Sample size is the number of respondents or observations needed to estimate a population parameter within a specified margin of error at a given confidence level.

What confidence level should I use?

95% is the most common standard. It means if you repeated the survey 100 times, 95 results would fall within your margin of error. Use 99% for medical or high-stakes studies.

What margin of error is acceptable?

A ±5% margin of error is typical for general surveys. For precise academic or clinical research, ±2% or ±1% is preferred. Smaller margin requires larger sample.

What is finite population correction?

When your population is small (e.g. 500 employees), the adjusted formula reduces the required sample: n_adj = n / (1 + (n−1)/N).

How does power analysis relate to sample size?

Power (1−β) is the probability of detecting a real effect. At 80% power and α=0.05, you need enough observations so you are unlikely to miss a true difference.

Sample Size Calculator

Calculate the required sample size for surveys, experiments, and A/B tests. Supports proportion and mean-based methods, finite population correction, and power analysis.

Confidence Level

Margin of Error (%) ?

Population Proportion (%) ?

Population Size (0 = infinite) ?

Required Sample Size

—

Adjusted Sample Size (finite population) —

Critical Z-Value —

Extended More scenarios, charts & detailed breakdown ▾

Confidence Level

Margin of Error (%)

Expected Proportion (%)

Population Size (0 = infinite)

Required Sample Size

—

FPC-Adjusted Sample Size —

Critical Z —

Professional Full parameters & maximum detail ▾

Confidence Level

Margin of Error (%)

Population Proportion (%)

Population Size (0 = infinite)

Expected Response Rate (%)

Design Effect (DEFF, 1 = simple random)

Statistical Power (%)

Alpha (significance level)

Sample Size Results

Basic Sample Size —

FPC-Adjusted Sample Size —

After Design Effect —

Response-Rate Adjusted (invites to send) —

Critical Values

Critical Z (α/2) —

Z for Power (β) —

Power Analysis

Sample Size for Power Analysis —

Actual MoE at given n —

Type II Error Rate (β) —

How to Use This Calculator

Select your confidence level (90%, 95%, or 99%).
Enter your desired margin of error (e.g. 5%).
Keep population proportion at 50% for the most conservative estimate, or enter a known proportion.
Optionally enter population size to apply the finite population correction.

Formula

n = Z² × p(1−p) / E² • Finite correction: n_adj = n / (1 + (n−1)/N) • Mean-based: n = (Z×σ/E)²

Example

95% CI, ±5% margin, p=50%: n = (1.96² × 0.25) / 0.05² = 384 respondents needed.

Frequently Asked Questions

Sample size is the number of respondents or observations needed to estimate a population parameter within a specified margin of error at a given confidence level.
95% is the most common standard. It means if you repeated the survey 100 times, 95 results would fall within your margin of error. Use 99% for medical or high-stakes studies.
A ±5% margin of error is typical for general surveys. For precise academic or clinical research, ±2% or ±1% is preferred. Smaller margin requires larger sample.
When your population is small (e.g. 500 employees), the adjusted formula reduces the required sample: n_adj = n / (1 + (n−1)/N).
Power (1−β) is the probability of detecting a real effect. At 80% power and α=0.05, you need enough observations so you are unlikely to miss a true difference.

Sample Size Calculator

Sample Size Results

Critical Values

Power Analysis

How to Use This Calculator

Formula

Example

Frequently Asked Questions

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