A shirt drops from $50 to $40. A salary rises from $60,000 to $66,000. A website’s traffic grows from 10,000 to 12,500 visits. All three are percentage changes, and all three use the same formula. Once you internalize it, percent problems stop being mysterious.
The Core Formula
To find the percentage change between an original value and a new value:
change % = (new - original) / original × 100
(40 - 50) / 50 × 100 = -20% (a 20% decrease)
(66000 - 60000) / 60000 × 100 = 10% (a 10% increase)The sign tells you the direction: positive is an increase, negative is a decrease.
Crunch percentages instantly
Find what percent one number is of another, plus increase and decrease.
The Mistake Everyone Makes
Percentage changes are not reversible. A 20% decrease followed by a 20% increase does not bring you back to the start. From $50 down 20% is $40; a 20% increase on $40 is only $8, landing at $48, not $50. When you stack changes, always apply each percentage to the current value — which is exactly why percentage points matter in finance and economics.
Related Calculations You Will Need
- What percent is X of Y? Divide X by Y and multiply by 100. Example: 25 is 12.5% of 200.
- Increase by a percentage: Multiply the original by (1 + percent/100).
- Decrease by a percentage: Multiply the original by (1 - percent/100).
- Reverse increase: If a price after a 10% increase is $110, the original is 110 / 1.10 = $100.
Sanity-Check Your Result
Quick mental checks catch most errors. A 100% increase doubles the number; a 100% decrease makes it zero; a 50% increase multiplies by 1.5. If your answer does not land in a believable range, recompute. For anything with decimals, a calculator removes the arithmetic risk so you can focus on whether the answer makes sense.