Sample Size Calculator

Sample Size For

Proportion

Survey/Poll

Mean

Continuous Data

Comparison

Two Groups

Confidence Level90%95%99%

Margin of Error (as decimal)

Expected Proportion (use 0.5 if unknown)

Population Size (optional)

For finite population correction

Calculate Sample SizeClear

Quick Reference: Common Sample Sizes

For Proportions (95% CI, p = 0.5)

±10%

97

±5%

385

±3%

1,068

±1%

9,604

Effect Size Guidelines (Cohen's d)

Small

d = 0.2

Medium

d = 0.5

Large

d = 0.8

How to Use the Sample Size Calculator

This calculator determines the minimum sample size needed for your research or survey. Choose from three calculation types based on your study design.

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Sample Size for Proportions

Use this when estimating a percentage or proportion (e.g., survey responses, conversion rates).

Formula

n = (z² × p × (1-p)) / e²

Where:

• z = z-score for confidence level (1.96 for 95%)
• p = expected proportion (use 0.5 if unknown)
• e = margin of error (as decimal)

Quick Reference Table

Margin of Error	90% CI	95% CI	99% CI
±10%	68	97	166
±5%	271	385	664
±3%	752	1,068	1,844
±2%	1,692	2,401	4,148
±1%	6,766	9,604	16,590

Assumes p = 0.5 (maximum variability)

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Sample Size for Means

Use this when estimating a continuous variable (e.g., average income, test scores).

Formula

n = (z × σ / e)²

Where:

• z = z-score for confidence level
• σ = population standard deviation (estimated)
• e = desired margin of error (same units as the mean)

Example

To estimate average income within ±$5,000 with 95$25,000:

n = (1.96 × 25,000 / 5,000)² = 96 people

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Sample Size for Comparing Two Groups

Use this when comparing two independent groups (e.g., treatment vs. control).

Formula

n per group = 2 × ((z_α + z_β) / d)²

Where:

• z_α = z-score for significance level (e.g., 1.96 for α = 0.05)
• z_β = z-score for power (e.g., 0.84 for 80% power)
• d = Cohen’s d (effect size)
• Result is per group

Effect Size Guidelines (Cohen’s d)

Effect	d	Example
Small	0.2	Subtle differences, large overlap
Medium	0.5	Noticeable difference
Large	0.8	Obvious difference, little overlap

Sample Sizes for Two-Group Comparison

Effect Size	80% Power	90% Power
d = 0.2	394/group	527/group
d = 0.5	64/group	86/group
d = 0.8	26/group	34/group

At α = 0.05, two-tailed

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Finite Population Correction

When sampling from a finite population (N), apply the correction:

n’ = n / (1 + (n-1)/N)

This reduces the required sample size when sampling a significant portion of the population.

Example

If you calculate n = 400, but your population is N = 1,000:

n’ = 400 / (1 + 399/1000) = 400 / 1.399 ≈ 286

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Factors Affecting Sample Size

Factor	Effect on Sample Size
↑ Confidence level	Larger sample needed
↑ Precision (↓ margin of error)	Larger sample needed
↑ Expected variability	Larger sample needed
↑ Effect size	Smaller sample needed
↑ Power	Larger sample needed

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Common Questions

Why use p = 0.5 for proportions?

When you don’t know the expected proportion, 0.5 gives the maximum sample size needed. Any other proportion would require fewer samples.

What confidence level should I use?

• 90%: Preliminary studies, quick estimates
• 95%: Standard for most research (recommended)
• 99%: When high certainty is critical

What is statistical power?

Power is the probability of detecting an effect if it exists. Standard is 80%, but 90% is better for important decisions.

How do I estimate standard deviation?

• Use data from previous similar studies
• Conduct a pilot study
• Use the range/4 as a rough estimate
• For proportions, use √(p(1-p))

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Frequently Asked Questions

How do I calculate sample size for a survey?

To calculate sample size for a survey: (1) Choose your confidence level (typically 95%), (2) Set your desired margin of error (e.g., ±5%), (3) Estimate the expected proportion (use 50% if unknown), (4) Use the formula: n = (z² × p × (1-p)) / e². Our calculator above does this automatically.

What sample size do I need for 95% confidence?

For 95% confidence with ±5% margin of error and p=0.5, you need approximately 385 respondents. For ±3% margin, you need about 1,068. For ±1% margin, you need approximately 9,604.

How many participants do I need for a study?

The number of participants depends on: (1) Expected effect size—smaller effects require more participants, (2) Desired power (typically 80-90%), (3) Significance level (typically 0.05), (4) Type of analysis. Use our calculator for comparing two groups or estimating means.

What is margin of error?

Margin of error represents the range within which the true population value likely falls. For example, if 60% of respondents prefer Option A with ±5% margin of error, the true population proportion is likely between 55% and 65%.

What is the minimum sample size needed?

General minimums: For descriptive statistics, n ≥ 30 is often sufficient. For regression, aim for 10-20 observations per predictor. For proportions, ensure np ≥ 10 and n(1-p) ≥ 10. For reliable estimates, more is generally better.

How does population size affect sample size?

For large populations (>10,000), population size has minimal effect on required sample size. For smaller populations, apply the finite population correction: n’ = n / (1 + (n-1)/N), which reduces required sample size.

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Design Considerations

Practical Sample Size

Always add extra to account for:

• Non-response (typically 10-50%)
• Invalid responses
• Subgroup analysis needs
• Dropout in longitudinal studies

Adjusted n = n / (1 - expected dropout rate)

Minimum Sample Sizes

• For normal approximation: n ≥ 30
• For proportions near 0 or 1: larger n needed
• For regression: n ≥ 10 × number of predictors

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Related Resources

• Confidence Intervals - Understanding intervals
• Hypothesis Testing - Power and significance
• Central Limit Theorem - Why sampling works
• Standard Error - Measuring precision
• Standard Deviation Calculator - Calculate variability