Statistics & Probability Calculators

Enter the number of favourable outcomes and the total to get P(A) as a decimal, a percentage and a simplified fraction, plus the complement and the odds.

Enter a mean, a standard deviation and a value x to get the PDF at x, P(X < x) and P(X > x), with the area under the curve shaded.

Enter a mean, a standard deviation, a sample size and a confidence level to get the interval, its margin of error and which critical value was used.

Paste two aligned lists of paired values to get the Pearson r, R², the sample size and a plain-language description of the strength.

Enter n and p to get the whole distribution: every P(X = k) as a chart and a table, with the mean, variance, standard deviation and most likely value.

Enter the number of favourable outcomes and the total to get P(A) as a decimal, a percentage and a simplified fraction, plus the complement and the odds.

Enter the joint probability of A and B and the probability of the condition B to get P(A | B), with the multiplication check written out.

Enter a prior P(A), a true-positive rate P(B | A) and a false-positive rate P(B | ¬A) to get the posterior P(A | B) and every step of the working.

Paste an outcome list and the matching probability list to get the expected value, the variance and σ, with each x·P(x) product listed.

Enter n and r to get nPr = n! ÷ (n − r)! as an exact integer, with the digit count and a scientific form for long results.

Enter n and r to get nCr = n! ÷ (r!(n − r)!) as an exact integer, with the digit count and the binomial-coefficient reading.

Enter n trials, a success probability p and a target k to get P(X = k), P(X ≤ k) and P(X ≥ k), plus the mean and variance.

Enter n and p to get the whole distribution: every P(X = k) as a chart and a table, with the mean, variance, standard deviation and most likely value.

Enter a mean rate λ and a count k to get P(X = k), P(X ≤ k) and P(X ≥ k), with the distribution charted and the mean-equals-variance check.

Enter a mean, a standard deviation and a value x to get the PDF at x, P(X < x) and P(X > x), with the area under the curve shaded.

Enter an observed value, a mean and a standard deviation to get the z-score plus P(X < x), the percentile and the two-tailed p-value.

Enter a standard deviation and a sample size to get SE = s ÷ √n, with the divisor shown so the square-root relationship is visible.

Enter a mean, a standard deviation, a sample size and a confidence level to get the interval, its margin of error and which critical value was used.

Enter a standard deviation, a sample size and a confidence level to get the margin of error, the standard error and the critical value behind them.

Enter a desired margin of error, a standard deviation and a confidence level to get the required sample size, rounded up, with the exact value shown.

Paste two aligned lists of paired values to get the Pearson r, R², the sample size and a plain-language description of the strength.

Paste two aligned lists of paired values to get the covariance in both the sample (n − 1) and population (n) forms, with the raw cross-product shown.

Paste two aligned lists of paired values to get the best-fit equation, its slope and intercept, the correlation and R², with a scatter plot and the fitted line.

Paste two aligned lists of paired values to get R² and the correlation r, with the percentage of variation the line explains spelled out.

Enter the number of favourable outcomes and the total to get P(A) as a decimal, a percentage and a simplified fraction, plus the complement and the odds.

Enter the joint probability of A and B and the probability of the condition B to get P(A | B), with the multiplication check written out.

Enter a prior P(A), a true-positive rate P(B | A) and a false-positive rate P(B | ¬A) to get the posterior P(A | B) and every step of the working.

Enter n and r to get nPr = n! ÷ (n − r)! as an exact integer, with the digit count and a scientific form for long results.

Enter n and r to get nCr = n! ÷ (r!(n − r)!) as an exact integer, with the digit count and the binomial-coefficient reading.

Paste an outcome list and the matching probability list to get the expected value, the variance and σ, with each x·P(x) product listed.

Enter n trials, a success probability p and a target k to get P(X = k), P(X ≤ k) and P(X ≥ k), plus the mean and variance.

Enter n and p to get the whole distribution: every P(X = k) as a chart and a table, with the mean, variance, standard deviation and most likely value.

Enter a mean rate λ and a count k to get P(X = k), P(X ≤ k) and P(X ≥ k), with the distribution charted and the mean-equals-variance check.

Enter a mean, a standard deviation and a value x to get the PDF at x, P(X < x) and P(X > x), with the area under the curve shaded.

Enter an observed value, a mean and a standard deviation to get the z-score plus P(X < x), the percentile and the two-tailed p-value.

Enter a standard deviation and a sample size to get SE = s ÷ √n, with the divisor shown so the square-root relationship is visible.

Enter a mean, a standard deviation, a sample size and a confidence level to get the interval, its margin of error and which critical value was used.

Enter a standard deviation, a sample size and a confidence level to get the margin of error, the standard error and the critical value behind them.

Enter a desired margin of error, a standard deviation and a confidence level to get the required sample size, rounded up, with the exact value shown.

Paste two aligned lists of paired values to get the Pearson r, R², the sample size and a plain-language description of the strength.

Paste two aligned lists of paired values to get the covariance in both the sample (n − 1) and population (n) forms, with the raw cross-product shown.

Paste two aligned lists of paired values to get the best-fit equation, its slope and intercept, the correlation and R², with a scatter plot and the fitted line.

Paste two aligned lists of paired values to get R² and the correlation r, with the percentage of variation the line explains spelled out.