Percentage change calculator
Math & numbersHow much did it go up or down in per cent?
The percentage increase or decrease from an old value to a new one, with the plain change and the formula.
What you enter stays on your device while you use this tool. Opening a shared link sends the settings in its address to HowToolbox to prepare the page.
Answer
-20%
From 150 to 120 is a decrease of 20%.
How it was worked out
- Formula
- (120 − 150) ÷ 150 × 100 = -20%
- Change
- -30
- Back from 120 to 150
- 25%
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The percentage increase or decrease from an old value to a new one, with the plain change and the formula.
How to use
- Choose what to calculate: a percent of a number, what percent one number is of another, a change, a difference, the whole from a part, or the value before a change.
- Enter the numbers. The answer and its formula update as you type.
- Copy the answer, or copy the link to share the same calculation.
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How it works
Per cent means “out of a hundred”: 20% is 20/100, or 0.2. So 20% of 150 is 20 ÷ 100 × 150 = 30, and 30 is 30 ÷ 150 × 100 = 20% of 150. Working backwards, if 30 is 20% of a number, the number is 30 ÷ 20 × 100 = 150.
A percentage change compares a new value B with an old value A: (B − A) ÷ |A| × 100. From 3 to 4 is an increase of 33⅓%, but from 4 back to 3 is a decrease of 25%, because each change is measured against its own starting point. A change from zero has no percentage.
When neither value is the starting point, the percentage difference measures the gap against their average: |A − B| ÷ ((|A| + |B|) ÷ 2) × 100. 100 and 120 differ by 20 ÷ 110 × 100 ≈ 18.18%, whichever way round you enter them. Other definitions exist (some divide by the larger value), so say which one you used.
A price after a 20% discount is 80% of the original, so the original is the price ÷ 80 × 100. Adding back 20% of the reduced price does not get you there. A change in a rate, such as 3% to 4%, is 1 percentage point but a 33⅓% increase. Formulas follow Wikipedia’s “Relative change” article.
Frequently asked 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 50 to 65: 15 ÷ 50 × 100 = 30% more.
How do I calculate a percentage decrease?
The same way; the result is negative. From 80 to 60: −20 ÷ 80 × 100 = −25%, a decrease of 25%.
Why is there no percentage for a change from zero?
A change is measured against the old value, and nothing can be divided by zero. Give the plain change instead, or compare the values with the percentage difference.
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