Percent Calculator Apps Percentage Calculator - Online Percentage Calculator Tool

Percent Calculator Apps Percentage Calculator - Online Percentage Calculator Tool

Percent Calculator Apps Percentage Calculator - Online Percentage Calculator ToolIn mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", or the abbreviations "pct.", "pct"; sometimes the abbreviation "pc" is also used. A percentage is a dimensionless number (pure number).

For example, 45% (read as "forty-five percent") is equal to  45100, 45:100, or 0.45. Percentages are often used to express a proportionate part of a total.

(Similarly, one can express a number as a fraction of 1,000 using the term "per mille" or the symbol "".)

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In Ancient Rome, long before the existence of the decimal system, computations were often made in fractions which were multiples of  1100. For example, Augustus levied a tax of  1100 on goods sold at auction known as centesima rerum venalium. Computation with these fractions was equivalent to computing percentages.

As denominations of money grew in the Middle Ages, computations with a denominator of 100 became more standard and from the late 15th century to the early 16th century it became common for arithmetic texts to include such computations. Many of these texts applied these methods to profit and loss, interest rates, and the Rule of Three. By the 17th century it was standard to quote interest rates in hundredths.

The term "per cent" is derived from the Latin per centum, meaning "by the hundred".The sign for "per cent" evolved by gradual contraction of the Italian term per cento, meaning "for a hundred". The "per" was often abbreviated as "p." and eventually disappeared entirely. The "cento" was contracted to two circles separated by a horizontal line, from which the modern "%" symbol is derived.

The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first compute the ratio  501250 = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.

To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:

50100 ×  40100 = 0.50 × 0.40 = 0.20 =  20100 = 20%.

It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% =  25100 = 0.25, not  25%100, which actually is  25100/100 = 0.0025. A term such as  100100% would also be incorrect, this would be read as 1 percent even if the intent was to say 100%.)

Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.

In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?

We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that  60100 ×  5100 =  3100 or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer:  3%10% =  30100 or 30% of all computer science majors are female.

This example is closely related to the concept of conditional probability.

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Percentage increase and decrease

Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%).

Some other examples of percent changes:

In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, 1 + 0.01x times the original amount).

Calculations

The percent value is computed by multiplying the numeric value of the ratio by 100. For example, to find 50 apples as a percentage of 1250 apples, first compute the ratio  501250 = 0.04, and then multiply by 100 to obtain 4%. The percent value can also be found by multiplying first, so in this example the 50 would be multiplied by 100 to give 5,000, and this result would be divided by 1250 to give 4%.

To calculate a percentage of a percentage, convert both percentages to fractions of 100, or to decimals, and multiply them. For example, 50% of 40% is:

50100 ×  40100 = 0.50 × 0.40 = 0.20 =  20100 = 20%.

It is not correct to divide by 100 and use the percent sign at the same time. (E.g. 25% =  25100 = 0.25, not  25%100, which actually is  25100/100 = 0.0025. A term such as  100100% would also be incorrect, this would be read as 1 percent even if the intent was to say 100%.)

Whenever we talk about a percentage, it is important to specify what it is relative to, i.e. what is the total that corresponds to 100%. The following problem illustrates this point.

In a certain college 60% of all students are female, and 10% of all students are computer science majors. If 5% of female students are computer science majors, what percentage of computer science majors are female?

We are asked to compute the ratio of female computer science majors to all computer science majors. We know that 60% of all students are female, and among these 5% are computer science majors, so we conclude that  60100 ×  5100 =  3100 or 3% of all students are female computer science majors. Dividing this by the 10% of all students that are computer science majors, we arrive at the answer:  3%10% =  30100 or 30% of all computer science majors are female.

This example is closely related to the concept of conditional probability.

Percentage increase and decrease

Due to inconsistent usage, it is not always clear from the context what a percentage is relative to. When speaking of a "10% rise" or a "10% fall" in a quantity, the usual interpretation is that this is relative to the initial value of that quantity. For example, if an item is initially priced at $200 and the price rises 10% (an increase of $20), the new price will be $220. Note that this final price is 110% of the initial price (100% + 10% = 110%).

Some other examples of percent changes:

In general, a change of x percent in a quantity results in a final amount that is 100 + x percent of the original amount (equivalently, 1 + 0.01x times the original amount).

Compounding percentages

Percent changes applied sequentially do not add up in the usual way. For example, if the 10% increase in price considered earlier (on the $200 item, raising its price to $220) is followed by a 10% decrease in the price (a decrease of $22), the final price will be $198, not the original price of $200. The reason for the apparent discrepancy is that the two percent changes (+10% and −10%) are measured relative to different quantities ($200 and $220, respectively), and thus do not "cancel out".

In general, if an increase of x percent is followed by a decrease of x percent, and the initial amount was p, the final amount is p(1 + 0.01x)(1 − 0.01x) = p(1 − (0.01x)2); thus the net change is an overall decrease by x percent of x percent (the square of the original percent change when expressed as a decimal number). Thus, in the above example, after an increase and decrease of x = 10 percent, the final amount, $198, was 10% of 10%, or 1%, less than the initial amount of $200. The net change is the same for a decrease of xpercent followed by an increase of x percent; the final amount is p(1 - 0.01x)(1 + 0.01x) = p(1 − (0.01x)2).

This can be expanded for a case where you do not have the same percent change. If the initial percent change is x and the second percent change is y, and the initial amount was p, then the final amount is p(1 + 0.01x)(1 + 0.01y). To change the above example, after an increase of x = 10 percent and decrease of y = −5 percent, the final amount, $209, is 4.5% more than the initial amount of $200.

As shown above, percent changes can be applied in any order and have the same effect.

In the case of interest rates, a very common but ambiguous way to say that an interest rate rose from 10% per annum to 15% per annum, for example, is to say that the interest rate increased by 5%, which could theoretically mean that it increased from 10% per annum to 10.05% per annum. It is clearer to say that the interest rate increased by 5 percentage points (pp). The same confusion between the different concepts of percent(age) and percentage points can potentially cause a major misunderstanding when journalists report about election results, for example, expressing both new results and differences with earlier results as percentages. For example, if a party obtains 41% of the vote and this is said to be a 2.5% increase, does that mean the earlier result was 40% (since 41 = 40 × (1 + 2.5/100)) or 38.5% (since 41 = 38.5 + 2.5)?

In financial markets, it is common to refer to an increase of one percentage point (e.g. from 3% per annum to 4% per annum) as an increase of "100 basis points".