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Normal Distribution Calculator

Compute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation.

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Jordan Normal Form Calculator (J, P and block structure)Exact Jordan form of a 1×1 to 6×6 matrix: the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing.Beta Distribution CalculatorCompute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.Exponential Distribution CalculatorCompute exponential-distribution probabilities for waiting times from the rate λ, including P(X≤x), P(X>x) and a range.Gaussian Distribution GeneratorNormally-distributed numbers via Box–Muller, with an optional seed and the sample mean and SD.Geometric Distribution CalculatorCompute the probability of the first success on trial k (or after k failures) from the per-trial success probability p.Hypergeometric Distribution CalculatorCompute hypergeometric probabilities of drawing k successes in n draws without replacement from a population of N with K successes.Negative Binomial Distribution CalculatorProbability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.Weibull Distribution CalculatorCompute Weibull reliability probabilities F(x) and R(x) for failure analysis from the shape β and scale η.

Normal Distribution Calculator works straight from this page — free, instant, nothing to install. It sits under Statistics & probability in our catalogue, alongside Jordan Normal Form Calculator (J, P and block structure) and Beta Distribution Calculator.

How to use it

  1. Open the tool — no signup or install needed.
  2. Enter your input or adjust the available options.
  3. Get your result instantly, then copy or download it.

Frequently asked questions

What does Normal Distribution Calculator do?

Compute normal probabilities P(X≤x), P(X>x), P(a≤X≤b) or find x for a percentile, from the mean and standard deviation.

When would I actually use this?

Summarising a dataset before drawing conclusions from it, checking whether a difference between two groups is real, and putting an interval around an estimate.

What is the most common mistake?

Reading a p-value as the probability that the hypothesis is wrong. It is the probability of seeing data at least this extreme if the null were true — a different statement, and a much weaker one.

How is Normal Distribution Calculator different from Jordan Normal Form Calculator (J, P and block structure)?

They sit next to each other but answer different questions: Jordan Normal Form Calculator (J, P and block structure) is the one to open when you need it to exact Jordan form of a 1×1 to 6×6 matrix: the blocks from the ranks of (A−λI)ᵏ, the transition matrix P built from generalized eigenvector chains, and A·P = P·J checked exactly. When the characteristic polynomial does not split over ℚ it says so instead of guessing. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Beta Distribution Calculator is the closest one after this: Compute beta-distribution probabilities on [0,1] from shape parameters α and β via the regularized incomplete beta function.

What else is worth having open alongside it?

Exponential Distribution Calculator and Gaussian Distribution Generator — they come up in the same task often enough to be worth a second tab.

Where do the figures come from?

Distributions and test statistics are computed from their standard definitions, not from a lookup table, so results carry more digits than a printed table would. The assumptions each test makes are stated with it.

Further reading

All guides →
ExplainerA 1 % Drop Rate Does Not Mean One Hundred RunsAt 1 %, a hundred attempts give you 63.4 % — not certainty. Ninety per cent takes 230 attempts and ninety-nine takes 459, and more than a third of players are still empty-handed at a hundred.ExplainerWhat Is a Z-Score? Standard Deviations Above the MeanA z-score is z = (x − μ) / σ — how many standard deviations a value sits from the mean. Learn how to compute it, read the standard normal curve, and turn it into a percentile.ExplainerMean, Median and Mode: What's the Difference?Mean, median and mode all describe the 'middle' of your data — but answer different questions. Here's what each means, with examples and when to use which.ExplainerGeometric vs Arithmetic Mean: Which to UseThe arithmetic mean adds and divides; the geometric mean multiplies and takes a root. Learn which fits growth rates, ratios, and averages.How-toHow to Calculate Standard Deviation (Step by Step)Standard deviation measures how spread out your data is. Here's the formula, a worked example, and the difference between population and sample.ExplainerProbability Basics, With ExamplesProbability measures how likely something is, from 0 to 1. Here's the basic idea, how to combine events with AND and OR, and the complement.