Sample Size Confidence Interval Margin of Error Calculator

Calculator

Study type

Confidence level (%)

Interval side

Z value mode

Custom z value

Margin of error

Margin unit for proportion

Proportion setting

Expected proportion (%)

Standard deviation for mean

Finite population size

Design effect

Expected response rate (%)

Planning notes

Formula Used

For a proportion: n0 = z² × p × (1 - p) ÷ E².

For a mean: n0 = (z × σ ÷ E)².

Finite population correction: n = n0 ÷ [1 + ((n0 - 1) ÷ N)].

Design adjustment: completed sample = corrected sample × design effect.

Response adjustment: contacts = completed sample ÷ response rate.

How to Use This Calculator

Select a proportion study for percentages or a mean study for averages.
Enter the confidence level and margin of error.
Use 50% for unknown proportions, or enter a pilot estimate.
For a mean, enter the expected standard deviation.
Add population size only when the full population is known.
Enter design effect and response rate for field planning.
Press the calculate button and review results above the form.
Download the result as a CSV or PDF file.

Example Data Table

Scenario	Type	Confidence	Margin	Main input	Population	Response	Recommended result
General survey	Proportion	95%	5%	p = 50%	Unknown	100%	385 completed responses
Small population poll	Proportion	95%	5%	p = 50%	2,000	80%	403 contacts
Average score study	Mean	95%	2 units	σ = 12	Unknown	100%	139 completed responses

Sample Size Planning Guide

A confidence interval gives a likely range for a population value. Sample size controls the width of that range. A larger sample usually creates a smaller margin of error. This calculator helps plan that number before data collection begins.

Why Margin of Error Matters

Margin of error is the allowed half width of the interval. In a proportion study, it may be three percentage points. In a mean study, it may be two units, five dollars, or any measured scale. Smaller error targets need more observations. This is because precision rises slowly as sample size grows.

Choosing Confidence Level

Confidence level sets the z value used in the formula. Common choices are 90%, 95%, and 99%. A higher confidence level gives stronger interval coverage. It also increases the required sample. The two sided option suits most published confidence intervals. The one sided option is useful when only an upper or lower bound matters.

Planning for Proportions

Use the proportion method for percentages, rates, votes, defects, conversion rates, or pass rates. If the expected proportion is unknown, use 50%. That value is conservative. It produces the largest sample for a fixed error and confidence level. When a reliable pilot estimate exists, enter that proportion to improve planning.

Planning for Means

Use the mean method for average weight, cost, score, time, length, or demand. The standard deviation must use the same units as the margin of error. A larger standard deviation means the data are more spread out. More spread requires more observations for the same precision.

Advanced Adjustments

Finite population correction reduces the sample when the total population is known and small. Design effect increases the sample when clustering, weighting, or complex sampling lowers efficiency. Response rate adjustment estimates how many people should be contacted. It does not change the number of completed responses needed. It only accounts for expected nonresponse.

Using Results Wisely

Treat the final number as a planning target. Round upward because partial people cannot be sampled. Add practical reserves for invalid answers, screening failures, and missing data. Review assumptions before fieldwork starts. Good assumptions make the interval more useful. Document every input so reviewers can later trace the final sample choice with confidence.

FAQs

What is a sample size calculator for confidence intervals?

It estimates how many observations are needed to reach a chosen confidence level and margin of error. It can support proportions, means, finite population correction, design effect, and response planning.

What margin of error should I choose?

Use a smaller margin when decisions need high precision. Many surveys use 5 percentage points. Sensitive research may use 3 points or less, which requires a larger sample.

Why does 50% create the largest proportion sample?

The term p × (1 - p) is largest when p equals 0.50. That makes 50% the safest option when the real proportion is unknown before sampling.

When should finite population correction be used?

Use it when the total population size is known and not very large. It reduces the required sample because each completed response covers more of the population.

What is design effect?

Design effect adjusts for complex sampling. Clustering, weighting, and uneven selection can reduce efficiency. A design effect above 1 increases the completed sample target.

How is response rate used?

Response rate estimates the number of contacts needed. It does not reduce the completed sample target. It only inflates invitations to cover likely nonresponse.

Can I use this for average scores or costs?

Yes. Select the mean option. Enter the expected standard deviation and margin of error in the same units, such as points, dollars, minutes, or kilograms.

Why are results rounded upward?

Sample size must be a whole number. Rounding upward protects the planned precision. Rounding down can make the final interval wider than expected.