Uniform Distribution Calculator
Calculate mean, variance, standard deviation, PDF, CDF, and interval probability for a continuous uniform distribution U(a, b).
Distribution Parameters
Interval Probability (optional)
Quick Examples
Enter bounds a and b to compute distribution statistics.
Distribution Statistics — U(a, b)
Mean
—
(a+b)/2
Variance
—
(b−a)²/12
Std Dev
—
√variance
1/(b−a)
—
Support
interval
—
Interval Probability P(x1 ≤ X ≤ x2)
P(x1 ≤ X ≤
x2) =
—
Range Visualization
μ
a
b
Full support [a, b]
Sub-interval [x1, x2]
Summary
Calculate mean, variance, standard deviation, PDF, CDF, and interval probability for a continuous uniform distribution U(a, b).
How it works
- Enter the lower bound a and upper bound b of your uniform distribution (a must be less than b).
- Optionally enter x1 and x2 to compute P(x1 ≤ X ≤ x2).
- The calculator computes mean = (a+b)/2, variance = (b-a)²/12, and standard deviation = √variance.
- PDF = 1/(b-a) — constant across the entire interval.
- CDF(x) = (x-a)/(b-a) for x in [a, b].
- P(x1 ≤ X ≤ x2) = (x2-x1)/(b-a) for x1, x2 inside [a, b].
- A range indicator visualizes the full interval and any sub-interval.
Use cases
- Model scenarios where all outcomes between two values are equally likely.
- Compute the probability that a random variable falls in a specific sub-range.
- Find mean and variance for uniform priors in Bayesian analysis.
- Solve textbook probability problems involving continuous uniform distributions.
- Simulate random number generation bounded within [a, b].
- Analyze waiting times or rounding errors modeled as uniform distributions.
Frequently Asked Questions
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Last updated: 2026-05-23 ·
Reviewed by Nham Vu