How to Calculate Percentage Change

Percentage change measures how much a number grew or shrank, relative to where it started. The formula is (new - old) / old x 100. A positive result means an increase; a negative result means a decrease. For example, going from 50 to 60 is a +20% change, while going from 60 to 50 is about -16.67%. You can run any pair of numbers through our free percentage change calculator.

The formula, step by step

1. Subtract the old value from the new value to get the difference.
2. Divide that difference by the original (old) value — not the new one.
3. Multiply by 100 to turn the decimal into a percent.

The key detail people miss is step 2: you always divide by the starting value, because percentage change asks "how big was the change compared to where we began?"

Two worked examples

• 50 up to 60: (60 - 50) / 50 = 10 / 50 = 0.20, so x 100 = +20% (an increase).
• 60 down to 50: (50 - 60) / 60 = -10 / 60 = -0.1667, so x 100 = about -16.67% (a decrease).

Notice the two are not mirror images. The same 10-unit gap is a different percentage because the starting point changed.

An increase and an equal decrease don't cancel

This trips up a lot of people. Start with 100, add 20%, and you get 120. Now take 20% off that 120 — that's 24 — and you land at 96, not back at 100. The second percentage is calculated from a larger number, so it removes more than the first one added. Whenever you stack changes, recalculate from the new base each time.

Percent change vs. percentage points

These sound alike but mean different things. If a rate moves from 40% to 50%, that's a rise of 10 percentage points, but the percentage change is (50 - 40) / 40 = 25%. When you read about statistics or test data, watch which one is being used — and remember that reported figures vary by source and year, so check the original numbers.

Run the numbers and learn the why

When you need a fast, reliable answer, drop your before-and-after values into the percentage change calculator, and for plain percentages use the percentage calculator. To understand the reasoning behind any result, COSMIQ's free voice tutor will walk you through it step by step.

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