Uniform Distribution Calculator

Calculate PDF, CDF, mean and variance for the continuous uniform distribution on [a, b].

About Uniform Distribution Calculator

The continuous uniform distribution assigns equal probability density to all values in the interval [a, b]. It is the simplest continuous distribution and serves as a model for 'equally likely' outcomes over a range.

Formulas

PDF

f(x) = 1/(b−a) for a ≤ x ≤ b, 0 otherwise

a: Lower bound
b: Upper bound

CDF

F(x) = (x−a)/(b−a) for a ≤ x ≤ b

x: Point of evaluation

Worked example

With the default values below, Uniform Distribution Calculator returns PDF f(x) of 0.10000000. Change any input above and every figure here is recalculated in your browser.

Inputs used

Lower Bound (a): 0
Upper Bound (b): 10
x value: 3

Results

PDF f(x): 0.10000000
P(X ≤ x): 0.30000000
Mean: 5.0000
Variance: 8.333333

Step by step

1Values used
2PDF
3CDF
4PDF f(x)= 0.10000000
5P(X ≤ x)= 0.30000000
6Mean= 5.0000
7Variance= 8.333333

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

What is the probability of an exact value in a continuous uniform distribution?

Zero. For any continuous distribution, P(X = exact value) = 0. Probability only applies to intervals.

What real-world situations follow a uniform distribution?

Random number generators, arrival times within a known window, and rounding errors are often modeled as uniform.