tooloctopus.

Central limit theorem calculator

Find the mean and standard error of a sampling distribution: SE = population SD/√n.

On your device · No account
Privacy details

Central limit theorem calculator processes your input in this browser. Inputs and results are excluded from analytics. Recent tools save tool names, visit counts and last-visit times. Saved tools store only their names. Draft saving is optional and stays on this device; delete saved text with the draft controls. Loading text from a URL is optional and contacts that server; its URL and your IP address are visible to the server. An optional “Use in” action keeps a handoff in this tab. The next tool removes it on arrival and ignores it if more than a minute has passed.

Copy link includes the inputs you choose to share in the address. Anyone with that link can reopen them. Files and generated results are excluded. Password and key tools share settings only.

More inputs and assumptions

Answer

…

Find the mean and standard error of a sampling distribution: SE = population SD/√n.

More results
Precision and calculation record
Rounding changes displayed numbers, not the calculation. Text, fractions, matrices and CSV schedules keep their own formatting. Automatic keeps up to 12 significant digits, with money shown to cents where applicable.
Step-by-step calculation
Inputs are substituted below. Each line evaluates the next operation; intermediate values are displayed to 12 significant digits while the calculation uses full precision.
    Saved scenario
    Save the current answer, then change an input to compare. This clears when you leave.
    Formula and assumptions
    Requires independent, identically distributed observations with finite variance. These moments do not prove normality; the quality of a normal approximation depends on the population distribution and sample size.
    Automatic precision shows numbers to 12 significant digits. Thousands separators such as 1,000 are accepted; use a dot for decimals.
    Scratch calculator
    Use +, −, ×, ÷, parentheses and %. A percentage is divided by 100. This does not change the main tool.
    Reset reloads the tool with its starting values and releases open files and device controls. Saved drafts stay on this device until you delete them.
    Links include your inputs and settings. Anyone with the link can see them, so leave out private text. Files and generated results are left out; random draws run again.
    Keyboard shortcuts
    Updated 
    Using Central limit theorem calculator
    Find the mean and standard error of a sampling distribution: SE = population SD/√n.
    Requires independent, identically distributed observations with finite variance. These moments do not prove normality; the quality of a normal approximation depends on the population distribution and sample size.
    Next: Normal distribution calculator
    A worked example
    Example inputs: population standard deviation = 10, independent sample size = 25, population mean = 100. Standard error of sample mean = 2.
    Before you use the result
    Requires independent, identically distributed observations with finite variance. These moments do not prove normality; the quality of a normal approximation depends on the population distribution and sample size.
    Example results for population standard deviation
    These examples use Independent sample size: 25; Population mean: 100. They are reference calculations, not recommended settings.
    Population standard deviationStandard error of sample mean
    51
    102
    204
    Cite this page
    ToolOctopus. “Central limit theorem calculator.” Updated 2026-09-26. https://tooloctopus.com/central-limit-theorem-calculator.
    Add an access date if your instructions require one.
    Citation formatting uses citeproc-js by Frank Bennett and Citation Style Language styles. Licence and source code.
    Find a tool
    Search by task. Use ↓ and ↑ to choose, Enter to open.