Uniform Distribution Calculator
Calculate probability for a continuous uniform distribution.
Uniform Distribution Formula
For a continuous uniform distribution on [a,b], the probability over an interval is its length divided by b−a.
Understanding a Uniform Distribution
A continuous uniform distribution assigns equal density to every value inside a defined interval. Probabilities depend on interval length rather than location.
Uniform Distribution Example
If a value is equally likely anywhere between 0 and 10, the probability of landing between 2 and 5 is 3/10, or 0.30.
When It Is Useful
This model is useful when no value inside a bounded interval is favored over another.
Frequently Asked Questions
Can values fall outside the interval?
Not under the model.
Is the mean at the midpoint?
Yes.
Does every exact continuous value have positive probability?
No. Probability is assigned to intervals, not individual points.
Understanding a Uniform Distribution
A continuous uniform distribution assumes every value within a defined interval from a to b is equally likely in terms of probability density. The probability of falling between two values is based on the length of that sub-interval divided by the total interval length.
Use this calculator when the model genuinely assumes no part of the allowed range is favored over another. If values are uniformly distributed from 0 to 10, for example, the probability of a result between 2 and 5 is 3/10, or 30%. Ensure the lower bound is smaller than the upper bound and that the requested interval lies within the distribution limits.
A uniform model is a simplifying assumption and may not match observed data. Before using the result for planning or analysis, consider whether the underlying process actually produces approximately equal density across the stated range.
Methodology, Assumptions and Interpretation
For a continuous uniform distribution on [a,b], equal-length intervals have equal probability and density is 1/(b−a). The endpoints themselves have zero probability in a continuous model even though they define the range.