Compare two prices
- Input or situation
- Percent change: old 120, new 150
- Result
- 25% increase
The increase is 30, and 30 ÷ 120 × 100 = 25. Comparing the same two prices in reverse gives a 20% decrease because the starting value becomes 150.
Math
Percentage Calculator
Find a percentage of a number, compare a percentage change or add and subtract a percentage. Choose the calculation and check the formula beside the result.
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The starting value.
The value after the change.
Fill in the fields above to see the result and its formula.
Percent change compares the new value to the original. Percent difference is not the same thing — it uses the average of the two values as its base.
How to use
- Percent change
- How much a value rose or fell. 120 → 150 is a 25% increase.
- Apply %
- Add or remove a percentage from a base. 200 with 15% gives 230 or 170.
- X% of Y
- A straight share of an amount. 12.5% of 800 = 100.
- What % is X of Y
- Turn a ratio into a percentage. 45 out of 180 = 25%.
Questions
How do I reverse a discount?
Divide by (1 − discount). An item reduced 20% to €80 was €80 ÷ 0.8 = €100 before the discount. Subtracting 20% from €80 gives the wrong answer.
Is percent change the same as percent difference?
No. Percent change measures the new value against the original. Percent difference uses the average of the two values as its base, so it gives a smaller figure and has no direction.
Why does a 50% rise followed by a 50% fall not return to the start?
Because the second percentage applies to a larger base. 100 → 150 → 75. Percentages do not cancel out; you need to divide by 1.5 to undo a 50% increase.
Examples and checks
Choose the calculation by the question you are answering. A change needs an old and a new value; a share needs a part and a whole. Using the wrong starting value can produce correct arithmetic for the wrong question.
Find a share
- Input or situation
- What % is X of Y: X = 45, Y = 180
- Result
- 25%
45 ÷ 180 × 100 = 25. For a discount of 25%, use Apply % instead: the discounted price is 75% of the original.
Before you use the result
- A change from zero has no finite percentage: report the absolute change instead.
- A rise from 100 to 150 followed by a 50% fall ends at 75. Each percentage applies to its own starting value.
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