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Central Limit Theorem Calculator

Probabilities for a sample mean from the population mean, standard deviation and sample size, with the standard error and the z-scores shown.

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Central Limit Theorem Calculator works straight from this page — free, instant, nothing to install. It sits under Statistics & probability in our catalogue, alongside Bayes Theorem Calculator and Binomial Theorem Expansion 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 Central Limit Theorem Calculator do?

Probabilities for a sample mean from the population mean, standard deviation and sample size, with the standard error and the z-scores shown.

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 Central Limit Theorem Calculator different from Bayes Theorem Calculator?

They sit next to each other but answer different questions: Bayes Theorem Calculator is the one to open when you need it to compute the posterior probability P(A|B) with the probability tree, the natural-frequency restatement and the base-rate lesson that makes a 99 % accurate test right only 16.7 % of the time. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Binomial Theorem Expansion Calculator is the closest one after this: Expand (a + b)ⁿ up to n = 50 with exact coefficients, the Pascal triangle row, the general term and any single term you ask for — negative b handled sign by sign.

What else is worth having open alongside it?

Rational Root Theorem Calculator and Pythagorean theorem calculator — 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 →
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.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.How-toCircle: Circumference and AreaCircumference is 2πr, area is πr². Here's how radius, diameter and π fit together, both formulas worked through, and how not to mix them up.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.