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Binomial Theorem Expansion Calculator

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.

Related tools

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Binomial Probability CalculatorGet P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution.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.Bayes Theorem CalculatorCompute 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.Central Limit Theorem CalculatorProbabilities for a sample mean from the population mean, standard deviation and sample size, with the standard error and the z-scores shown.Rational Root Theorem CalculatorEvery ±p/q candidate, deduplicated and sorted, then actually tested — with the real roots, their multiplicity and the depressed polynomial left after dividing them out.Pythagorean theorem calculatorFind any side of a right triangle — hypotenuse or leg — from the two you know, with the three squares drawn.ANOVA Calculator (One-Way)Full one-way ANOVA table — SS, df, MS, F and p — plus η², ω² and Cohen's f, because a significant F on its own tells you nothing about how large the difference is. The equal-variance assumption is stated, not buried.Average Deviation Calculator (mean absolute deviation)The average absolute deviation from the mean AND from the median — the median is the point that minimises it, which is worth seeing. Every |x − centre| is listed, and the standard deviation sits beside it for contrast: squaring makes SD react hard to a single outlier while the average deviation barely moves. The outlier preset is built to show exactly that.

Binomial Theorem Expansion Calculator is free to use as often as you like, directly from this page. You will find it under Statistics & probability, with Binomial Probability Calculator and Negative Binomial Distribution Calculator for the neighbouring cases.

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 Binomial Theorem Expansion Calculator do?

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.

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 Binomial Theorem Expansion Calculator different from Binomial Probability Calculator?

They sit next to each other but answer different questions: Binomial Probability Calculator is the one to open when you need it to get P(X=k) and every cumulative form at once for up to 1000 trials, with the mean, variance, mode and a chart of the whole distribution. Pick whichever matches what you're starting from — both are free.

Is there a tool for the next step?

Negative Binomial Distribution Calculator is the closest one after this: Probability of reaching the r-th success, counted either in failures before it or in total trials, with both parameterisations kept distinct.

What else is worth having open alongside it?

Bayes Theorem Calculator and Central Limit 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.
Binomial Theorem Expansion Calculator — OneKitly