How to Calculate Sample Size for Surveys

How many people do you need to survey to get reliable results? This is one of the most important questions in research design, and the answer depends on your desired precision, confidence level, and the variability in your population. Survey too few people and your results have wide margins of error. Survey too many and you waste time, money, and resources for negligible gains in precision.

This guide explains the sample size formula, walks you through calculations for both proportions and means, shows you how to adjust for finite populations, and provides practical guidelines for designing surveys that deliver meaningful, trustworthy results.

Why Sample Size Matters

Sample size directly determines the precision and reliability of your survey results. A survey with too few respondents produces wide confidence intervals that make it impossible to draw actionable conclusions. Consider two hypothetical survey results:

Both surveys found 60% approval, but only Survey B provides a precise enough estimate to support confident decision-making. The difference is entirely due to sample size.

Beyond precision, sample size affects statistical power — the ability to detect real effects. An underpowered study might fail to detect a genuine difference between two groups, leading to a false conclusion that no difference exists. This is why calculating sample size before collecting data is essential, not an afterthought.

The Sample Size Formula

For Estimating Proportions

When your survey asks yes/no or categorical questions and you want to estimate the percentage of the population with a certain characteristic:

For Estimating Means

When your survey collects numerical data and you want to estimate the population average with a specific margin of error:

Step-by-Step Calculation Examples

Adjusting for Finite Populations

The standard sample size formula assumes an infinitely large population. When your sample represents more than about 5% of the total population, you should apply the finite population correction (FPC) to reduce the required sample size:

The correction becomes more significant as the sampling fraction (n/N) increases. For a population of five hundred and an initial calculation requiring 385 respondents, the corrected sample size drops to about 218 — a substantial reduction. For a population of 100,000, the correction barely changes the result because 385 is only 0.39% of the population.

Factors That Influence Sample Size

Four main factors determine how large your sample needs to be, and understanding each helps you make informed trade-offs during study design:

• Confidence level — Higher confidence requires larger samples. Moving from 95% to 99% confidence increases the required sample size by about 78% (because the z-score increases from 1.96 to 2.576).
• Margin of error — Tighter margins require dramatically larger samples. Halving the margin of error quadruples the sample size because the relationship is inverse-square. Going from ±5% to ±2.5% multiplies the requirement by 4.
• Population variability — More variable populations require larger samples. For proportions, maximum variability occurs at p = 0.5. If you know your population is more homogeneous (p closer to 0 or 1), you can use a smaller sample. For means, higher standard deviation means larger samples.
• Population size — Only matters for smaller populations (under 20,000). For large populations, the required sample size plateaus because the standard error is dominated by the sample size, not the sampling fraction.

Sample Size Reference Table

This table shows required sample sizes for estimating proportions at different confidence levels and margins of error, assuming unknown population proportion (p = 0.5) and an infinitely large population.

Notice how dramatically the required sample size increases as the margin of error decreases. Going from ±5% to ±1% multiplies the sample size by about 25 times. This is why national polls that report ±2% margins typically survey over 2,000 people.

Practical Guidelines for Research Design

Calculating the mathematically required sample size is just one step in designing a successful survey. These practical guidelines help you bridge the gap between theoretical requirements and real-world data collection.

• Always calculate sample size before collecting data. Determining sample size after data collection (post-hoc power analysis) is widely considered poor practice because it does not change the precision you actually achieved. Plan your sample size during the design phase.
• Budget for non-response. Response rates for email surveys typically range from 10% to 30%, phone surveys from 5% to 15%, and in-person interviews from 50% to 80%. Divide your target completed sample by the expected response rate to determine how many people to contact initially.
• Consider subgroup analysis. If you plan to analyze results by subgroups (age, region, gender), each subgroup needs its own adequate sample size. A survey of 400 might be sufficient overall but only gives you 50 respondents per subgroup if you have 8 categories — often too few for meaningful analysis.
• Use pilot studies to estimate variability. If you do not know the population standard deviation or proportion, run a small pilot study of 20 to 50 respondents first. This gives you a reasonable estimate to plug into the sample size formula and helps identify problems with your survey design.
• Document your assumptions. Report the confidence level, margin of error, estimated proportion or standard deviation, and any adjustments you made for non-response or finite population. This transparency allows others to evaluate the credibility of your methodology.

Common Mistakes to Avoid

• Using population size as the primary driver. Many people assume that surveying a fixed percentage of the population (like 10%) is sufficient. In reality, the margin of error is primarily determined by the absolute sample size, not the sampling fraction. A sample of 385 provides ±5% precision whether the population is 5,000 or 5 million.
• Ignoring the effect of clustering. If your survey uses cluster sampling (sampling entire classrooms, hospitals, or neighborhoods), the effective sample size is smaller than the number of individual respondents because people within clusters tend to be more similar. Apply a design effect multiplier, typically between 1.5 and 3.0.
• Forgetting to round up. Always round up to the next whole number when the formula gives a non-integer. Rounding down gives you a slightly larger margin of error than intended. Rounding 384.16 down to 384 instead of up to 385 is a small error, but it violates your precision specification.
• Neglecting non-response bias. Increasing sample size to compensate for non-response addresses the precision problem but not the bias problem. If non-respondents systematically differ from respondents, even a very large sample will produce biased estimates. Invest in follow-up strategies and response rate improvement.
• Using p = 0.5 when you have better information. While p = 0.5 is appropriately conservative when you have no prior knowledge, using it when you know the true proportion is around 0.1 or 0.9 wastes resources. A more accurate estimate of p reduces the required sample size substantially.

Last updated: February 23, 2026