What is the percentage change formula?

Percentage change equals (V2 minus V1) divided by the absolute value of V1, multiplied by 100 — where V1 is the initial value and V2 is the new value.

Why does the formula use the absolute value of V1?

The denominator uses the absolute value of V1 so the sign of the result always matches the direction of the change (positive for an increase, negative for a decrease) — even when V1 itself is negative.

Does the order of the two values matter?

Yes. Percentage change is not symmetric — going from 3.50 to 2.625 is a 25% decrease, but going from 2.625 back to 3.50 is a 33.33% increase, because each direction measures against a different starting value.

What's the difference between percentage change and percentage difference?

Percentage change assumes an order — a starting value and an ending value — and its sign shows increase or decrease. Percentage difference compares two values with no before/after order, and is always reported as a positive number relative to their average.

Can percentage change be more than 100%?

Yes. If a value more than doubles, the percentage change exceeds 100%. Going from 25 to 75, for example, is a 200% increase.

What does a percentage change of 0% mean?

It means the new value equals the initial value — nothing changed.

Percentage Change Calculator

What is percentage change?

Percentage change measures how much a value moved from an initial point (V₁) to a new point (V₂), expressed as a percentage. A positive result means the value increased; a negative result means it decreased.

$\text{Percentage change} = \frac{V_2 - V_1}{|V_1|} \times 100$

Tip: Order matters. V₁ is always the starting value and V₂ is always the ending value — swapping them changes the answer, not just its sign.

Why the formula uses |V₁|

The denominator is the absolute value of the initial value, not the raw value. This keeps the sign of the result meaningful even when V₁ is negative.

Example — from −25 to 25.

$\frac{25 - (-25)}{|-25|} \times 100 = \frac{50}{25} \times 100 = +200\%$

Without the absolute value, dividing by a negative −25 would flip the sign of a genuine increase into a misleading negative number.

Why order matters

Percentage change always measures against the starting value — reversing the two values changes the answer, not just its sign.

Example — 3.50 down to 2.625.

$\frac{2.625 - 3.50}{|3.50|} \times 100 = -25\%$

Reversed — 2.625 up to 3.50.

$\frac{3.50 - 2.625}{|2.625|} \times 100 \approx +33.33\%$

Both examples describe the same two numbers, but a 25% drop and a 33.33% rise are not mirror images of each other — each percentage is relative to a different base.

Worked examples

Both values negative — temperature from −25° to −50°.

$\frac{-50 - (-25)}{|-25|} \times 100 = \frac{-25}{25} \times 100 = -100\%$

A drop from −25° to −50° is a 100% decrease.

Revenue from 50,000 to 65,000.

$\frac{65000 - 50000}{|50000|} \times 100 = \frac{15000}{50000} \times 100 = +30\%$

Revenue grew by 30%.

Percentage change vs. percentage difference

Tip: Use percentage change when you have a clear "before" and "after." Use a percentage difference calculator instead when comparing two values with no natural order — it always returns a positive percentage relative to the average of the two.

Percentage Increase and Percentage Decrease calculators use this exact same formula, just with the direction already labeled.

Common mistakes

Dividing by the wrong value. The denominator is always V₁ (the starting value), never V₂.
Forgetting the absolute value. Skipping |V₁| produces a sign error whenever the starting value is negative.
Assuming the reverse gives the same percentage. A 25% decrease does not "undo" with a 25% increase — reversing 3.50 → 2.625 to 2.625 → 3.50 gives 33.33%, not 25%.

Where percentage change shows up

Finance — stock price movement, revenue growth, cost increases.
Science — temperature swings, population growth or decline.
Everyday comparisons — price changes, weight loss or gain, test score improvement.