Use this sample size calculator to determine how many observations or completed responses you need for reliable research. Enter the population size, confidence level, and margin of error to calculate the recommended sample size.
The calculator is suitable for population research, customer feedback, market research, employee studies, opinion polls, and other quantitative studies that estimate a population proportion.
When the expected population proportion is unknown, the calculator uses 50%. This is the most conservative assumption because it produces the largest recommended sample size.
How to Use the Sample Size Calculator
The calculator converts your research requirements into a recommended number of observations. To calculate sample size, enter three values: population size, confidence level, and margin of error.
- Enter the population size. This is the total number of people or units your research is intended to represent.
- Enter the confidence level. Common values are 90%, 95%, and 99%.
- Enter the margin of error. This defines the level of precision required for the result.
- Review the calculated sample size. Use the result as the minimum target for valid observations or completed responses.
The calculated result represents completed and usable observations. If you are conducting a survey, it does not represent the number of invitations you need to send.
What Is Sample Size?
Sample size is the number of observations included in a study. A sample represents a larger population and allows researchers to estimate population characteristics without collecting data from every individual or unit.
For example, a company with 10,000 customers may not need to collect feedback from every customer. An appropriately selected sample can provide a useful estimate of customer opinions while reducing the time and cost of data collection.
Larger samples generally provide greater precision. However, collecting more data than necessary can increase costs without producing a meaningful improvement in accuracy. A sample size calculation helps balance statistical precision, confidence, time, and available resources.
Why Is Sample Size Important?
Choosing an appropriate sample size reduces the risk of drawing conclusions from too little data. A sample that is too small may produce unstable estimates, while an unnecessarily large sample may waste time and resources.
A suitable sample size helps researchers:
- estimate a population proportion with a defined level of precision;
- reduce random sampling error;
- plan research costs and timelines;
- avoid collecting more data than necessary;
- report the statistical assumptions behind the results.
Sample Size Calculator Inputs
Population Size
Population size is the total number of people, accounts, objects, or other units that the study is intended to represent.
Examples of a population include:
- all active customers of a company;
- all employees in an organization;
- all registered users of an online service;
- all students at a university;
- all residents of a selected city;
- all accounts within a defined market.
Use a specific population size when researching a closed and measurable group. For very large populations, further increases in population size have only a small effect on the required sample.
Confidence Level
Confidence level describes how consistently the sampling method would produce an interval containing the true population value if the study were repeated many times under the same conditions.
- 90% confidence may be suitable for exploratory, directional, or low-risk research.
- 95% confidence is commonly used for general quantitative research.
- 99% confidence provides greater certainty but requires a larger sample.
Increasing the confidence level increases the required sample size. The appropriate level depends on the purpose of the study and the consequences of making an incorrect decision.
Margin of Error
Margin of error indicates how far a sample estimate may be from the true population value under the assumptions of the calculation.
For example, suppose 60% of participants select a particular answer and the margin of error is ±5 percentage points. The corresponding population value is estimated to be approximately between 55% and 65%.
- ±10% provides a broad directional estimate and requires a relatively small sample.
- ±5% is commonly used for general research.
- ±3% provides greater precision but requires more observations.
- ±1% requires a much larger sample and is generally used when high precision is necessary.
Reducing the margin of error significantly increases the required sample. For a large population at 95% confidence, changing the margin of error from ±5% to ±3% increases the required sample from approximately 385 to 1,068 observations.
Expected Population Proportion
The expected population proportion is the estimated percentage of the population that has the characteristic being measured.
This calculator uses an expected proportion of 50%. When the actual proportion is unknown, 50% is the most conservative assumption because it produces the highest variability and the largest recommended sample.
Sample Size by Confidence Level and Margin of Error
The table below shows common sample sizes for a large population. The values assume simple random sampling and a 50% expected population proportion.
| Margin of Error | 90% Confidence | 95% Confidence | 99% Confidence |
|---|---|---|---|
| ±10% | 68 | 97 | 166 |
| ±5% | 271 | 385 | 664 |
| ±3% | 752 | 1,068 | 1,844 |
| ±2% | 1,692 | 2,401 | 4,145 |
| ±1% | 6,765 | 9,604 | 16,588 |
All values are rounded up to the next whole observation. A finite population may require a smaller sample after the finite population correction is applied.
