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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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