Central Limit Theorem Calculator

Calculate the sampling distribution of the mean using the Central Limit Theorem

Population Mean (μ):

Population Standard Deviation (σ):

Sample Size (n):

Sample Mean (x̄) - Optional:

About the Central Limit Theorem

The Central Limit Theorem states that the sampling distribution of the sample mean approaches a normal distribution as sample size increases, regardless of the population distribution.

Key Formulas:

Standard Error: SE = σ / √n
Z-Score: z = (x̄ - μ) / SE
Rule of thumb: n ≥ 30 for CLT to apply

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

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Formula Source: Standard Mathematical References

by Various

ðŸ”„Last reviewed: May 2026

âœ“Formula checks are based on standard references and internal QA review.