Uniform Distribution Calculator
Probability, mean and variance for a continuous uniform.
Enter your values
Results update instantly as you type — no submit needed.
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)
At a glance
| What it does | Probability, mean and variance for a continuous uniform. |
|---|---|
| Category | Statistics |
| Inputs needed | Lower bound a, Upper bound b, From x₁, To x₂ |
| Main output | P(x₁ ≤ X ≤ x₂) |
| Formula | P = (x₂ − x₁) ÷ (b − a) |
| Cost | Free — no sign-up, no download |
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.
Inputs explained
- Lower bound a
- Enter the lower bound a you are working with.
- Upper bound b
- Enter the upper bound b you are working with.
- From x₁
- Enter the from x₁ you are working with.
- To x₂
- Enter the to x₂ you are working with.
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.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.