Percentage calculation with the Percent Calculator

Percentage Calculator - Simply Calculate Percentages (%)

Percentage Calculation ﹣ Calculator

Percentage calculation tasks crop up all the time in everyday life. With the online percentage calculator, you are prepared for all kinds of percentage calculations. In the calculator, you can select examples of typical questions on percentage calculation. In this way, the percentage calculator guides you intuitively to your goal.

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The most important topics for the Percentage Calculator

Functions of the Percentage Calculator

Aside from the usual proportional percentage calculation, the percentage increase or decrease of the basic value is calculated with the percentage calculator using the percentage value and percentage number. In the info text of the calculator, the calculation path to the result of the percentage calculation is explained in detail, and the corresponding percentage formula is displayed.

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Input Help for the Percentage Calculator

The following entries are required in the percentage calculator for the percentage calculation:

Input "Typical question"

Percentage Calculator: Typical questions

Simply select a typical question suitable for your percentage calculation in the percentage calculator. According to the subdivision of the example questions, the percentage calculator offers different calculation types: In addition to the normal percentage calculation, there is also the possibility of calculating the percentage increase or decrease of the base value using percentage number and percentage value.

Input "Enter your values"

You can replace the example values given in the questions with your own values under "Enter your values" in order to carry out your own individual percentage calculation.

Depending on the typical question selected for the percentage calculation, the percentage calculator provides different input fields.

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What is the Percentage Formula?

The percentage calculation can of course be expressed as a formula. The terms for percentage calculation are defined as follows:

  • Basic value G: The initial value corresponding to 100% to which the percentage refers.
  • Percentage value W: The value derived from the basic value according to the percentage.
  • Percentage p: Proportion of the percentage value to the basic value, expressed as a percentage.

The general percentage formula for calculating the percentage value W is:

Percentage Value = Basic Value × Percentage/100
or also
W = G × p

This equation can now be rearranged as desired, depending on which quantity is known and which is not. If, for example, the calculation of the basic value is determined, the percentage number and percentage value can be entered into the calculator. The percentage calculator thus calculates either the percentage value, the basic value or the percentage. Two of these values must be entered in each case, in order to calculate the third value.

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Definition of Technical Terms

The terms "Basic Value", "Percentage Value" and "Percentage" (also known as "Percentage Number") form the basis of all formulas in percentage calculation. The Percentage Value and the Basic Value always have the same unit (e.g., kg or euro), and the Percentage Number is a simple number. In the Percentage Calculator, as well as in general, two of the three values can be used for each question in order to calculate the third.

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What is the Basic Value in Percentage Calculation?

In percentage calculation, the Base Value is the initial value that corresponds to 100 percent and to which the percentage refers. In formulas, this value is abbreviated with a G.

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How is the Percentage Value Defined?

The Percentage Value has the same unit as the Basic Value (e.g., kg or euro). The Percentage Value can be smaller or larger than the Basic Value. The Percentage Value is the value derived from the Basic Value according to the Percentage. In formulas, this value or amount is abbreviated with a W.

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What is the Percentage?

A percentage is the ratio of the percentage value to the basic value, expressed as a percentage. The percentage thus indicates the ratio of the two quantities in hundredths. In formulas, the percentage is abbreviated as p. Colloquially, this value is also called a percentage number and is always indicated with the percent sign. Percentages can also be well represented in decimal notation:

19 Percent = 19/100 = 0.19
119 Percent = 119/100 = 1.19

This simplifies, for example, the conversion of net amounts into gross amounts in bookkeeping, i.e., taking into account the VAT and, conversely, also the deduction of VAT.

The concepts of percentage calculation in practical examples

ExampleBasic ValuePercentage ValuePercentage (%)
5 is 20% of 100100520
110 is 110% of 100100110110
15 is a 50% reduction from 30301550
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How does percentage calculation by rule of three work?

