Free Sample Size Calculator for Surveys (Academic-Grade)

Calculate your required sample size using the same formula researchers use in peer-reviewed studies. No signup required.

→ Use the Sample Size Calculator

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What This Calculator Does

Our sample size calculator uses Cochran's formula, the standard approach for determining how many responses you need to estimate a proportion with a given margin of error.

You input:

• Confidence level (90%, 95%, or 99%)
• Margin of error (how precise you need to be)
• Expected proportion (your best guess at the result, or 50% for maximum sample size)
• Population size (optional, for finite population correction)

The calculator returns the minimum sample size required to achieve your target precision.

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When This Calculator Applies

This formula works when you're:

1. Estimating a proportion (e.g., "What percentage of users prefer option A?")
2. Using simple random sampling (every member of the population has equal chance of selection)
3. Planning a single survey (not longitudinal or multi-wave)

For comparing groups, detecting small effects, or complex sampling designs, you'll need more specialized power analysis tools.

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When Calculators Don't Tell the Whole Story

Here's the uncomfortable truth: sample size calculators assume your design is already sound.

A calculator will happily tell you that 385 responses gives you ±5% margin of error at 95% confidence. What it won't tell you:

• If your questions are poorly worded, 10,000 responses won't save you
• If your sampling is biased, precision doesn't equal accuracy
• If non-responders differ systematically from responders, your confidence interval is lying

We wrote a full guide on why more responses doesn't mean better data. The short version: sample size reduces random error. It does not fix bias, bad constructs, or poor design.

I've seen teams celebrate hitting their sample size target while completely ignoring a 15% response rate that made the data worthless. The calculator said they were done. The data said otherwise.

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The Formula

For those who want to see the math:

Cochran's Formula (infinite population):

n₀ = (Z² × p × q) / e²

Where:

• Z = Z-score for your confidence level (1.96 for 95%)
• p = expected proportion (0.5 for maximum variability)
• q = 1 - p
• e = margin of error as a decimal (0.05 for ±5%)

Finite Population Correction:

n = n₀ / (1 + ((n₀ - 1) / N))

The calculator handles all of this automatically. The formula section in the tool shows your specific values.

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Why We Built This

Most sample size calculators online are either:

• Buried in vendor marketing pages
• Missing finite population correction
• Offering no explanation of assumptions

We wanted a tool that researchers could trust and cite. One that shows its work and acknowledges its limitations.

If your sample size assumptions matter, your tooling should too.

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Related Resources

• Sample Size Guide: Deep dive on sample size methodology
• Survey Validity & Reliability: What sample size can and can't fix
• Margin of Error Calculator: Calculate precision from existing data
• All Free Tools: 4 calculators for survey research

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About the Author
The Lensym Team builds survey research tools for people who care about methodology. We believe that good research tools should show their work and acknowledge their limitations.

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→ Calculate Your Sample Size Now