About Uniform Distribution Calculator
This uniform distribution calculator treats every value between a minimum a and a maximum b as equally likely. It opens on a range of 0 to 10 and finds the chance of landing between 2 and 5. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
Because the density is flat, a probability is just the length of the interval divided by the length of the whole range. Between 2 and 5 on a 0 to 10 range is 3 ÷ 10 = 0.3.
It models a random wait with a known maximum, such as a bus that comes every 10 minutes at an unknown phase, or the output of a random number generator.
How to use Uniform Distribution Calculator
- Choose the distribution from the list. Each has its own parameters, such as the mean and standard deviation for the normal.
- Enter the parameters. The hint under each field says what is allowed.
- Choose what to calculate: a lower tail, an upper tail, an interval, a density or point probability, or the inverse.
- Enter x, or a and b for an interval, or the probability for the inverse. The result updates as you type.
- Read the answer, the mean and variance, and the shaded chart. Open the working to see which CDF values were used.
- Copy the result with the copy button.
Features
- Nine distributions: normal, binomial, Poisson, geometric, exponential, uniform, Student t, chi-square and F.
- Lower and upper tails, strict and non-strict, and intervals P(a ≤ X ≤ b).
- Density for continuous and point probability for discrete distributions.
- Inverse (quantile) calculation, including critical values for t, chi-square and F.
- Mean, variance and standard deviation, shown as undefined where they do not exist.
- Bell curve with shaded tail or interval for continuous distributions, and a bar chart for discrete ones.
- Upper tails computed directly, so very small p-values keep their precision.
- Formula of the distribution in KaTeX and a short worked step for every answer.
Uniform distribution
The density is the same everywhere on the range and zero outside it.
f(x) = 1 / (b − a), a ≤ x ≤ b
F(x) = (x − a) / (b − a)
mean = (a + b) / 2
variance = (b − a)² / 12Worked examples
a = 0, b = 10: P(2 ≤ X ≤ 5) gives 0.3
(5 - 2) ÷ (10 - 0) = 0.3.
a = 0, b = 10: the 90th percentile gives 9
a + 0.9 × (b - a) = 9.
Privacy: how it works
- Everything is calculated by code running in your browser tab. Nothing you enter is sent to Ulkaa or to any other server, and there is nothing to sign in to.
Tips
- For a discrete distribution, P(X < 3) and P(X ≤ 3) are different. For a continuous one they are the same.
- For a two-sided critical value, such as the 95% value of t, put the inverse probability at 0.975.
- A density can be above 1 when the spread is small. It is not a probability.
- If your question is "at least k", use P(X ≥ x), not P(X > x).
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your numbers are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
What is the probability of one exact value?
It is zero for a continuous uniform. Only intervals have positive probability. The density f(x) is the same constant everywhere in the range.
Where is the mean of a uniform distribution?
Exactly halfway between a and b, and it equals the median.
Is the discrete uniform the same?
No. A fair die is a discrete uniform on 1 to 6. This calculator is for the continuous version.
More Probability Distribution Calculator pages
- Probability Distribution CalculatorPick a distribution, set its parameters and get PDF, CDF, interval probabilities, quantiles, mean and variance with a chart.
- Normal Distribution CalculatorEnter a mean and standard deviation to get tail probabilities, intervals and percentiles on a bell curve.
- Binomial Distribution CalculatorEnter the number of trials and the chance of success to get P(X = k), P(X ≤ k), P(X ≥ k) and ranges.
- Poisson Distribution CalculatorEnter the average rate λ to get the chance of exactly k events, at most k, at least k or a range.
- Geometric Distribution CalculatorEnter the success probability to get the chance that the first success happens on or by trial k.
- Exponential Distribution CalculatorEnter the rate λ to get the chance a waiting time exceeds, or stays below, a value, and its percentiles.
- Student t Distribution CalculatorEnter the degrees of freedom to get t critical values, tail areas and p-values on a shaded t curve.
- Chi-Square Distribution CalculatorEnter the degrees of freedom to get chi-square p-values, critical values and tail areas.
- F Distribution CalculatorEnter both degrees of freedom to get F p-values, critical values and tail areas.