What sample size do I need for my survey?

The required sample size depends on your confidence level, margin of error, and population size. For a standard market research survey with 95% confidence and plus or minus 5% margin of error, you typically need 384 participants from a large population. For a narrower plus or minus 3% margin, you need approximately 1,067 participants. Use 50% for expected proportion if unknown, as this provides the most conservative estimate. Smaller populations require fewer participants due to finite population correction. For example, surveying a company of 500 employees would require only 217 responses for plus or minus 5% margin at 95% confidence.

How does confidence level affect sample size?

Confidence level directly impacts required sample size. Higher confidence requires larger samples. Common levels: 90% confidence (Z equals 1.645) requires about 271 participants for plus or minus 5% margin; 95% confidence (Z equals 1.96) requires about 384 participants; 99% confidence (Z equals 2.576) requires about 663 participants. The relationship is quadratic - increasing confidence from 95% to 99% (21% increase) requires 72% more participants. Most research uses 95% as it balances confidence with practical sample size requirements. Clinical trials often use 99% for critical safety endpoints.

What is margin of error and how does it work?

Margin of error quantifies the precision of your estimate. A plus or minus 5% margin means if 60% of your sample says yes, the true population value is likely between 55% and 65% at your chosen confidence level. Smaller margins require exponentially larger samples: plus or minus 10% needs about 96 participants, plus or minus 5% needs about 384, plus or minus 3% needs about 1,067, plus or minus 1% needs about 9,604 (all at 95% confidence). There are diminishing returns - reducing margin from 5% to 3% requires 3 times more participants but only improves precision by 2 percentage points. Consider whether that precision gain justifies the additional cost and time.

How do I calculate sample size for A/B testing?

A/B testing sample size requires: (1) baseline conversion rate, (2) minimum detectable effect (e.g., improving from 5% to 6% equals 20% relative increase), (3) significance level (typically 95%), and (4) statistical power (typically 80%). Power is the probability of detecting a true effect. For a baseline 10% conversion rate, detecting a 20% relative improvement (10% to 12%) at 95% confidence with 80% power requires approximately 3,850 participants per variant (7,700 total). Smaller effect sizes require much larger samples - detecting a 10% relative improvement would need about 15,300 per variant. Run tests long enough to capture weekly patterns (minimum 1 to 2 weeks).

What is statistical power and why does it matter?

Statistical power is the probability of detecting a true effect when it exists (avoiding a false negative or Type II error). Standard power is 80%, meaning an 80% chance of detecting a real effect. Higher power (90%, 95%) reduces the risk of missing real effects but requires larger samples. Power depends on: (1) sample size (larger equals higher power), (2) effect size (larger effects easier to detect), (3) significance level (alpha equals 0.05 standard), and (4) variability in data. Low power (less than 60%) risks concluding no effect when one exists. For exploratory research, 70 to 80% power may suffice; for confirmatory studies or safety-critical decisions, aim for 90%+ power.

Should I use finite population correction?

Use finite population correction when your sample will be a significant fraction (more than 5%) of the total population. The correction formula: n adjusted equals n divided by (1 + (n - 1) / N), where n is uncorrected sample size and N is population size. For example, surveying 500 employees: uncorrected formula suggests 384 participants for plus or minus 5% margin at 95% confidence, but finite correction reduces this to 217 (44% reduction). The correction becomes negligible for large populations - for populations over 100,000, it reduces sample size by less than 1%. Always apply the correction for small, defined populations (companies, schools, associations) but not for general public surveys where the population is millions.

