Percentage Change Calculator
Works out how much a value rose or fell as a percentage when it moved from one number to another.
Recent
Formula
How the calculation works
Percentage change answers the question a plain difference cannot: a rise of 10 is large from 50 but small from 5000, and the percentage is what makes the two comparable.
The formula divides the difference by the starting value, because the starting value is the base the change is measured against. Reversing the direction does not undo the percentage: a 50% rise followed by a 50% fall leaves you below where you began.
Because the base changes, equal percentage steps do not cancel. That is why a price that doubles and then halves returns to the start, but one that rises 50% and falls 50% does not.
Common mistakes
- Dividing by the final value instead of the starting value. That measures the change against the wrong base and gives a different, smaller percentage.
- Assuming a rise and a fall of the same percentage cancel. From 100 a 50% rise gives 150, and a 50% fall from there returns to 75, not 100.
- Reading a negative percentage as a mistake. A negative result is simply a fall, so the sign is information, not an error.
When to use it
- Use it for prices, salaries, traffic or any figure you track over time, to say how big a move was in a way two different bases can be compared.
- For a discount or a tax on a single price, a percentage of a number tool is simpler; for a growth rate spread evenly over many years, use a compound or CAGR tool instead.
Worked example
Going from 50 to 60 is a rise of 10, a 20% change.
Common questions
Is the same formula used for a fall?
Yes. When the value falls the difference is negative, so the percentage change is negative too, which is how a fall shows up.
Which value is it divided by?
Always the starting value, because the change is measured against that base; dividing by the final value gives a different answer.
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