Solve uniform distribution problems with probability outputs. Review density, cumulative probability, spread, and interval measures. Use clear inputs to study bounded random variables confidently.
| a | b | x | Interval | p | PDF at x | CDF at x | Interval Probability | Quantile |
|---|---|---|---|---|---|---|---|---|
| 2 | 10 | 6 | [4, 8] | 0.75 | 0.125000 | 0.500000 | 0.500000 | 8.000000 |
| 0 | 20 | 5 | [3, 9] | 0.40 | 0.050000 | 0.250000 | 0.300000 | 8.000000 |
| -4 | 4 | 1 | [-2, 2] | 0.90 | 0.125000 | 0.625000 | 0.500000 | 3.200000 |
Uniform random variable: X ~ U(a, b), where a < b.
Probability density function: f(x) = 1 / (b - a), for a ≤ x ≤ b. Otherwise, f(x) = 0.
Cumulative distribution function: F(x) = 0 for x < a, F(x) = (x - a) / (b - a) for a ≤ x ≤ b, and F(x) = 1 for x > b.
Interval probability: P(x1 ≤ X ≤ x2) = overlap length / (b - a).
Mean: (a + b) / 2
Variance: (b - a)² / 12
Standard deviation: √Variance
Quantile: Q(p) = a + p(b - a)
A uniform distribution calculator helps you study a continuous random variable that is equally likely across a fixed interval. Every value between the lower bound and upper bound has the same density. This makes the model simple, clear, and useful in many probability tasks.
The continuous uniform distribution is often used when outcomes are spread evenly over a range. It appears in simulation, quality control, waiting time examples, randomized testing, and basic statistical teaching. Because the shape is flat, the probability density function stays constant inside the interval.
This page computes the PDF at a chosen x value, the CDF at that point, and the probability across a selected interval. It also returns the mean, median, variance, standard deviation, quantile, skewness, and excess kurtosis. These outputs give a practical summary of location, spread, and probability behavior.
The PDF shows the constant density for all valid values inside the bounds. The CDF shows the cumulative probability up to x. The interval probability measures how much of the chosen interval overlaps with the full support. The quantile tells you which value matches a selected cumulative probability level.
Use this calculator when you know the minimum and maximum possible values and want a fast probability check. It works well for educational examples, bounded measurements, random sampling practice, and process assumptions where every point is treated evenly. It is also helpful when comparing manual probability formulas with computed outputs.
A strong uniform distribution calculator saves time and reduces formula mistakes. You can test different bounds, export results, and review example data in one place. That makes this page useful for students, analysts, teachers, engineers, and anyone working with simple probability models.
It is a probability model where every value inside a fixed interval has the same density. The variable is limited by a lower bound and an upper bound.
It is useful when values are assumed to be evenly spread over a known range. Common examples include simulations, teaching, and bounded measurement problems.
The PDF gives the constant density inside the valid interval. It is not the probability at one exact point. For continuous variables, probabilities come from intervals.
The CDF shows the probability that the random variable is less than or equal to x. It increases from 0 to 1 across the interval.
The interval width must be positive. If the bounds are equal or reversed, the distribution is not valid and the formulas no longer work correctly.
The calculator finds how much of your selected interval overlaps the full support. That overlap length is divided by the total width, b minus a.
The quantile result is the value linked to a chosen cumulative probability p. For example, p = 0.75 gives the point where 75% of outcomes lie below it.
Yes. This page includes CSV export for table data and PDF export for a simple report. Both downloads use the values currently entered in the calculator.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.