Uniform Distribution Calculator
Probability, mean and variance for a continuous uniform.
Enter your values
Enter the lower bound a you are working with.
Enter the upper bound b you are working with.
Enter the from x₁ you are working with.
Enter the to x₂ you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
What do I need to enter into the Uniform Distribution Calculator?
Just 4 values: lower bound a, upper bound b, from x₁, to x₂. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Uniform Distribution Calculator work out the answer?
In a continuous uniform distribution every value between a and b is equally likely, so P(x₁ ≤ X ≤ x₂) = (x₂ − x₁) ÷ (b − a). It applies the formula P = (x₂ − x₁) ÷ (b − a) and shows the working so you can check each step by hand.
Is the Uniform Distribution Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.