📏 Uniform Distribution Calculator
Analyze a continuous uniform distribution, where every value between a minimum and maximum is equally likely.
What the uniform distribution models
The continuous uniform distribution describes a situation where every value between a minimum (a) and a maximum (b) is equally likely to occur, so the probability density is perfectly flat across that range. It’s the mathematical model behind things like a random number generator that picks any value in a range with equal chance.
How this calculator works
Enter the minimum and maximum bounds of the distribution and a value x. The calculator returns the constant probability density f(x) = 1 / (b – a) for any x within the range (and 0 outside it), and the cumulative probability P(X ≤ x) = (x – a) / (b – a). It also reports the mean, (a + b) / 2, and the variance, (b – a)² / 12.
This tool models the continuous uniform distribution, not the discrete uniform distribution (like a fair die), and is intended for general statistics education and analysis.