Percent change calculator
Percent change
- Change
- Percent change
- Percent difference
The value before a change
- Value before
- Amount of the change
Percentage points or percent?
- Change
- Relative change
Percent change is the change divided by the starting value, times 100. Sales that rise from $40,000 to $50,000 grew by $10,000, and $10,000 ÷ $40,000 is a 25% increase. Always divide by the starting value, never the new one.
Formula
Percent change = (New − Old) ÷ Old × 100Percent difference = |A − B| ÷ ((A + B) ÷ 2) × 100Change in percentage points = Rate 2 − Rate 1Value before a change = Value after ÷ (1 + Percent change ÷ 100)
Worked example
Monthly sales rise from $24,000 to $30,000. What is the percentage increase?
- $30,000 − $24,000 = $6,000.
- $6,000 ÷ $24,000 = 0.25 = 25%.
Answer: 25%
Do it in your head: Divide by what is left
- Say what share of the original is left: 20% off leaves 80%.
- Divide the sale price by that share, written as a decimal.
- Check: the discount taken off your answer should give the sale price.
A rise, and the fall that undoes it
| Rise | Fall back to the start |
|---|---|
| 10% | 9.09% |
| 20% | 16.67% |
| 25% | 20% |
| 50% | 33.33% |
| 100% | 50% |
Try three
-
Monthly sales fall from $7,000 to $5,250. By what percentage did they fall?
Show the answer
25%
- Percent fall = (old − new) ÷ old = ($7,000 − $5,250) ÷ $7,000 = $1,750 ÷ $7,000 = 25%.
- Always divide by the starting value.
-
A profit margin moves from 20% to 24%. Relative to where it started, by what percent did it rise?
Show the answer
20%
- Relative change = point change ÷ starting rate = (24 − 20) ÷ 20 = 4 ÷ 20 = 20%.
-
After 50% off, a toaster costs $65. What was the original price?
Show the answer
$130.00
- $65 is 50% of the original, so divide by 0.5: 65 ÷ 0.5 = $130.
That’s the idea. Keep going: 4 warm-up problems, no sign-up →
Learn it properly: Percentages in Business →
Questions
Do I divide by the old or the new number?
By the old one, the starting value. From $40,000 to $50,000 is +25%; back from $50,000 to $40,000 is −20%, because the start is different.
What is the difference between percent change and percent difference?
Percent change has a start and an end. Percent difference compares two values with no order, dividing by their average: $40,000 and $50,000 differ by 22.2%.
What are percentage points?
The plain difference between two percents. A rate that goes from 20% to 25% rose 5 percentage points, which is a 25% rise relative to where it started.
Do a 10% rise and a 10% fall cancel?
No. 100 up 10% is 110, and 110 down 10% is 99: an overall change of −1%.
How do I undo a discount?
Divide by what is left. After 30% off, $84 is 70% of the original: $84 ÷ 0.7 = $120.