Percentage Change Calculator | Increase or Decrease

How the Percentage Change Formula Works

The formula divides the difference between two values by the absolute value of the original:

Percentage Change = ((New Value − Original Value) / |Original Value|) × 100

Using the absolute value of the original in the denominator ensures the formula works correctly even when the original value is negative. For example, going from −20 to −10 is a 50% increase, not a −50% increase.

A positive result means the value increased. A negative result means it decreased. If the result is exactly zero, the two values are identical.

Note that the original value cannot be zero — dividing by zero is undefined, so "percentage change from zero" has no mathematical meaning. If your starting point is 0, you'd need a different measure like absolute difference.

Percentage Change vs. Percentage Difference

These two calculations answer different questions and are often confused:

Percentage change has a clear direction — it tells you how much a value moved from an original to a new value. The order matters: going from 100 to 150 is a 50% increase, but going from 150 to 100 is a 33.3% decrease.

Percentage difference compares two values without assigning one as the starting point. It divides the absolute difference by the average of both values. This is useful when neither value is the "original" — for example, comparing prices between two stores.

If you know which value came first in time or priority, use percentage change. If you're comparing two parallel values, use percentage difference.

When You'd Use Percentage Change

Percentage change is the go-to metric any time you're measuring growth, decline, or movement between two points:

Finance: Tracking stock price movements, investment returns, revenue growth quarter over quarter, or year-over-year changes in expenses. A share moving from $80 to $96 is a 20% gain — much more meaningful than saying it went up "$16" if you're comparing it to a stock that moved from $800 to $816.

Business: Measuring sales performance, conversion rate shifts, customer churn changes, or cost fluctuations. Knowing that your customer acquisition cost dropped 12% is actionable; knowing it dropped $3.40 requires more context.

Education: Test score improvements, grade tracking, enrollment changes. Going from 65 to 78 on a test is a 20% improvement.

Daily life: Price changes at the grocery store, rent increases, salary negotiations, weight loss or gain. Converting absolute numbers to percentages makes it easier to judge whether a change is significant.

Handling Negative Numbers

Percentage change works fine with negative values. The key is taking the absolute value of the original in the denominator. Going from −40 to −20 is a 50% increase (the value moved closer to zero — it "grew" in the positive direction). Going from −20 to −40 is a 100% decrease.

This can feel counterintuitive with temperatures or debt. If your debt was $5,000 and is now $7,500, that's a 50% increase in debt — the number got larger, even though the financial impact is negative. The calculator reports the mathematical direction; interpreting what "up" or "down" means in your context is up to you.

The one scenario that truly doesn't work is an original value of zero. There's no valid percentage relationship to a zero starting point.

Frequently Asked Questions

What is the difference between percentage change and percentage points?

Percentage change measures the relative shift between two values (e.g., going from 50 to 75 is a 50% change). Percentage points measure the simple numerical difference between two percentages (e.g., an interest rate moving from 3% to 5% increased by 2 percentage points, but the percentage change is 66.7%).

Why can't I calculate percentage change from zero?

The formula divides by the original value. Dividing by zero is undefined in mathematics — there's no meaningful way to express "how much larger something is compared to nothing." If your starting point is zero, use absolute difference instead.

Does the order of the values matter?

Yes. Percentage change is directional. Going from 100 to 150 is a +50% increase. Going from 150 to 100 is a 33.3% decrease. Always enter the earlier or baseline value as the "Original" and the later or comparison value as "New."

How do I reverse a percentage change?

A common mistake is thinking a 20% increase followed by a 20% decrease gets you back to the starting point. It doesn't. If 100 increases by 20%, you get 120. A 20% decrease from 120 is 96, not 100. To reverse a percentage change, use the formula: reverse % = -(change / (100 + change)) × 100.

Can the percentage change be more than 100%?

Absolutely. If a value triples (e.g., 50 to 150), that's a 200% increase. There's no upper limit. Decreases can also exceed 100% when the value crosses zero — for example, going from 50 to −50 is a 200% decrease.

How does this handle negative original values?

The calculator uses the absolute value of the original in the denominator, following the standard mathematical convention. Going from −20 to −10 is a 50% increase (the value moved in the positive direction). Going from −20 to −40 is a 100% decrease.