# Documentation/Calc Functions/BINOM.DIST

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## Function name:

BINOM.DIST

## Category:

Statistical Analysis

## Summary:

Returns the individual term binomial distribution probability.

## Syntax:

BINOM.DIST(**X**; **Trials**; **SP**; **C**)

## Returns:

Returns a real number which is either a probability or a sum of probabilities defined by the binomial distribution. The value ranges from 0 to 1, i.e. [0,1].

## Arguments:

**X** is a positive integer value or a reference to the cell containing that number which is the number of successes in a set of trials.

**Trials**is a positive integer value or a reference to the cell containing that number which is the number of independent trials.

**SP** is a real number between 0 and 1(both inclusive) or a reference to the cell containing that value which is the probability of success on each trial.

**C** is a logical value that determines the form of the function. C = 0 or False to calculate the probability density function. It can be any other value like 1 or True to calculate the cumulative distribution function.

- If
**X**and**Trials**are a non-integer value, then the function uses their floor value, i.e. they are truncated to an integer value. - If
**X**and**Trials**are less than zero then the function returns an error value. Also if**X**is greater than "Trials**after truncation, then the function returns an error value.** - If
**SP**is greater than 1 or less than 0, then the function returns an error value.

## Additional details:

- The formula for BINOM.DIST for probability density function (when
**C**=0)is:

where:

is COMBIN(n,x)

- The formula for BINOM.DIST for the cumulative binomial distribution (when
**C**=1) is:

- For more details on the binomial distribution, visit
**Wikipedia**.

## Examples:

Formula | Description | Returns |
---|---|---|

=BINOM.DIST(5;12;0.5;0) | shows the probabilities for 12 flips of a coin that Heads will come up exactly 5 times |
0.193359375 |

=BINOM.DIST(4;12;0.5;1) | shows the cumulative probabilities for the same series. Here the cumulative probability of the series is 0, 1, 2, 3 or 4 times Heads (non-exclusive OR) |
0.19384765625 |

## Related LibreOffice functions:

## ODF standard:

None

## Equivalent Excel functions:

BINOM.DIST