Why is 50% the default proportion?

Using p=50% (0.5) maximizes p×(1−p), which gives the largest and most conservative sample size estimate. If you have prior data on the proportion, use that for a more precise estimate.

What confidence level should I use?

95% is the most common standard in research and business. 99% is used when errors are costly (medical, financial). 90% is acceptable for preliminary or low-stakes research.

What is finite population correction?

When your sample is a significant fraction of a small population, you can reduce the required sample size using the finite population correction factor. Enter the total population size to apply it.

What margin of error is acceptable?

±5% is the standard for most surveys. ±3% is used when precision is critical (political polls, medical studies). ±10% is acceptable for exploratory research.

Does sample size affect accuracy?

Yes. Larger samples reduce the margin of error and increase confidence in your results. However, returns diminish rapidly — doubling precision requires quadrupling the sample size.

Math

↵ to calculate

Sample Size Calculator - Statistical Margin Error Online

Calculate the required sample size for surveys and studies based on confidence level, margin of error, and population size.

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How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

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In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The sample size calculator determines how many participants you need in a study or survey to achieve statistically valid results at your chosen confidence level and margin of error. It supports finite population correction for known population sizes.

Confidence Level

Margin of Error (%)

Population Proportion (%)

Population Size (optional)

What is Sample Size Calculator - Statistical Margin Error Online?

How to use it

1️⃣ Select your desired confidence level (90%, 95%, or 99%).
2️⃣ Enter the margin of error as a percentage (e.g., 5 for ±5%).
3️⃣ Enter the population proportion if known (default 50% gives the most conservative estimate).
4️⃣ Optionally enter the total population size for finite population correction.
5️⃣ Click Calculate to see the required sample size.

Formula

n = Z² × p × (1−p) / e². Finite population correction: n_adj = n / (1 + (n−1)/N). Z-values: 90%→1.645, 95%→1.96, 99%→2.576.

💡 See it in action — a real example

95% confidence, ±5% margin, 50% proportion: n = 1.96² × 0.5 × 0.5 / 0.05² = 384.16 ≈ 385. With population N=1000: n_adj = 385 / (1 + 384/1000) ≈ 278.

❓ Common questions

Why is 50% the default proportion?: Using p=50% (0.5) maximizes p×(1−p), which gives the largest and most conservative sample size estimate. If you have prior data on the proportion, use that for a more precise estimate.
What confidence level should I use?: 95% is the most common standard in research and business. 99% is used when errors are costly (medical, financial). 90% is acceptable for preliminary or low-stakes research.
What is finite population correction?: When your sample is a significant fraction of a small population, you can reduce the required sample size using the finite population correction factor. Enter the total population size to apply it.
What margin of error is acceptable?: ±5% is the standard for most surveys. ±3% is used when precision is critical (political polls, medical studies). ±10% is acceptable for exploratory research.
Does sample size affect accuracy?: Yes. Larger samples reduce the margin of error and increase confidence in your results. However, returns diminish rapidly — doubling precision requires quadrupling the sample size.

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Confidence Interval Calculator P-Value Calculator Statistics Calculator