How to Calculate Percentage Change

Percentage change describes how much a value has grown or shrunk relative to where it started. It’s one of the most common calculations in news reports, business updates and personal finance, and also one of the most commonly misread. This guide covers the formula, the related measures it gets confused with, and the traps that catch people out.

The formula

Subtract the original value from the new value, divide by the original value, and multiply by 100:

Percentage change = ((New − Original) ÷ Original) × 100

If a monthly bill goes from $52 to $65, the difference is $13. Dividing by the original $52 gives 0.25, so the bill rose by 25%. A positive result is an increase and a negative result is a decrease.

The original value is always the reference point, so the direction matters. Going back from $65 to $52 is the same $13 gap, but divided by $65 it’s a 20% decrease, not 25%. To check your own numbers, the percentage change calculator shows each step of the sum.

Percentage change, percentage difference and percentage points

These three terms are often used interchangeably, but they measure different things.

Percentage change has a clear before and after. It answers “how much did this move from where it started?”

Percentage difference compares two values with no natural starting point, such as prices at two shops on the same day. Instead of choosing one value as the base, it divides the gap by the average of the two:

Percentage difference = |A − B| ÷ ((A + B) ÷ 2) × 100

For $52 and $65, the gap of $13 divided by the average of $58.50 is about 22.22%. The answer is the same whichever value you list first, which is the point of the measure.

Percentage points describe the simple subtraction between two percentages. If a savings rate goes from 2% to 3%, it rose by 1 percentage point. As a percentage change, the rate rose by 50%, because 1 is half of 2. Both statements are correct, but “rose by 1%” is ambiguous, because it could mean either. When the values you’re comparing are already percentages, such as interest rates, unemployment rates or poll results, say “percentage points” for the absolute gap.

When the starting value is negative or zero

The formula breaks down at the edges.

A starting value of zero makes percentage change undefined, because you can’t divide by zero. Going from 0 to 40 customers isn’t an infinite percentage increase. It’s a change with no meaningful percentage. Report the absolute change instead.

A negative starting value produces misleading signs if you apply the formula literally. Suppose a business goes from a loss of $40,000 to a profit of $10,000. The difference is +$50,000, an improvement. Dividing by −40,000 gives −125%, which wrongly suggests a decline. The usual fix is to divide by the size of the original value, ignoring its sign:

Percentage change = ((New − Original) ÷ |Original|) × 100

This gives a 125% increase, which at least points in the right direction. Even so, percentages around negative or sign-changing values are hard to interpret, so many analysts avoid them. For figures like profit and loss, phrases such as “swung from a $40,000 loss to a $10,000 profit” are clearer.

Why a 50% fall needs a 100% rise to recover

Losses and gains are measured against different bases. If an investment worth $1,000 falls 50%, it’s worth $500. A 50% rise from there adds only $250, leaving $750. To get back to $1,000, the $500 has to double, which is a 100% gain.

In general, recovering from a fall of L (as a decimal) needs a gain of L ÷ (1 − L):

Fall	Gain needed to recover
10%	11.11%
20%	25%
25%	33.33%
50%	100%
75%	300%
90%	900%

The required gain grows much faster than the loss. This is why large drawdowns are so damaging to long-term returns, and why a 20% discount followed by a 20% markup leaves a price 4% lower than it started.

If you know a value after a percentage change and want the value before it, divide rather than subtract. A price of $96 after a 20% increase was $96 ÷ 1.20 = $80, not $76.80. The reverse mode of the percentage calculator does this for you.

Combining successive changes

Percentage changes in a row multiply rather than add. Turn each change into a growth factor (1 + change as a decimal), multiply the factors, then subtract 1.

• Two years of 10% growth: 1.10 × 1.10 = 1.21, a 21% increase overall, not 20%.
• A 10% rise followed by a 10% fall: 1.10 × 0.90 = 0.99, a 1% decrease overall, not zero.
• Rises of 5% and 8% followed by a 3% fall: 1.05 × 1.08 × 0.97 ≈ 1.1000, an increase of almost exactly 10%.

To express several periods as a single typical rate, use the geometric mean, not the simple average. For the last example, the cube root of 1.09998 is about 1.0323, so the average change is about 3.23% per period. Averaging 5, 8 and −3 directly gives 3.33%, which overstates the result. The same compounding logic is behind the compound interest calculator.

Quick checklist

1. Identify which value is the original, and divide by it.
2. Check whether you’re comparing percentages. If you are, decide between percentage points and percentage change.
3. Avoid percentage change when the original value is zero, and treat negative bases with care.
4. To combine changes, multiply growth factors. Don’t add percentages.
5. To undo a change, divide by the growth factor. Don’t apply the opposite percentage.