Sample Size Calculator
Find the right survey sample size for any confidence level and margin of error.
Smaller margin means larger sample.
Use 50% if you are unsure.
Finite population correction is applied if entered.
Used to estimate how many people to invite.
Required sample size
385
Completed responses needed.
Invites needed
385
Based on expected response rate.
Large population n₀
385
Adjusted sample size
385
Confidence level
95%
Z-score
1.96
Margin of error
5%
Estimated proportion
50%
Formula used
n₀ = (Z² × p × (1 − p)) ÷ e²
(1.96² × 0.5 × 0.5) ÷ 0.05²
Sample Size Formulas
Large Population Sample Size
n₀ = (Z² × p × (1 − p)) ÷ e²
Finite Population Correction
n = n₀ ÷ (1 + ((n₀ − 1) ÷ N))
Response Rate Adjustment
Invites Needed = Required Completed Responses ÷ Expected Response Rate
Margin of Error
e = Z × √((p × (1 − p)) ÷ n)
Variable Explanations
n
Adjusted required sample size.
n₀
Sample size for a large or unknown population.
Z
Z-score for the selected confidence level.
p
Estimated proportion or response distribution.
e
Margin of error as a decimal.
N
Population size.
Response rate
Expected percentage of invited people who complete the survey.
What Sample Size Means
Completed responses
Sample size is the number of completed responses or observations needed.
Precision
Larger samples generally improve precision.
Confidence
Higher confidence means more certainty but requires more responses.
Margin of error
Smaller margin of error means tighter estimates but larger samples.
Bias warning
Sample size does not fix biased sampling.
Research planning
Useful for surveys, research studies, quality checks, and market research.
Worked Examples
95% confidence, 5% margin, 50% proportion
Formula: n₀ = (1.96² × 0.5 × 0.5) ÷ 0.05²
Rounded-up result: 385
Common large-population survey estimate.
99% confidence, 5% margin
Formula: n₀ = (2.576² × 0.5 × 0.5) ÷ 0.05²
Rounded-up result: 664
Higher confidence requires more responses.
95% confidence, 3% margin
Formula: n₀ = (1.96² × 0.5 × 0.5) ÷ 0.03²
Rounded-up result: 1,068
Smaller margin of error increases sample size.
Finite population N = 1,000
Formula: n = n₀ ÷ (1 + ((n₀ − 1) ÷ N))
Rounded-up result: 278
Finite population correction lowers the required sample.
Estimated proportion 30%
Formula: n₀ = (1.96² × 0.3 × 0.7) ÷ 0.05²
Rounded-up result: 323
A proportion away from 50% often needs fewer responses.
Response rate adjustment
Formula: Invites = 385 ÷ 0.40
Rounded-up result: 963 invites
Invite more people if not everyone responds.
Why 50% is conservative
Formula: p × (1 − p) is largest at p = 0.5
Rounded-up result: Largest sample
Use 50% when unsure.
Invalid margin of error
Formula: 0% margin
Rounded-up result: Invalid
A zero margin of error would require an impossible sample size.
Confidence Level, Margin of Error, and Population Size
Confidence level
Controls how confident the estimate is.
Margin of error
Controls how precise the estimate should be.
Estimated proportion
50% is usually the most conservative choice.
Population size
Matters most for smaller finite populations.
Finite Population Correction
Large-population sample size assumes the population is very large. Finite population correction adjusts the required sample when the population size is known. The correction matters more when the sample is a meaningful share of the population. For very large populations, the adjusted sample is close to the large-population estimate.
Common Use Cases
For A/B tests, use a dedicated power calculator when you need power, effect size, baseline rate, and minimum detectable effect.
Common Sample Size Mistakes
Understanding Your Results
Required sample size
Completed responses needed.
Rounded-up sample size
Practical whole-number target.
Z-score
Confidence-level multiplier.
Margin of error
Acceptable range around the estimate.
Finite population adjustment
Smaller sample needed when population is limited.
Invites needed
Estimated outreach count based on response rate.
Frequently Asked Questions
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