X is what percent of Y?
X is Y% of what?
With the percentage calculator, you can calculate:
- How much is X% of Y. Example - 20% of 100 is what? 20
- How much % is X out of Y. Example - 40 out of 200 is how much percent? 20%
- X% of what is Y. Example - 20% of WHAT is 50. 250
- Percentage Change Calculator
- Percentage Increase Calculator
- Percentage Decrease Calculator
- Percentage Difference Calculator
- Percentage Error Calculator
- Add or Subtract Percentage Calculator
- Percent to Fraction Calculator
What is percentage?
In math, percentage is a number which denotes the amount as a fraction of 100. Most commonly, a percentage is signified by the sign “%” and is often shortened to pct., or pc. In other words, a percent is a pure number and cannot be measured in units.
Discovery of Percentage
In ancient Rome, calculations were usually made in fractions, in multiples of 1/100.
For instance, during the reign of Augustus, a tax of 1/100 was levied on goods that were sold at auctions, known as “centesima rerum venalium”. Hence using this form of fraction computing is the same as calculating percent.
However, as currency denominations increased and became gradually higher in the Middle Ages, it became a standard practice to make calculations with a denominator of 100. So much so, that from late 15th century to the earliest 16th century, it became common practice for arithmetic tests to include such fraction calculations.
Most such computations were regularly applied to interest rates, profit and loss and the Rule of Three. By the end of the 17th century, it became standard to quote interest rates in fraction of a hundred.
How is Percentage calculated?
The value of percentage is calculated by multiplying the numeric value of the ratio by 100. So, the formula to calculate percentage is (N1/N2)*100.
For instance, if you want to find the percentage of 50 apples out of 1250 apples, you will first need to calculate the ratio of 50/1250 which is equal to 0.04. Then you need to multiply this value by 100 to obtain the percentage, which in this case comes to 4%.
Another method to calculate percentage involves first multiplying instead of the second step. For instance, the 50 apples should be multiplied by 100, which give us 5,000. The next step requires dividing this value by 1250, which also bring us the answer as 4%.
How about calculating the percentage of a percentage?
To do this, you will first need to convert the percentages into fractions of 100, or into decimal numbers and then multiplying them finally. So, what would be the value of 50% of 40%?
Here’s how to calculate percentage of a percentage:
50/100 x 40/100 = 0.50 x 0.40 = 0.20 OR 20/100 = 20%
However, you need to remember that it is not allowed to divide by 100 and then use the percentage sign simultaneously. Whenever talking about percentage, it is essential to specify the relative which is the total that corresponds to 100%.
How to Compound Percentage?
Adding percentages sequentially will not get you the correct answer.
For instance, if relative value of ”p” is increased by “x” percentage and then decreased again by “x” percentage then the percentage is calculated as follows:
P (1 + 0.01x) (1 – 0.01x) = p (1 – (0.01x)²
Hence the overall change in the all-round decrease by x percentage of x percent (which is the square of the original numeric value and expressed in decimal numbers).
In finance, an increase by 1% usually means an increase by 100 base points.