Uniform Distribution Calculator

A uniform distribution gives every value in a range an equal chance.

How the Math Works

The Uniform Distribution Calculator uses the formula P(X ≤ x) = (x - a)/(b - a) to determine the probability that a continuous random variable falls at or below a specific value. Here, 'a' represents the minimum possible value, 'b' the maximum, and 'x' the threshold you're testing. This formula works because in a uniform distribution, all outcomes within the range [a, b] are equally likely, so the probability is simply the length of the interval from a to x divided by the total length from a to b. The calculator also computes related statistics like mean (a+b)/2, variance (b-a)^2/12, and standard deviation sqrt((b-a)^2/12).

Practical Applications

To use this calculator, enter your distribution's minimum (a) and maximum (b) bounds, then specify your target value (x) or range. For example, if you're analyzing wait times that are uniformly distributed between 5 and 20 minutes, you can quickly find the probability a customer waits less than 10 minutes, or determine what percentage of customers wait more than 15 minutes. This is particularly useful in quality control, simulation modeling, and academic statistics problems where equal probability across an interval is assumed.

Day-to-Day Use

This calculator helps with everyday decisions involving uncertainty and planning. You might use it to estimate the likelihood of arriving somewhere within a certain time window, determine fair random selection methods for giveaways or experiments, or evaluate if a process is producing uniformly distributed results. It's valuable for project management when estimating task durations, for game design when balancing random elements, or simply for satisfying curiosity about probabilities in situations where outcomes are evenly spread across a range.

Worked example

a 0, b 10, x 7 → P 0.7, mean 5.

FAQ