What is a Sample Size? Definition, Examples & Best Practices
Sample size answers a simple research question: how many people or observations are needed to estimate something with acceptable precision. In survey research, it determines how confidently a team can report results such as customer preference, brand awareness, satisfaction, purchase intent or market demand.
A sample and sample size are related but different. The sample is the group selected from the wider population. The sample size is the number of people in that group. A market research survey with 1,000 respondents has a sample size of 1,000.
Sample size matters because survey results are estimates, not exact population values. A sample size calculator usually asks for confidence level, margin of error, population size and expected proportion. Experimental research may instead use power analysis, such as G*Power, to estimate the number of participants needed to detect an effect.
A larger sample is not automatically better if the sample is biased. A smaller, well-targeted sample can be more useful than a large sample drawn from the wrong audience.
The Logic Behind Sample Size
Sample size calculation sits at the intersection of sampling theory, statistics and research design. Cochran (1977) gave one of the most widely used treatments of sample size for survey research, especially for estimating proportions. Krejcie and Morgan (1970) published a widely cited table and formula for determining sample size for research activities. Faul, Erdfelder, Lang and Buchner (2007) introduced G*Power 3 as a flexible statistical power analysis programme for social, behavioural and biomedical research.
For a simple survey proportion, the common formula is: sample size = z squared multiplied by p multiplied by 1 minus p, divided by e squared. In plain terms, z reflects the confidence level, p is the expected proportion, and e is the desired margin of error.
Worked example: for a 95% confidence level, z is 1.96. If the expected proportion is unknown, researchers often use p = 0.5 because it gives the largest required sample. With a 5% margin of error, the calculation is 1.96 squared multiplied by 0.5 multiplied by 0.5, divided by 0.05 squared. That equals 384.16, so the required sample size is usually rounded up to 385.
Real survey organisations report sample size and uncertainty together. Pew Research Center reported in May 2026 that one American Trends Panel wave had 5,103 respondents from 5,898 sampled panelists, giving a survey-level response rate of 87%. Pew also explains that larger samples usually have smaller margins of error, while smaller subgroup samples have wider error bars. NIST’s statistical handbook also links confidence intervals to sample estimate, standard error and confidence level.
A limitation is that formulas only address sampling error under specific assumptions. They do not fix nonresponse bias, poor questionnaire design, unrepresentative panels, coverage error or badly defined audiences.
How to Calculate Sample Size
For a market research survey estimating a proportion, the standard sample size formula is:
n = z² × p(1 - p) / e²
In this formula, n is the required sample size, z is the z-score for the confidence level, p is the expected proportion, and e is the margin of error. At a 95% confidence level, z is 1.96. At a 99% confidence level, z is about 2.576.
Example: a product team wants to estimate the share of UK shoppers interested in a new subscription box. They want 95% confidence and a margin of error of plus or minus 4 percentage points. They do not know the expected proportion, so they use p = 0.5.
n = 1.96² × 0.5 × 0.5 / 0.04²
n = 3.8416 × 0.25 / 0.0016
n = 600.25
The team needs about 601 completed responses.
If the total population is small, researchers may apply a finite population correction. Some people use Slovin’s formula: n = N / (1 + N e²), where N is population size and e is margin of error. Slovin’s formula is simple, but it is less defensible than Cochran-style formulas because it does not explicitly include confidence level or expected variability. For experiments, power analysis is usually better because it accounts for effect size, significance level and desired statistical power.
How Sample Size Is Used in Practice
A UK D2C pet food brand wants to measure demand for a premium cat food subscription before investing in packaging and fulfilment. The target population is 250,000 UK cat owners who buy pet food online. The team wants a 95% confidence level and a plus or minus 5 percentage point margin of error.
Using the standard proportion formula with p = 0.5, the required sample size is 385 completed responses. The brand collects 420 valid responses from screened online cat food buyers. The survey finds 34% top-2-box purchase intent, with a 95% confidence interval of roughly plus or minus 4.5 percentage points.
Because even the upper end of the range is below the team’s 45% threshold, the brand does not launch nationally. It narrows the proposition to senior-cat nutrition, where purchase intent is 48% among 96 respondents, then commissions a larger follow-up sample for that segment.
Sources Cited
Cochran, W. G. (1977). Sampling Techniques. John Wiley & Sons.
Faul, F., Erdfelder, E., Lang, A. G. and Buchner, A. (2007). “G*Power 3: A Flexible Statistical Power Analysis Program for the Social, Behavioral, and Biomedical Sciences.” Behavior Research Methods.
Krejcie, R. V. and Morgan, D. W. (1970). “Determining Sample Size for Research Activities.” Educational and Psychological Measurement.
National Institute of Standards and Technology (accessed 2026). “What Are Confidence Intervals?” NIST/SEMATECH e-Handbook of Statistical Methods.
Pew Research Center (2025). “Understanding Error Bars in Charts.” Pew Research Center.
Pew Research Center (2026). “Methodology: Americans’ Views of the U.S. Role in the World.” Pew Research Center.
Qualtrics (2021). “Margin of Error Guide and Calculator.” Qualtrics.
Yamane, T. (1967). Statistics: An Introductory Analysis. Harper and Row.
Frequently Asked Questions
Sample size is the number of respondents, observations or cases included in a research study. In a survey, it is the number of completed responses used for analysis. A sample size of 1,000 means the results are based on 1,000 respondents, not the full population.
To calculate sample size for a survey, choose the confidence level, margin of error and expected proportion. For a 95% confidence level, 5% margin of error and unknown expected proportion, the common formula gives about 385 responses. A sample size calculator automates this calculation using the same inputs.
The common sample size formula for estimating a proportion is n = z² × p(1 - p) / e². Here, n is sample size, z is the confidence-level value, p is expected proportion, and e is margin of error. If p is unknown, researchers often use 0.5 to produce a conservative estimate.
Slovin’s formula is n = N / (1 + N e²), where N is population size and e is margin of error. It is often used as a quick sample size shortcut. Its weakness is that it does not explicitly include confidence level, expected variability or research design, so it should be used carefully.
Probability proportional to size is a sampling method where larger units have a higher chance of selection. For example, in a school survey, schools with more pupils may be more likely to be selected than smaller schools. It is useful in cluster sampling when units differ greatly in size.
G*Power is a statistical power analysis programme used to calculate sample size for tests such as t-tests, F-tests, chi-square tests and regression models. It is more common in experiments and academic research than basic market surveys because it uses effect size, significance level and desired power.
A bigger sample size usually reduces sampling error, but it does not guarantee better research. If the sample is drawn from the wrong population, has poor screening or suffers from nonresponse bias, a larger sample can still produce misleading results. Representativeness matters as much as the number of responses.
“Sample size was calculated” means the researcher used a formula, calculator, power analysis or sampling table before fieldwork to estimate how many responses were needed. The calculation should state the assumptions, such as confidence level, margin of error, expected proportion, effect size or statistical power.