How to calculate percent change
Percent change = (new − old) ÷ old × 100
A positive answer is an increase, a negative answer a decrease. If Saturday’s sales went from $800 last week to $920 this week: (920 − 800) ÷ 800 × 100 = a 15% increase.
Percent change examples
How to find the percentage change between two numbers, worked through for common examples:
| Change | Calculation | Percent change |
|---|---|---|
| 6 to 3 | (3 − 6) ÷ 6 × 100 | −50% (decrease) |
| 10 to 7 | (7 − 10) ÷ 10 × 100 | −30% (decrease) |
| 5 to 1 | (1 − 5) ÷ 5 × 100 | −80% (decrease) |
| 2 to 1 | (1 − 2) ÷ 2 × 100 | −50% (decrease) |
| 10 to 3 | (3 − 10) ÷ 10 × 100 | −70% (decrease) |
| 50 to 60 | (60 − 50) ÷ 50 × 100 | +20% (increase) |
| 80 to 100 | (100 − 80) ÷ 80 × 100 | +25% (increase) |
| 200 to 150 | (150 − 200) ÷ 200 × 100 | −25% (decrease) |
Percentage increase
Raising a price from $24 to $27: (27 − 24) ÷ 24 × 100 = 12.5% increase. To find the new price from a percentage, multiply by 1 plus the increase: $24 × 1.125 = $27.
Percentage decrease
A sale price of $30 on a $40 item: (30 − 40) ÷ 40 × 100 = −25%, a 25% decrease. To apply a decrease, multiply by 1 minus it: $40 × 0.75 = $30.
Percentage difference
When neither number is the “before”, like comparing two suppliers’ prices, use percentage difference. It divides by the average of the two, so the answer is the same whichever way round you enter them. $40 and $60 differ by $20, their average is $50, so the percentage difference is 40%.
Why percentage changes don’t cancel out
A 20% discount followed by a 20% increase doesn’t get you back to the start: $100 → $80 → $96. To undo a 20% drop you need a 25% rise, because the second change is measured from a smaller number. Keep this in mind when you mark prices down and back up.
Working on prices? The profit margin calculator shows what a price change does to your margin.
Frequently asked questions
How do I calculate percent change?
Percent change = (new − old) ÷ old × 100. From $50 to $60: (60 − 50) ÷ 50 × 100 = 20% increase.
What’s the difference between percent change and percentage difference?
Percent change measures from an old value to a new one. Percentage difference compares two values without a before and after, using their average as the base.
Why isn’t a 20% drop undone by a 20% rise?
Because the base changes. $100 down 20% is $80, and $80 up 20% is only $96. Going back to $100 needs a 25% increase.