 # Calculating Random Numbers with the Random Number Generator

Calculate random numbers within a desired number range with the Random Number Generator. Negative and decimal numbers can be used for the limits of the number range. Duplicate numbers can be excluded during generation (Urn model: "Draw without putting back") or allowed (Urn model: "Draw with putting back"). The output of the randomly generated numbers can also be sorted in ascending or descending order.

## Input Aids for the Random Number Generator

In the following, you will find information on the individual input fields of the random number generator.

### Number Range

Please specify the number range for which the random numbers are to be calculated. Therefore, please specify the upper and lower ends of the desired interval. It is also possible to enter negative numbers as well as decimal numbers.

### Random Number Count Please enter the number of random numbers you want the number generator to calculate.

This number generator can generate up to 9.999 random numbers.

### Decimal Places Please select whether the generated random numbers should have decimal places, and if so, how many. With this number generator, up to 5 decimal places can be taken into account.

### Allow Duplicates Please select whether the random numbers generated may occur several times or should all be different. For example, when rolling several dice, several identical results are also possible. In a lottery, on the other hand, i.e., the drawing of a specific set of numbers from a limited set of numbers, only different results are possible.

If several identical random numbers are allowed, this corresponds to the urn model "Drawing with laying back": Once a number has been drawn, it can be drawn again. If each random number may only be generated once, this corresponds to the urn model "Draw without laying back", in which a number drawn once cannot be drawn again.

### Sorting Please select whether the generated random numbers should be unsorted, sorted in ascending order or sorted in descending order. For example, the result of a lottery is normally displayed in ascending order.

## Examples of the Use of Random Numbers

The generation of equally distributed random numbers by means of a random number generator has numerous applications, for which we would like to list a few examples in the following.

### What do random numbers have to do with rolling dice?

Rolling dice is a common application for generating random numbers. When playing a board game, for example, you will usually be asked to roll a dice at some point during the game to determine how many spaces you can advance on the board. In this case, a random number is used to determine what number the dice will show. There are also many popular dice games with one or more dice that can be played without real dice rolling by using the random number generator. For this purpose, the number range in the calculator can be preset to 1 to 6, allowing for double results.

### What are random numbers used for in computer games?

Another common example of the use of random numbers is in computer games. In many computer games, random numbers are used to create random events or outcomes that make the game more interesting and unpredictable. For example, in a role-playing game, random numbers could be generated by a random number generator to determine which enemies you encounter in battle or what rewards you receive for completing tasks.

### What are random numbers used for in science?

In science, random numbers are often used to obtain objective results and to avoid bias in the results. An example of this is the use of random numbers when conducting clinical trials. For example, when testing a new drug, random numbers may be used to allocate the drug to the subjects so that the groups receiving the drug and the placebo are as equal as possible. In this way, the results of the trial can be more accurate and reliable.

### What do random numbers have to do with cryptography?

In cryptography, random numbers are often used to create secure encryption methods. An example of this is the RSA algorithm, which is used to encrypt data. This algorithm is based on the fact that it is very difficult to factorise large prime numbers. In the RSA method, two large, randomly selected prime numbers are used to create a public key and a secret key. The public key is used to encrypt messages, while the secret key is used to decrypt the encrypted messages. In this way, secure communications can take place without third parties being able to read the messages.

### How are random numbers used in the context of statistics?

In statistics, random numbers are often used to model uncertainties and unknowns in data and to make estimates of populations. An example of this is the use of random numbers in sampling. For example, if the opinions of 1000 citizens in a particular city differ, random numbers can be used to select a sample of 100 citizens that is representative of the entire population. In this way, the results of the survey can be more accurate and reliable.

### What do random numbers have to do with children's birthdays?

An example of using random numbers at a children's birthday party would be to use random numbers when playing birthday games. For example, in the classic "stop dance", you could generate random numbers with the random number generator to determine which child has to stop dancing next when the music stops. This could be done by drawing random numbers from a pot of all the children's names to ensure that each child has an equal number of turns and that no child is disadvantaged. This way, the birthday games can be fair and fun for all the children.

Another example of using random numbers at a children's birthday party would be to use random numbers when distributing gifts. Instead of the birthday child unwrapping the gifts themselves and distributing them to the other children, the gifts could be numbered, and the children could be selected at random to choose a gift. This way, the gifts can be distributed fairly, and all children have an equal chance to receive a gift of their choice.

Overall, random numbers at a children's birthday party offer many opportunities to make the games and activities fair and fun for all children.

## How the Random Number Generator Works

The random numbers are generated randomly and equally distributed by the random generator using the function Math.random(). Math.random() is a built-in function in JavaScript that makes it possible to generate random numbers that can be used in various applications, such as computer games, scientific calculations and simulations.

It depends on the browser used which exact random number generator is used. To generate pseudo-random numbers, most modern browsers now use an algorithm called Xorshift128+. These are numbers that look random but are generated using deterministic algorithms and are therefore not random. Xorshift128+ is a random number generator that is both fast and efficient while producing high-quality numbers. The algorithm is based on the concept of bit shifting and the XOR operator, which makes it highly resistant to interference and therefore difficult to predict.

## Creating Pseudo-Random Numbers with Number Generator

As a rule, a random number generator produces only pseudo-random numbers. Pseudorandom numbers are numbers that look random but are actually generated by a deterministic algorithm. These algorithms use an initial state called a seed and a series of calculations to generate a sequence of numbers that look random. Conceivable seeds are, for example, the current time in milliseconds combined with the current coordinates of the mouse pointer. However, the numbers generated by these algorithms are not truly random; they are predictable if you know the seed and the algorithm.

In contrast, true random numbers are numbers that are actually generated by random effects, for example, by the radioactivity of atoms or electronic interference. These numbers are truly random and unpredictable. However, true random numbers are very difficult to generate in practice, which is why pseudo-random numbers are usually used.

In cases where a high degree of randomness is required, such as in the encryption of data or in complex simulations, several pseudorandom number generators are often combined to achieve a higher quality of pseudorandom numbers. In this way the results can be more accurate and reliable.

## Source information

As source for the information in the 'Random Number Generator' category, we have used in particular:

## Last update

This page of the 'Random Number Generator' category was last edited or reviewed by Stefan Banse on February 20, 2023. It corresponds to the current status.