Sample Size by Population Size
The following examples use a 95% confidence level, a ±5% margin of error, and a 50% expected population proportion.
| Population Size | Required Sample Size |
|---|---|
| 100 | 80 |
| 300 | 169 |
| 500 | 218 |
| 1,000 | 278 |
| 5,000 | 357 |
| 10,000 | 370 |
| 100,000 | 383 |
| Large or Unknown | 385 |
Population size has the greatest effect when the population is relatively small. Once the population becomes large, the required sample changes only slightly.
How to Calculate Sample Size
For a large or unknown population, sample size can be estimated using the standard formula for a population proportion:
n0 = Z2 × p × (1 − p) / e2
In this formula:
- n0 is the initial required sample size;
- Z is the z-score corresponding to the selected confidence level;
- p is the expected population proportion;
- e is the margin of error expressed as a decimal.
Confidence Levels and Z-Scores
| Confidence Level | Z-Score |
|---|---|
| 80% | 1.282 |
| 90% | 1.645 |
| 95% | 1.960 |
| 99% | 2.576 |
Finite Population Correction
When the population size is finite, the initial result can be adjusted using the finite population correction:
n = n0 / (1 + (n0 − 1) / N)
In this formula:
- n is the corrected sample size;
- n0 is the initial sample size for a large population;
- N is the total population size.
The calculation uses a normal approximation for estimating a population proportion. It assumes simple random sampling and independent observations.
Sample Size Examples
Customer Research
A company has 10,000 active customers and wants to measure a customer characteristic using a 95% confidence level and a ±5% margin of error. The recommended sample is approximately 370 observations.
Employee Research
An organization with 300 employees wants to conduct an internal study. At 95% confidence and a ±5% margin of error, the recommended sample is approximately 169 observations.
Market Research
A business studying a large consumer population wants a 95% confidence level and a ±3% margin of error. The recommended sample is approximately 1,068 observations.
University Research
A university has a population of 5,000 students and uses a 95% confidence level with a ±5% margin of error. The recommended sample is approximately 357 observations.
How Many People Should You Invite?
When research depends on voluntary responses, the number of invitations should be higher than the calculated sample size. Not every invited participant will provide a complete and usable response.
Estimate the required number of invitations using the following formula:
Invitations needed = Required sample size / Expected response rate
For example, if you need 385 completed responses and expect a 25% response rate:
385 / 0.25 = 1,540 invitations
| Expected Response Rate | Invitations Needed for 385 Responses |
|---|---|
| 10% | 3,850 |
| 20% | 1,925 |
| 25% | 1,540 |
| 30% | 1,284 |
| 50% | 770 |
Consider adding a further 10–20% buffer if observations may be incomplete, duplicated, disqualified, or removed during data cleaning.
How to Choose the Right Sample Size Settings
| Research Scenario | Confidence Level | Margin of Error |
|---|---|---|
| Exploratory internal research | 90% | ±5% to ±10% |
| General customer research | 95% | ±5% |
| Employee research | 95% | ±3% to ±5% |
| Market research | 95% | ±3% to ±5% |
| High-precision quantitative research | 99% | ±1% to ±3% |
These values are starting points rather than universal requirements. The appropriate settings depend on the purpose of the research, the cost of collecting data, and the consequences of making an incorrect decision.
How Sample Size Affects Margin of Error
Margin of error decreases as sample size increases, but the relationship is not linear. Doubling the sample does not cut the margin of error in half. To reduce the margin of error by approximately half, the sample generally needs to be about four times larger.
This is why moving from a ±5% margin of error to ±1% requires a major increase in sample size. Researchers should select a level of precision that is both useful and practical.
Sample Size Does Not Eliminate Research Bias
A sufficiently large sample reduces random sampling error, but it does not automatically make a study representative or reliable. Research quality also depends on how participants or observations are selected and how the data is collected.
Common sources of bias include:
- Selection bias: some population groups have a greater chance of being included than others.
- Nonresponse bias: participants who respond differ systematically from those who do not respond.
- Coverage bias: the collection method does not reach important parts of the target population.
- Measurement bias: the questions or collection process influence the recorded results.