You can also calculate percentages using the “rule of three”. For example, if you want to calculate 5 percent of 300 euros, you can use the triple rule method to make the following calculation:

100 percent equals 300 euros

1 percent equals 300 euros / 100

5 percent equals 300 euros / 100 × 5 = 15 euros

Rule of three calculator

With our triple rule calculator, you can also solve numerous percentage problems in this way.
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Examples of Percentage Calculation with Formulas

The total of nine selectable questions in the Percentage Calculator cover the typical tasks for calculating percentages:

  • Calculation of the proportion of a value in percent
  • Determining the percentage increase of a value, or
  • Determining the percentage decrease of an amount

For each of these tasks, one of the three values is calculated using the other two set values with the Percentage Calculator.

The formula for the percentage calculation can be rearranged as follows:

If the basic value is unknown:Basic Value = Percentage Value × 100 / Percentage
If the percentage value is to be calculated:Percentage Value = Basic Value × Percentage / 100
When the percentage is missing:Percentage = Percentage Value × 100 / Basic Value
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Example 1: Proportional Calculation - Calculation of the Percentage Value

Percentage task

The following question can be selected with the percentage calculator and then filled in with your own numbers:

How much is 10 percent of 120?

Mathematical formula for calculation

Percentage/100 × Basic Value = Percentage Value

Concrete percentage calculation

For a percentage of 10 percent and a base value of 120, the Percentage Calculator performs the following concrete calculation for the percentage value:

10/100 × 120 = 12

Solution

10 percent of 120 is 12.

Application example

In practice, such a calculation often occurs in the case of a home loan: A loan amount is to be repaid at an initial interest rate of 2%. What is the annual repayment for a financing amount of 400,000 euros? The calculation: 2 percent × €400,000 = €8,000.

Example 2: Proportional Calculation - Calculation of the Percentage

Percentage task

Here, the following question was selected with the percentage calculator, which can then be substantiated with your own figures:

What percentage is 12 out of 120?

Percentage formula

Percentage Value / Basic Value × 100 = Percentage

Concrete percentage calculation

With a percentage value of 12 and a base value of 120, the Percentage Calculator performs the following concrete calculation for the percentage:

12 / 120 × 100 = 10

Solution

12 out of 120 is 10 percent.

Application example

A question from everyday life could be: A bank statement shows an interest charge of 240 euros for the previous year. The loan amount for the instalment credit is still 6,000 euros. What is the interest rate? The calculation: €240 / €6,000 × 100 = 4%.

Example 3: Proportional Calculation - Calculation of the Basic Value

Percentage task

The following question can be selected with the percentage calculator and then assigned your own figures:

12 is 10 percent of how much?

Mathematical formula for calculating

Percentage Value / (Percentage/100) = Basic Value

Concrete percentage calculation

With a percentage value of 12 and an amount of 10 percent, the percentage calculator performs the following concrete calculation for the basic value:

12 / (10/100) = 120

Solution

12 is 10 percent of 120.

Application example

Here is another example: The borrower finds the interest charge of 240 euros on the statement of account; he also knows that he is supposed to pay 4 percent per year on the outstanding balance. How much is left? The calculation: €240 / 4 percent = €6,000

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Example 4: Percentage Increase - Calculation of the Percentage Value

Percentage task

The following question can be selected and then substantiated with your own figures:

How much is 120 plus 10 percent?

Formula

The percentage calculator uses the following general formula to calculate the percentage value for the percentage problem or question at hand:

Basic Value × (1 + Percentage/100) = Percentage Value

Concrete percentage calculation

With a base value of 120 and a percentage equal to 10 percent:

120 × ( 1 + 10/100) = 132

Solution

120 plus 10 percent is 132.

This calculation is often used for

  • the calculation of interest and interest rate
  • the increase of an asset
  • the determination of a financial amount with the addition of VAT
  • the calculation of the increase in salary in the case of a salary increase
  • general price increase and the price increase for goods and services

Application example

In the public sector, a 5 percent pay increase on the salary paid has been agreed upon.. What is the salary then, if it is currently 2,800 euros? Calculation: €2,800 + 5% = €2,800 × 1.05 = €2,940

Example 5: Percentage Increase - Calculation of the Percentage

Percentage task

The following question can be selected with the calculator and then assigned your own figures:

How many percent more is 132 compared to 120?

