The triangular distribution is a continuous probability distribution with a probability density function shaped like a triangle.

It is defined by three values:

- The minimum value
*a* - The maximum value
*b* - The peak value
*c*

The name of the distribution comes from the fact that the probability density function is shaped like a triangle.

The triangular distribution has the following PDF and CDF:

**PDF:**

**CDF:**

The following examples show how to use the Triangular distribution to calculate probabilities in Excel.

**Example 1: Restaurant Sales**

Suppose a restaurant estimates that their total sales for the upcoming week will be a minimum of $10,000, a maximum of $30,000, and most likely $25,000.

**What is the probability that the restaurant makes less than $20,000 total sales?**

According to the CDF, we can use the following formula to find the probability that total sales will be less than $20,000:

- P(X < x) = (x-a)
^{2}/ ((b-a)(c-a))

Here’s how to calculate this probability in Excel:

The probability that the restaurant makes less than $20,000 total sales is **.333**.

**Example 2: Number of Customers**

Suppose a shop estimates that the number of customers that will enter in a given week will be a minimum of 500, a maximum of 2,000, and most likely 1,200.

**What is the probability that more than 1,500 customers enter the shop in a given week?**

According to the CDF, we can use the following formula to find the probability that the total number of customers will be greater than 1,500:

- P(X > x) = 1 – [1 – (b-x)
^{2}/ ((b-a)(b-c))]

Here’s how to calculate this probability in Excel:

The probability that more than 1,500 customers enter the shop is **.208.**

**Additional Resources**

The following tutorials explain how to work with other probability distributions in Excel:

How to Use the Binomial Distribution in Excel

How to Use the Poisson Distribution in Excel

How to Use the Uniform Distribution in Excel