Uniform Distribution Calculator

A uniform distribution is a probability distribution where all values between a minimum (a) and maximum (b) are equally likely to occur. The probability density is constant across the range. It's also called a rectangular distribution due to its shape.

Discrete uniform: Finite number of equally likely outcomes (e.g., rolling a fair die: 1,2,3,4,5,6). Continuous uniform: Infinite outcomes in a range with constant probability density (e.g., random decimal between 0 and 1). This calculator handles continuous uniform distributions.

Examples include: Random number generators (0 to 1), arrival times within a time window when no pattern exists, rounding errors in measurements, lottery ball selection, and spinning a perfectly balanced wheel. Any scenario with "equally likely" outcomes over a continuous range.

For continuous uniform: P(X ≤ x) = (x - a) / (b - a). Probability density f(x) = 1/(b-a) for a ≤ x ≤ b. For any interval [c,d] within [a,b]: P(c ≤ X ≤ d) = (d - c) / (b - a). All intervals of equal length have equal probability.

Mean (μ) = (a + b) / 2 (midpoint). Variance (σ²) = (b - a)² / 12. Standard deviation (σ) = (b - a) / √12 ≈ (b - a) / 3.464. These formulas apply to continuous uniform distributions.