Uniform Distribution Calculator
Probability, mean and variance for a continuous uniform.
Enter your values
ⓘ Live results
Results
- P(x₁ ≤ X ≤ x₂)
- 30%
- Density f(x)
- 0.1
- Mean
- 5
- Variance
- 8.3333
- Standard deviation
- 2.8868
Quick answer
In a continuous uniform distribution every value between a and b is equally likely, so P(x₁ ≤ X ≤ x₂) = (x₂ − x₁) ÷ (b − a).
P = (x₂ − x₁) ÷ (b − a)
How to use the Uniform Distribution Calculator
- 1Enter the interval bounds a and b.
- 2Enter the sub-range you want the probability for.
- 3Read the probability plus the summary statistics.
Worked example
Using the values the calculator loads with:
Inputs
- Lower bound a0
- Upper bound b10
- From x₁2
- To x₂5
Results
- P(x₁ ≤ X ≤ x₂)30%
- Density f(x)0.1
- Mean5
- Variance8.3333
- Standard deviation2.8868
Frequently asked questions
What is the mean of a uniform distribution?
The midpoint (a + b) ÷ 2, because the density is flat across the whole interval.
Why is the variance (b − a)²/12?
It comes from integrating the squared deviation across a flat density between a and b.
About this calculator
- Built and reviewed by James Whitfield · How we build and test calculators
- Report an error
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.