Triangular Distribution Calculator

The triangular distribution calculator determines the probability, mean, median, mode, and variance based on given distribution data.

Minimum Value (a):

Maximum Value (b):

Peak Value (c):

Random Variable (x):

Probability (a ≤ x < c):

Mean (μ):

Median (M):

Mode:

Variance (σ²):

How to Use the Triangular Distribution Calculator?

First, input the minimum, maximum, and peak values. Also, enter the value for the random variable (x).
Press the 'Calculate' button.
The tool returns the probability P(a ≤ x < c), mean, median, mode, and variance of the triangular distribution.

The probabilities can be found using the following formulas:

P(x < a) = 0

P(a ≤ x < c) =

2(x - a)

(b - a) (c - a)

P(x = c) =

(b - a)

P(c < x ≤ b) =

2(b - x)

(b - a) (b - c)

P(b < x) = 0

F(x ≤ a) = 0

F(a ≤ x ≤ c) =

(x - a)²

(b - a) (c - a)

F(c < x < b) =

1 - (b - x)²

(b - a) (b - c)

F(b ≤ x) = 1

The mean, mode, and variance are calculated using the following formulas:

Mean (μ) =

a + b + c

Mode = c

Variance (σ²) =

(a² + b² + c² – ab – ac – bc)

Where,
a = Minimum Value,
b = Maximum Value,
c = Peak Value,
x = Random Variable.