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Sample Size Calculator

Calculate sample size using explicit client-side inputs.

Sample Size Calculator Inputs

Results computed instantly — your data never leaves your device.

Live Sample Size Calculator Results

Real-Time

Required sample size

385

Rounded up from the proportion and margin assumptions.

100% Client-SidePrivate & Secure

How to Use the Sample Size Calculator

  1. 1

    Enter the confidence z-score.

  2. 2

    Enter the expected population proportion as a percent.

  3. 3

    Enter the desired margin of error as a percent.

  4. 4

    Review the rounded-up sample-size estimate.

Formula & Mathematical Basis

n = z²p(1−p) ÷ e², rounded up.

Variable Key

z

Critical z-score for the chosen confidence level

p

Expected population proportion as a decimal

e

Margin of error as a decimal

📝 The interface accepts p and e as percentages and converts them to decimals before applying the formula; a zero margin returns a guarded zero.

Step-by-Step Examples

1

95% confidence planning estimate

Scenario: Use z = 1.96, p = 50%, and a 5% margin of error.

  1. 1.Convert 50% to p = 0.50 and 5% to e = 0.05.
  2. 2.Square the z-score: 1.96² = 3.8416.
  3. 3.Apply n = 3.8416 × 0.50 × 0.50 ÷ 0.05².
  4. 4.Round up to obtain 385 observations.
The estimated minimum sample size is 385 observations before nonresponse or design adjustments.

Practical Use Cases

  • Plan a basic proportion survey.
  • Explain how confidence and precision affect sample size.
  • Compare sample requirements under different assumptions.

Common Pitfalls

  • Entering 0.05 when the field already expects 5%.
  • Using a z-score that does not match the confidence level.
  • Treating the estimate as a substitute for a complex survey design.

Frequently Asked Questions

Why is the result rounded up?

A sample cannot contain a fraction of an observation, so the estimate is rounded upward.

Does this include finite-population correction?

No. The route uses the simple proportion estimate shown in its formula.

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