This returns the percentage change as a number. Alternatively, format the cell as a percentage and use =(B1-A1)/A1 to skip the ×100.