Statistics & Probability

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Uniform Distribution Calculator.

Calculate this statistic instantly with validated formulas.

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Set your values

Results update as you type.

Result: PDF f(x): 0.10000000 CDF P(X ≤ x): 0.40000000 Mean: 5.00000000 Variance: 8.33333333

Result

PDF f(x): 0.10000000 CDF P(X ≤ x): 0.40000000 Mean: 5.00000000 Variance: 8.33333333

Use Cases

Modeling equally likely outcomes

Use this calculator to analyze scenarios where every value within a range is equally probable, such as random number generation or quality control measurements.

Example: Entering 10, 20, 30, 40, 50 will set min=10, max=50, and compute the uniform distribution statistics.

Teaching and learning statistics

Quickly compute key properties of a uniform distribution for homework or exam preparation, verifying manual calculations.

Example: Check the mean and variance for a uniform distribution with min=0 and max=10.

Frequently Asked Questions

What is a continuous uniform distribution?
A continuous uniform distribution is a probability distribution where all outcomes in a given interval are equally likely. It is defined by a minimum and maximum value, and the probability density function (PDF) is constant between these bounds.
How do I use the calculator with my data?
Enter your data values separated by commas or spaces. The calculator will determine the minimum and maximum values from your data, then compute the PDF, CDF, mean, and variance for the uniform distribution defined by those bounds.
What do the outputs mean?
PDF gives the height of the probability density function at a given point, CDF gives the cumulative probability up to that point, mean is the average of the distribution (midpoint of min and max), and variance measures the spread of the distribution.

Tips & Common Mistakes

Tips

  • Ensure your data values are numeric and separated by commas or spaces for accurate calculation.
  • The calculator uses the minimum and maximum of your entered values as the bounds; make sure they represent the intended range.
  • For a uniform distribution, the mean is simply (min + max) / 2, and the variance is ((max - min)^2) / 12.
  • Use the CDF to find the probability that a random variable falls below a certain value within the range.

Common Mistakes to Avoid

  • Entering non-numeric characters or mixing separators incorrectly, which may cause errors.
  • Assuming the calculator uses the entered values as individual data points rather than just the min and max.
  • Forgetting that the uniform distribution assumes equal likelihood, so the PDF is constant only between the min and max.

Last updated: August 13, 2026