Percentage Change: Increase and Decrease

The formula

Percentage change measures how much a value has moved relative to where it started: (new − old) ÷ old × 100. The difference on top says how much it moved; dividing by the old value turns that into a proportion of the starting point; the ×100 makes it a percentage. If a price rises from $80 to $100, that is 20 ÷ 80 × 100 = 25%. The starting value on the bottom is the part people most often get wrong.

Increase vs decrease

The sign of the answer tells you the direction. If the new value is bigger, the top is positive and you get an increase; if it is smaller, the top is negative and you get a decrease. From 80 to 100 is +25%; from 100 to 80 is −20%. The formula is identical either way — you don't need a separate one for drops. A result of −20% simply means the value fell by 20% of its starting size.

Why increase and decrease aren't symmetric

Here is the classic trap: a 25% rise followed by a 20% fall brings you right back to the start, not to a loss. Going 80 → 100 is +25%, but 100 → 80 is only −20%, because the second change is measured against the larger base of 100. The same $20 move is a different percentage depending on where you start. That is why a stock that drops 50% must then rise 100% to recover — the base shrank.

Everyday uses

Percentage change is everywhere once you look. It is a price rise or a sale discount, a pay increase, the growth of a business month to month, a population figure, or the change in a test score. Because it is relative, it lets you compare moves of very different sizes fairly: a $5 rise on a $20 item (25%) is a bigger deal than a $5 rise on a $200 one (2.5%), and the percentage makes that instantly clear.

Frequently asked questions

How do I calculate a percentage increase?

Use (new − old) ÷ old × 100; a positive result is the increase.

Why is a 25% rise cancelled by a 20% fall?

Because the fall is measured against a bigger base, so the same amount is a smaller percentage.

Do I divide by the old or new value?

Always the old (starting) value — that's the base the change is measured against.