The percentage to be calculated is the percentage increase.

Mathematical formula

According to the percentage task or question posed here, the online calculator uses the following general formula to calculate the percentage:

(Percentage Value / Basic Value − 1) × 100 = Percentage

Concrete percentage calculation

With a percentage value of 132 and a basic value of 120, the calculator performs the following concrete calculation for the percentage:

(132 / 120 − 1) × 100 = 10

Solution

132 compared to 120 is 10 percent more.

Application example

An example from everyday life: A public-service employee wants to check how much the percentage salary increase on his pay slip is. Up to now, he has earned a gross salary of 3,000 euros, now 3,150 euros is shown. The calculation: (€3,150 / €3,000 − 1) × 100 = 5%.

Example 6: Percentage Increase - Calculation of the Basic Value

Percentage task

The following question can be selected with the tool and then substantiated with your own figures:

132 is 10 percent more than how much?

Mathematical formula

According to the percentage task or question posed, the tool uses the following calculation formula for the basic value:

Percentage Value / (1 + (Percentage/100)) = Basic Value

Concrete percentage calculation

With a percentage value of 132 and a percentage in the amount of 10 percent, our calculator performs the following concrete calculation for the basic value:

132 / (1 + (10/100)) = 120

Solution

132 is 10 percent more than 120.

Application example

Here is another example from everyday life: In Germany, the average price of a liter of diesel this year was 1.10 euros, which is a 4 percent increase compared to the previous year. What was the price last year? The calculation: €1.10 / (1 + 4/100) = €1.10 / 1.04 = €1.058.

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Example 7: Percentage Decrease - Calculation of the Percentage Value

Percentage task

The following question can be selected with the percentage calculator and then assigned your own figures:

How much is 120 minus 10 percent?

Mathematical formula

The percentage calculator uses the following general calculation formula for the percentage value to suit the percentage task or question at hand:

Basic Value × (1 − Percentage/100) = Percentage Value

Concrete percentage calculation

With a basic value of 120 and a percentage in the amount of 10 percent, the percentage calculator performs the following concrete calculation for the percentage:

120 × (1 − 10/100) = 108

Solution

120 minus 10 percent is 108.

Application example

The practical example of this is: Our above-mentioned average diesel price above 1.10 euros is expected to fall again this year by 2 percent. What value do the statisticians expect? The calculation: €1.10 × (1 − 2/100) = 1.10 × 0.98 = €1.078.

Example 8: Percentage Decrease - Calculation of the Percentage

Percentage task

The following question can be selected with the online calculator and then backed up with your own figures:

How many percent less is 120 compared to 132?

Percentage formula

The percentage calculator uses the following general calculation formula for the percentage to suit the percentage task or question at hand:

(Basic Value / Percentage value − 1) × 100 = Percentage

Concrete percentage calculation

With a basic value of 120 and a percentage value of 132, the percentage calculator performs the following concrete calculation for the percentage:

(120 / 132 − 1) × 100 = -9.090909...

Solution

120 compared to 132 is 9.090909... percent less.

Example 9: Percentage Decrease - Calculation of the Basic Value

Percentage task

The following question can be selected with the percentage calculator and then assigned your own figures:

120 is 10 percent less than how much?

Mathematical formula

The percentage calculator uses this formula for the calculation of the percentage task or question at hand:

Percentage Value / (1 − Percentage/100) = Basic Value

Concrete percentage calculation

With a percentage value of 120 and a percentage in the amount of 10 percent, the percentage calculator performs the following concrete calculation for the basic value:

120 / (1 − 10/100) = 133.333333...

Solution

120 is 10 percent less than 133.333333...

Source information

As source for the information in the 'Percentage Calculation' category, we have used in particular:

Last update on December 16, 2022

The pages of the 'Percentage Calculation' category were last editorially reviewed by Michael Mühl on December 16, 2022. They all correspond to the current status.

Previous changes on December 16, 2020

  • 16.12.2022: Publication of the Percent Calculator
  • Editorial revision of all texts in this category