Uniform Distribution Calculator

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The minimum value of the uniform distribution. All values below this have zero probability.
The maximum value of the uniform distribution. Must be strictly greater than the lower bound.
The point at which to evaluate P(X <= x) and P(X > x). Must be within [a, b].
Lower bound for interval probability P(c <= X <= d). Leave blank to skip.
Upper bound for interval probability P(c <= X <= d). Leave blank to skip.
Probability Density f(x)Middle half
0.1

The constant probability density: 1 / (b - a)

P(X <= x)0.4
P(X > x)0.6
P(c <= X <= d)0.4
Mean (mu)5
Variance (sigma^2)8.333333
Standard Deviation (sigma)2.886751
Median5
Range (b - a)10
P(X <= x)0.4
P(X > x)0.6

Uniform distribution on [0, 10]: every subinterval of equal length is equally probable.

  • Any value in [0, 10] is equally likely. The probability density is 0.100000 per unit, constant across the entire interval.
  • At x = 4: P(X <= 4) = 40.00%, P(X > 4) = 60.00%.
  • The chance X lands between 3 and 7 is 40.00%. This is proportional to the width of that sub-interval relative to (b - a).
  • Mean = 5.0000, Standard deviation = 2.8868. The distribution is symmetric, so skewness is 0 and the median equals the mean.

Next stepFor a finite set of equally likely outcomes (dice, cards, lottery draws), use the discrete uniform distribution instead: P(X = k) = 1/n for n equally likely integers.

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