Percentage Calculator

Percentage Calculator using everyday speech phrases

The application of percentage

A percentage is a hundredth of a number taken as an integer. The percentage is expressed in terms of 100 units of a given quantity. For instance, an investor may be interested in knowing the fraction of the profit or loss earned compared to the amount invested. A teacher may be interested in seeing the fraction of the students who passed a given test in relation to the total number of students in the class. A project manager may be interested in knowing the fraction of the funds injected into the project that corresponds to the total funding. In all these cases, percentages are the best form for presenting such summaries.

When an investor injects $ 12,000 into an investment and earns a profit of $ 3,000 at the end of the investment period, the yield represents \$\frac{3,000}{12,000}=\frac{1}{4}\$ of the investment. To express this fraction as a percentage, we multiply it by 100%, where % is the percentage symbol.

Therefore, we get:

$$\frac{3,000}{12,000} × 100\% = 25\%$$

The value of 25% implies that for every 100 dollars, the investor earns 25 dollars in profit. Since 25 is a quarter of 100, one can also say that the investor makes a quarter of the investment in profit for every dollar invested.

Therefore, if T is the total amount of the investment (the base value), the profit p represents a percentage of:

$$\frac{p}{T} × 100\%$$

We are going to use the context of investment in this article.

How to interpret different values of a percentage

The percentage is interpreted based on the base value of a given quantity. In the above example, the base value is the total amount invested. Using the context of investment and profit:

• 0% implies that the investment had no profit, and funds realized at the end of the investment period equal the amount invested.
• 50% implies that the investment realized a profit equal to half the amount invested.
• 100% implies that the investment realized a profit equal to the amount invested.
• Greater than 100% implies that the profit was greater than the amount invested.
• Less than 0% implies that the investment recorded a loss.

The detailed percentage formula

Given that T is invested and a total of A is realized, the profit is

$$p = A - T$$

The percentage profit is:

$$\frac{A-T}{T} × 100\%$$

If the total amount, A, realized is less than the investment amount, T, then we have a negative value of p, that is, a loss with no profit. We have a loss whose percentage is:

$$\frac{T-A}{T} × 100\%$$

Application of the calculator

The percentage calculator is used to compute the following quantities:

• the percentage of a number;
• initial number, the percentage of which is given;
• the percentage increase from one number to another;
• the percentage decrease from one number to another;
• the percentage of the difference between two numbers to the average of the numbers.

How to compute the percentage of a number

Assume that the investor makes $3,000 profit and is planning to withdraw 20% of the profit and retain the rest of the investment. Then the amount withdrawn would be 20% of 3,000, which is equal to:

$$\frac{20}{100} × 3,000 = 600$$

The amount retained in the investment would be (100%-20%)=80% of 3,000, which is equal to:

$$\frac{80}{100} × 3,000 = 2,400$$

One can compute these two values using the Percentage Calculator.

How to compute the percentage increase or decrease

Assume that the investor initially invested $ 12,000 at the beginning of the year and $ 15,000 at the beginning of the following year. The invested amount increased by $ 3,000.

$$15,000 – 12,000 = 3,000$$

The percentage is calculated concerning the initial amount, $ 12,000. Therefore, the percentage increase in the amount invested is:

$$\frac{15,000-12,000}{12,000} × 100\% = \frac{3,000}{12,000} × 100\% = 25\%$$

Therefore, the investment increased by 25%.

How to Enter Values

We have a percentage difference calculator to calculate the value, which will tell us whether the change is an increase or decrease. Since $12,000 was the first investment amount, we key it into the "value 1" box. In the "value 2" box, we key in $15,000, then press the "calculate" button. The calculator determines the percentage difference as 25%, and this percentage represents an increase.

However, the result will be entirely different if you enter $15,000 in the first box and $12,000 in the second box. The second investment of $12,000 will be a 25% decrease from $15,000.

Furthermore, if the investment earned a profit of $3,000 at the end of the year and $2,700 at the end of the following year, then the profit of the following year decreased by $300 ($3,000 - $2,700). The decrease in percentage profit is calculated based on the initial profit of $3,000. The decrease in the percentage profit would be:

$$\frac{3,000-2,700}{3,000}×100\%=\frac{300}{3,000}×100\%=10\%$$

Therefore, the profit decreased by 10%.

Rules and recommendations for using the calculator

The calculator computes different percentages of values based on various inputs. It can work with negative values. However, it is better to enter positive values. In this way, it is much easier to understand and interpret the outcomes of the calculator.

There are six calculators on the page, some of which carry out duplicate roles. The main calculator is the first one on the page. It can carry out, potentially, all the functions of the other calculators after some precalculations are done on paper. However, the other calculators are provided to make it easier for the users to use without making any prior computations.

The percentage's History

The concept of consistently expressing parts of a whole in the same fractions, driven by practical needs, dates back to ancient Babylon. The cuneiform tablets of the Babylonians included calculations related to proportions and percentages, reflecting their advanced understanding of mathematics. The Babylonians employed a base-60 numbering system known as sexagesimal for their mathematical calculations.

Indian mathematicians calculated percentages by applying the so-called triple rule by using proportion. They were also able to do more complicated calculations with percentages.

The percentage was also widespread in ancient Rome. The word "percent" comes from the Latin "pro centum," which means "for a hundred."

The Romans called a percent the sum of money a debtor paid to a lender for each hundred. The Roman Senate had to set a maximum percentage to be charged to the debtor because some lenders were zealous in taking interest money.

From the Romans, percent passed on to the other nations of Europe.

Due to the extensive trade development during the Middle Ages in Europe, the ability to calculate percentages became essential. At that time, one had to calculate not only percent but also percent on percent, i.e., compound interest, as we call it nowadays. Individual enterprises developed their unique tables to make the calculation of percentages easier, which constituted the firm's trade secret.

It is believed that the concept of "percent" was introduced to science by the Belgian scientist Simon Stevin, an engineer from the city of Bruges. In 1584, he published tables for calculating percentages.

The sign % is thought to come from the Latin word cento, often abbreviated "cto" in percent calculations. From here, by further simplifying cursive writing, the letter t transformed into a slant (/), and the modern symbol for percentage emerged.

There is another version of the origin of the percent sign. This sign could have appeared due to a typographical error by a typesetter. In 1685 Mathieu de la Porte's "Guide to Commercial Arithmetic" was published in Paris, where the typesetter mistakenly typed % instead of "cto".

Humanity has used percentages for a long time to calculate profits and losses for every 100 units of money. Percentages were primarily used in trade and monetary transactions. Then the application field expanded, and nowadays, the percentages are used in economic and financial calculations, statistics, science, and technology.