Quick start
- Type the starting value in Old value, for example last month's bill of 80.
- Type the new value, for example 92.
- Read the percent change, the multiplier, and the change needed to get back.
The formula
Percent change = (new − old) ÷ old × 100. A positive answer is an increase and a negative answer is a decrease. Always divide by the old value, the one you are comparing against.
Examples
| From | To | Working | Change |
|---|---|---|---|
| 80 | 92 | 12 ÷ 80 × 100 | +15% |
| 250 | 200 | −50 ÷ 250 × 100 | −20% |
| 1,200 | 1,500 | 300 ÷ 1,200 × 100 | +25% |
| 45 | 30 | −15 ÷ 45 × 100 | −33.33% |
Why going back needs a different percentage
A price that falls from 250 to 200 has dropped 20%. To climb back from 200 to 250 it must rise 25%, because the second change is measured from the smaller number. In the same way, a share that loses 50% needs to gain 100% to recover.
Percent change or percentage points?
When the values are themselves percentages, be careful. An interest rate moving from 4% to 5% rose by 1 percentage point, but by 25% in relative terms. Both statements are correct; they answer different questions.
Percent difference
Percent change has a clear before and after. When two values have no natural order, such as two shop prices, the percent difference compares the gap with their average instead. The calculator shows this too.
Common questions
How do I calculate a percentage increase?
Subtract the old value from the new one, divide by the old value and multiply by 100. From 80 to 92 is 12 ÷ 80 × 100 = 15%.
How do I calculate a percentage decrease?
Use the same formula. The answer comes out negative. From 250 to 200 is −50 ÷ 250 × 100 = −20%, a 20% decrease.
Can a percentage increase be more than 100%?
Yes. Going from 20 to 50 is a 150% increase, because the rise of 30 is one and a half times the starting value.
Why can't the old value be zero?
Percent change divides by the old value, and dividing by zero is undefined. Describe the change as an absolute amount instead.