Sample Size Calculator - Statistical Power & Research Sample Calculator | AICalculator

Quick Templates

Calculation Parameters

Calculation Type *

For surveys with yes/no or categorical responses

Confidence Level *

95.0%

Higher confidence requires larger sample sizes

Margin of Error (%) *

±5.0%

Smaller margin requires larger sample sizes

Expected Proportion (%)

Use 50% if unknown (most conservative estimate)

Population Size (Optional)

Leave large (1M+) if population is unknown

Apply finite population correction

Results

Select your study parameters and click "Calculate Sample Size" to see results

Try one of the quick templates above to get started

Understanding Sample Size: Why It Matters for Your Research

Determining the correct sample size is one of the most crucial steps in designing any research study, survey, or experiment. A well-calculated sample size ensures that your results are statistically significant, reliable, and generalizable to the larger population you are studying. Too small a sample risks missing important effects and wasting resources on inconclusive research, while too large a sample unnecessarily increases costs without meaningful improvements in precision. This comprehensive guide will walk you through the key concepts, formulas, and practical considerations for calculating sample size effectively.

What is Sample Size and Why is it Important?

The sample size is the number of individuals or observations included in a study. It is a subset of the population that is chosen to represent the entire group. The importance of an appropriate sample size cannot be overstated, as it directly impacts three critical factors:

Statistical Power: The probability of detecting a true effect when it exists. Larger samples increase power, reducing the risk of false negatives (Type II errors). With adequate power, you are less likely to conclude no effect when a real effect exists.
Precision: The width of your confidence intervals and margin of error. Larger samples provide more precise estimates, allowing you to make more confident conclusions about population parameters.
Cost-Effectiveness: An optimal sample size balances the need for statistical rigor with practical constraints like budget, time, and resources. Too large a sample wastes resources, while too small a sample yields inconclusive results.

Key Concepts in Sample Size Determination

Confidence Level (Reliability)

The confidence level indicates how confident you can be that your sample results accurately reflect the true population. It is expressed as a percentage (e.g., 90%, 95%, 99%). A 95% confidence level means that if you were to repeat the study 100 times, 95 of those times, your results would fall within the specified margin of error.

Common confidence levels and their corresponding Z-scores:

90% confidence: Z = 1.645
95% confidence: Z = 1.96 (most commonly used)
99% confidence: Z = 2.576 (used for critical decisions, safety studies)

Margin of Error (Precision)

The margin of error defines how much difference is acceptable between the sample result and the actual population value. For example, a plus or minus 3% margin of error means your estimate is likely within 3 percentage points of the true population value.

The relationship between sample size and margin of error is inverse and non-linear. Halving the margin of error requires quadrupling the sample size, creating strong diminishing returns.

Sample Size Formulas

For Proportion Estimation

This is used for categorical data, such as survey questions with Yes/No answers:

n = (Z² × p × (1-p)) / E²

where n = sample size, Z = Z-score, p = expected proportion, E = margin of error

For example, with 95% confidence, 5% margin of error, and 50% expected proportion: n = (1.96² × 0.5 × 0.5) / 0.05² = 384 participants

Finite Population Correction

When your sample size is a significant proportion (typically more than 5%) of the total population, you can apply a finite population correction to reduce the required sample size.

n_adjusted = n / (1 + (n-1)/N)

where n = uncorrected sample size, N = population size

Additional Resources

For more information on sample size and research methodology, visit:

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Quick Templates

Calculation Parameters

Results

Understanding Sample Size: Why It Matters for Your Research

What is Sample Size and Why is it Important?

Key Concepts in Sample Size Determination

Confidence Level (Reliability)

Margin of Error (Precision)

Sample Size Formulas

For Proportion Estimation

Finite Population Correction

Additional Resources

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Sample Size Calculator - Calculate Survey, Research, and A/B Test Sample Sizes with Statistical Power Analysis

Quick Templates

Calculation Parameters

Results

Understanding Sample Size: Why It Matters for Your Research

What is Sample Size and Why is it Important?

Key Concepts in Sample Size Determination

Confidence Level (Reliability)

Margin of Error (Precision)

Sample Size Formulas

For Proportion Estimation

Finite Population Correction

Additional Resources

Related Calculators

Statistics Calculator

Confidence Interval Calculator

Z-Score Calculator

P-value Calculator

T-Test Calculator

Chi-Square Calculator

ANOVA Calculator

Standard Deviation Calculator