Uniform Distribution Calculator
For a value equally likely to land anywhere in a range.
P(lower < X < upper)
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Share sends a link that reopens these numbers. Copy details pastes the full breakdown as a list.
P(X < lower) —
P(X > upper) —
Density —
Mean —
Variance —
Standard deviation —
Reading this —
The formula
density = 1 ÷ (b − a) mean = (a + b) ÷ 2 variance = (b − a)² ÷ 12
The chance of landing in a range is its width divided by the full width. Parts of the range outside a to b do not count.
What to watch out for
A rounding error is a common real example: within half a unit either way, with no preferred value.
Frequently Asked Questions
What is a worked example?
On 0 to 10, the chance of being between 2 and 5 is 0.3. The mean is 5 and the variance is 8.33333.
What is the standard deviation?
The width divided by √12, or about 0.2887 times the width.