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Statistics · Sampling & confidence

Sample Size for a Mean Calculator

Plan a simple-random-sample size for estimating a mean to a chosen margin of error.

Statistics · Sampling & confidence

Enter your statistical inputs

Private in-browser calculation · explicit assumptions
Planning balances the effect worth detecting, sample size, false-positive rate, and target power.
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
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Enter plain numbers without measurement units. Datasets accept commas, spaces, semicolons, or line breaks and are limited to 10,000 values. Results stay in this browser.

Statistics result

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Understand sampling uncertainty

How sample-size and power planning fit together

Sample Size for a Mean. Planning starts with an effect worth detecting, a significance level, a target power, and assumptions about variation or baseline rates.

Method used

n=ceil[(z*σ/E)²], with optional finite-population correction.

The result targets interval precision around a mean; it is not a power calculation for detecting a difference.

What the result cannot establish

Power is a long-run probability under the assumed effect and model. It is not a guarantee of significance, data quality, or practical importance.

Assumption: The planning standard deviation must be defensible, observations independent, and nonresponse or design effects added separately.

Quick guide

How to use this calculator

  1. Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
  2. Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
  3. Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.

Calculation method

How the sample size for a mean calculator works

n=ceil[(z*σ/E)²], with optional finite-population correction.

The result targets interval precision around a mean; it is not a power calculation for detecting a difference.

Worked example

Sample Size for a Mean example

At 95% confidence, σ=12 and margin 3 require 62 observations before any population correction.

n=ceil[(z*σ/E)²], with optional finite-population correction.

Supported inputs

Precision and limits

Model and design

The planning standard deviation must be defensible, observations independent, and nonresponse or design effects added separately.

Numerical scope

Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.

Interpretation

The result targets interval precision around a mean; it is not a power calculation for detecting a difference.

Decision boundary

The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.

Privacy

Entered values and calculated results stay in this browser and are not sent to an analytics service.

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