20% of 150 is 30: multiply 150 by 20 and divide by 100. The calculator above answers the five percentage questions people ask most often – a percentage of an amount, what percent one number is of another, how much something changed, and an amount plus or minus a percentage – and shows each step, so you can check the arithmetic yourself.
The five formulas
| You want | Formula | Example |
|---|---|---|
| X% of Y | Y × X ÷ 100 | 20% of 150 = 30 |
| X as a percent of Y | X ÷ Y × 100 | 42 of 50 = 84% |
| Change from X to Y | (Y − X) ÷ X × 100 | 80 → 100 = +25% |
| Y plus X% | Y × (1 + X ÷ 100) | 150 + 20% = 180 |
| Y minus X% | Y × (1 − X ÷ 100) | 150 − 20% = 120 |
Why −20% and then +20% does not get you back
A percentage always applies to the value you have now, not the one you started with. 100 minus 20% is 80; 80 plus 20% is 96. After a fall, you need a bigger rise to recover. The table below is worth keeping in mind for prices, salaries and investments:
| After a fall of | You need a rise of |
|---|---|
| 10% | 11.11% |
| 20% | 25% |
| 25% | 33.33% |
| 50% | 100% |
| 75% | 300% |
The same works in reverse: going from 100 to 120 is a 20% increase, but going from 120 back to 100 is a 16.67% decrease. The reference value always matters.
Percent or percentage points?
When a percentage itself changes, there are two honest ways to describe it, and mixing them up is the most common mistake in news headlines:
| Change | Percentage points | Percent |
|---|---|---|
| Interest rate from 5% to 6% | +1 point | +20% |
| Sales tax from 8% to 10% | +2 points | +25% |
| Unemployment from 4% to 3% | −1 point | −25% |
“The rate went up by 1%” is ambiguous. “Up by one percentage point” is clear: the rate is now 20% higher than before.
Increases compound
Three 10% raises are not 30%. A salary of 50,000 raised by 10% three times becomes 55,000, then 60,500, then 66,550 – a total increase of 33.1%. A single 30% raise would have given 65,000. The longer the chain, the bigger the gap.
Removing a tax that is already included
To find the price before a 20% tax, divide by 1.20 – do not subtract 20%. A price of 120 that includes 20% tax was 100 before tax (120 ÷ 1.20). Subtracting 20% from 120 gives 96, which is wrong by 4.
Common mistakes
- Using the wrong base. From 80 to 100 is +25%; from 100 to 80 is −20%.
- Adding successive discounts. 50% off and then another 20% off is 60% off in total, not 70%.
- Confusing points with percent. From 8% to 10% is 2 points, but a 25% increase.
- Forgetting that a percentage of a percentage is still a percentage. 20% of 50% is 10%.
Before you rely on a result, check three things: which value is the reference (the old one, the new one or the total), whether the amount already includes the percentage (as a price with tax does), and whether the percentages apply one after another or all to the same amount.
Once zet4u is saved on your device, the calculator works offline as well.
Frequently asked questions
How do I work out a percentage of a number?
Multiply the number by the percentage and divide by 100. For example, 20% of 150 = 150 × 20 ÷ 100 = 30.
How do I find what percent one number is of another?
Divide the part by the whole and multiply by 100. Getting 42 questions right out of 50 is 42 ÷ 50 × 100 = 84%.
How do I calculate a percentage increase or decrease?
Subtract the old value from the new one, divide by the old value and multiply by 100. A price that goes from 80 to 100 has risen by 25%.
If a price drops 20% and then rises 20%, is it back where it started?
No. 100 minus 20% is 80, and 80 plus 20% is 96. To get from 80 back to 100 you need a 25% increase.
What is the difference between percent and percentage points?
If an interest rate goes from 5% to 6%, it rose by 1 percentage point. In percent, it rose by 20%, because 1 is 20% of 5.
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