Mean sample size
Estimate the sample size needed for a population mean using standard deviation, confidence level, and margin of error.
Free statistics calculator
Sample Size Calculator for Mean, Proportion, and Survey Margin of Error
Calculate the sample size needed to estimate a mean, survey proportion, percentage, or yes/no outcome. Choose the confidence level, target margin of error, variability estimate, and optional finite population correction to get the minimum whole-number sample size.
- For means Plan sample size from standard deviation and margin of error.
- For proportions Plan surveys, percentages, and yes/no outcomes.
- Finite population Adjust the sample size when the population size is known.
- Rounded result Get the minimum whole-number sample size to meet the target.
Calculate Required Sample Size
Use mean when your outcome is numeric. Use proportion when the outcome is a percentage, yes/no result, success rate, pass/fail result, or share of a group. Leave population size blank when the population is very large or unknown.
Use a prior study, pilot sample, or reasonable estimate.
Use the same units as the mean, such as points or dollars.
Use 50% if no prior estimate is available.
Example: enter 5 for plus or minus 5 percentage points.
Use this only when the total population size is known.
Results
Sample size for a mean
Required Sample Size
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Method
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Confidence Level
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Z Critical
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Target Margin
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Initial Sample Size
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FPC Adjusted Size
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Achieved Margin
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Sampling Fraction
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Interpretation
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This calculator plans sample size for estimation, not hypothesis-test power. Complex sampling designs may require design effects, clustering adjustments, or expert review.
What This Calculator Includes
Sample size planning depends on confidence level, margin of error, variability, and whether the population is effectively infinite or finite.
Proportion sample size
Estimate the sample size needed for a population proportion, survey percentage, or yes/no outcome.
Finite population
Apply a finite population correction when the population size is known and not very large.
Rounded result
Get the rounded-up minimum sample size, achieved margin of error, and planning interpretation.
Sample Size Formulas
The initial sample size is calculated for a very large population. If a finite population size is supplied, the calculator applies a finite population adjustment.
| Goal | Formula idea | Use when |
|---|---|---|
| Estimate a mean | n = (z * sd / E)^2 |
The outcome is numeric and the standard deviation is estimated or known. |
| Estimate a proportion | n = z^2 * p * (1 - p) / E^2 |
The outcome is yes/no, success/failure, or a percentage. |
| Finite population | n = n0 / (1 + (n0 - 1) / N) |
The total population size N is known and not very large. |
How to Calculate Sample Size Step by Step
Sample size homework usually asks you to show the formula, identify each input, round up, and explain why the final n is large enough.
- Decide whether the target parameter is a population mean or a population proportion.
- Choose the confidence level, such as 90%, 95%, or 99%.
- Choose the target margin of error. For proportions, enter it as percentage points.
- For a mean, enter a reasonable standard deviation from a prior study, pilot sample, or assignment prompt.
- For a proportion, enter the expected percentage. Use 50% when no prior estimate is available.
- If the total population size is known, apply the finite population correction.
- Always round up to the next whole number so the target margin of error is met.
Sample Size Examples
These examples are useful for checking Excel, calculator, or hand-calculation answers. Rounded-up sample sizes are intentional because partial participants are not possible.
| Question type | Inputs | Required sample size | Why |
|---|---|---|---|
| Mean sample size | 95% confidence, SD = 15, margin of error = 3 | 97 observations | The initial sample size is 96.0365, so it rounds up to 97. |
| Survey proportion sample size | 95% confidence, p = 50%, margin of error = 5% | 385 responses | Using p = 50% gives the conservative maximum sample size. |
| Finite population survey | 95% confidence, p = 50%, margin of error = 5%, population = 10,000 | 370 responses | The finite population correction reduces the required sample from 385 to 370. |
Common Mistakes to Avoid
- Using a margin of error as a percent for a mean measured in units such as points, dollars, minutes, or pounds.
- Choosing a very small margin of error without realizing it can require a much larger sample size.
- Using an estimated proportion far from 0.50 when no prior estimate is available.
- Treating this as a power calculator for hypothesis tests. This page is for estimating a mean or proportion with a target margin of error.
Sample Size Calculator FAQs
Should I use the mean or proportion calculator?
Use mean when the outcome is numerical, such as score, time, cost, or weight. Use proportion when the outcome is yes/no, pass/fail, success/failure, or a percentage.
Why is 0.50 often used for an unknown proportion?
A proportion of 0.50 gives the largest p times 1 minus p value, so it produces the most conservative sample size when no better estimate is available.
When should I use finite population correction?
Use it when you know the population size and your planned sample is a meaningful share of that population. It usually matters more when the sample is more than about 5% of the population.
Is this the same as statistical power?
No. This calculator plans sample size for estimating a mean or proportion with a target margin of error. Power calculations also require an effect size, alpha, and desired power.
What margin of error should I enter for a survey?
For a survey proportion, enter the margin of error in percentage points. For example, enter 5 if you want a result within plus or minus 5 percentage points.
Why does sample size increase when confidence level increases?
A higher confidence level uses a larger z critical value, which makes the required sample size larger for the same margin of error.
Can I use this for a class project?
Yes, if your assignment asks for sample size needed to estimate a population mean or proportion. If it asks for power, effect size, or minimum detectable difference, you need a power analysis instead.
Need Help Planning a Statistics Assignment?
Sample size planning can depend on the research design, expected variability, desired precision, sampling method, and whether your assignment is about estimation or power.
Related Statistics Help
Use Calculators Responsibly
Use this calculator to check formulas, plan estimates, and prepare questions. For graded work, follow the method and assumptions required by your instructor.