- Duplicate or low-quality observations: invalid data distorts the final estimates.
Reliable research requires both an adequate sample size and an appropriate sampling process. Define the target population clearly, apply consistent eligibility rules, remove invalid data, and report the assumptions behind the results.
Calculating Sample Size for Audience Segments
The calculated sample applies to the overall population. If you need reliable conclusions for separate audience segments, each important segment may require its own adequate sample.
Common segments include:
- new and returning customers;
- different countries or regions;
- different age groups;
- free and paying users;
- departments or employee levels;
- different customer acquisition channels.
A study with 400 total observations may be sufficient for an overall estimate but insufficient for comparing several small subgroups. Consider segment-level requirements before beginning data collection.
Sample Size Calculator FAQ
What is a good sample size?
A good sample size depends on the population size, confidence level, and acceptable margin of error. For a large population, approximately 385 observations are required for a 95% confidence level and a ±5% margin of error when the expected population proportion is 50%.
What sample size is needed for a 95% confidence level and a 5% margin of error?
For a large or unknown population, the required sample size is approximately 385. A smaller finite population may require fewer observations after the finite population correction is applied.
How do I calculate sample size?
To calculate sample size for a population proportion, you need the population size, confidence level, margin of error, and expected population proportion. When the expected proportion is unknown, 50% provides the most conservative estimate.
What if the population size is unknown?
If the population is very large or cannot be determined, use the large-population estimate. At a 95% confidence level and a ±5% margin of error, the required sample is approximately 385 observations.
Why does the calculator use a 50% population proportion?
A 50% expected proportion produces the highest statistical variability and therefore the largest required sample. It is a conservative assumption when no previous research or pilot data is available.
Does population size always affect sample size?
Population size has the greatest effect on relatively small populations. Its effect becomes limited as the population grows. At a 95% confidence level and a ±5% margin of error, a population of 10,000 requires approximately 370 observations, while a population of 100,000 requires approximately 383.
Why does a smaller margin of error require a larger sample?
A smaller margin of error requires greater precision. Because sampling uncertainty decreases gradually as the sample grows, achieving a substantially smaller margin of error requires many more observations.
What is finite population correction?
Finite population correction reduces the required sample when the sample represents a substantial portion of a relatively small population. It prevents researchers from collecting more observations than necessary from a closed group.
Does sample size mean completed responses or invitations?
The calculated sample size represents completed and valid responses. It does not represent the number of invitations you need to send. Divide the required sample size by the expected response rate to estimate the number of invitations.
Should I add a buffer to the calculated sample size?
A buffer of approximately 10–20% may be useful when observations can be incomplete, duplicated, disqualified, or removed during data cleaning. The appropriate buffer depends on the research method and expected data quality.
Does a larger sample eliminate research bias?
No. A larger sample reduces random sampling error but cannot correct selection bias, nonresponse bias, poor targeting, duplicate data, or systematic measurement errors.
Do I need a separate sample for each population segment?
If you need reliable conclusions for individual population segments, each segment should contain an adequate number of observations. A sufficient overall sample may still be too small for reliable subgroup comparisons.
Can this sample size calculator be used for surveys?
Yes. The calculator can estimate the number of completed responses required for customer surveys, employee studies, opinion polls, market research, and other studies that estimate a population proportion.
Can this sample size calculator be used for A/B testing?
This calculator estimates sample size for a single population proportion. An A/B test comparing a control and variation requires a different calculation using inputs such as baseline conversion rate, minimum detectable effect, significance level, and statistical power.
Calculation Method and Assumptions
- Method: population-proportion sample size formula with finite population correction.
- Expected population proportion: 50%.
- Sampling assumption: simple random sampling.
- Observation assumption: observations are independent.
- Result: minimum recommended sample size rounded up to a whole number.
- Scope: quantitative studies estimating a population proportion.
- Last reviewed: August 2026.
Calculate the Right Sample Size
The right sample size helps you collect enough data to support useful conclusions without spending unnecessary time and resources. Start by defining the target population, then choose a confidence level and margin of error appropriate for the research decision.
Remember that sample size is only one part of reliable research. Use an appropriate sampling method, collect valid observations, monitor data quality, and clearly report the assumptions behind the results.