Sample Size Calculator

Sample Size is evaluated from Confidence Level, Margin of Error and Expected Proportion. The calculation reports Required Sample Size and Adjusted n.

Results

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About the Sample Size Calculator

Sample Size is treated here as a quantitative relation between Confidence Level, Margin of Error, Expected Proportion and Population Size and Required Sample Size and Adjusted n.

The calculator uses a multi formula configuration. Each reported value is read as a direct evaluation of the stored rules with the declared field formats and units.

Formula basis:
n = (Z^2 x p x (1-p)) / E^2
Use p=0.5 when proportion is unknown (worst case).

Interpret the outputs in the order shown by the result fields. Optional inputs affect only the outputs that depend on those variables.

Formula & How It Works

The calculation applies the following relations exactly as recorded in the metadata:

n = (Z^2 x p x (1-p)) / E^2
Use p=0.5 when proportion is unknown (worst case).

Each output field is produced by substituting the supplied inputs into the relevant relation and then applying the declared rounding or text format.

Worked Examples

Example 1: Political poll: 95% confidence, ±3% margin of error, unknown proportion

Inputs

confidence: 95 margin_error: 3 proportion: 50
Required Sample Size: 1,068. Adjusted n: 10

With Confidence Level = 95, Margin of Error = 3 and Expected Proportion = 50 as the stated inputs, the result is Required Sample Size = 1,068 and Adjusted n = 10. Each value corresponds to the declared output fields.

Example 2: Medical study: 99% confidence, ±5% margin, expected 30% prevalence

Inputs

confidence: 99 margin_error: 5 proportion: 30
Required Sample Size: 558. Adjusted n: 10

With Confidence Level = 99, Margin of Error = 5 and Expected Proportion = 30 as the stated inputs, the result is Required Sample Size = 558 and Adjusted n = 10. Each value corresponds to the declared output fields.

Example 3: Customer satisfaction: 95% confidence, ±5% margin, large company

Inputs

confidence: 95 margin_error: 5 proportion: 50
Required Sample Size: 385. Adjusted n: 10

With Confidence Level = 95, Margin of Error = 5 and Expected Proportion = 50 as the stated inputs, the result is Required Sample Size = 385 and Adjusted n = 10. Each value corresponds to the declared output fields.

Example 4: Small town survey: 95% confidence, ±5% margin, town population = 2,500

Inputs

confidence: 95 margin_error: 5 proportion: 50 population: 2500
Required Sample Size: 385. Adjusted n: 334

With Confidence Level = 95, Margin of Error = 5, Expected Proportion = 50 and Population Size = 2,500 as the stated inputs, the result is Required Sample Size = 385 and Adjusted n = 334. Each value corresponds to the declared output fields.

Common Use Cases

  • Calculate minimum sample size for a survey
  • Determine sample size for clinical trials
  • Plan sample size for market research