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Category: Calculators
Percentage Calculator
Percent of a number, percentage change, add or subtract a percent.
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Result
- Percent of a number
- 30
Calculation
20 ÷ 100 × 150
Calculation inputs
What is 20% of 150?
Details
About this tool
Five questions people call percentages, kept apart because the arithmetic differs: what is X% of Y, what percentage X is of Y, the change from X to Y, and X raised or reduced by a percentage. Pick the question and fill in two numbers.
They are separated deliberately. A single box labelled "percentage" invites the wrong sum, and the two mistakes it produces are the most common in everyday arithmetic. The first is confusing a percentage with a percentage point: an interest rate moving from 4% to 5% has risen by one percentage point but by 25 per cent, and both numbers are correct answers to different questions. The second is applying a change to the wrong base.
That second one is why a discount and a mark-up of the same size do not cancel. Take 100, reduce it by 20% to get 80, then add 20% - but 20% of 80 is 16, not 20, so you land on 96. The percentage was applied to a smaller number the second time. The same asymmetry is why a stock that falls 50% needs to double, a 100% rise, just to get back to where it started, and why "we made up the loss with a 50% recovery" is usually wrong.
The change mode reports both the relative change and the difference in percentage points where that makes sense, so the ambiguity is resolved on the page rather than in your head. Everything is computed in your browser, and results are rounded for display while the arithmetic runs at full precision.
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Good to know
Questions people actually ask
- Why doesn't −20% then +20% return to the start?
- Because the second percentage is taken from a smaller number. 100 less 20% is 80; 20% of 80 is 16, so adding it back gives 96, not 100. To reverse a 20% cut you need to add 25%. This is the single most common percentage mistake and it costs real money in pricing.
- What is the difference between a percentage and a percentage point?
- A percentage point is the arithmetic difference between two percentages; a percentage is the relative change between them. A rate going from 4% to 5% rose by one percentage point and by 25 per cent. Both are correct, they answer different questions, and headlines routinely use whichever sounds bigger.
- How do I work out what percentage one number is of another?
- Divide the part by the whole and multiply by 100 - 30 out of 150 is 30 ÷ 150 × 100, which is 20%. The mode named "what percentage is X of Y" does exactly this. The usual error is dividing the wrong way round, which for these numbers would give 500%.
- How do I calculate a percentage increase?
- Subtract the old value from the new, divide by the OLD value, and multiply by 100. Dividing by the new value instead is a common slip and always understates a rise. From 80 to 100 is a 25% increase; from 100 to 80 is a 20% decrease - the same 20 units, different percentages, because the base changed.
- How do I remove VAT or a discount from a total?
- Divide rather than subtract. To take 23% VAT out of a gross price, divide by 1.23; subtracting 23% of the gross gives a different and wrong answer. The dedicated VAT calculator does this both ways and knows the rates by country.