Skip to content

Sample Size Calculator

Determine the required sample size for surveys given confidence level, margin of error, and population.

Loading...
1. Select your desired confidence level from the options - 90%, 95%, or 99%. 2. Set the acceptable margin of error as a percentage, such as 3% or 5%. 3. Enter the total population size if known, or leave it blank for a large or unknown population. 4. Review the calculated minimum sample size required to achieve statistically valid results. 5. Adjust the confidence level and margin of error to see how they trade off against the required sample size.

About This Tool

Collecting data is expensive and time-consuming, so knowing exactly how many responses you need before you start is critical for any survey or research project. This sample size calculator tells you the minimum number of participants required to achieve statistically meaningful results based on your desired confidence level, acceptable margin of error, and estimated population size. No more guessing or collecting too few (or too many) responses.

The calculator supports the most common confidence levels (90%, 95%, and 99%) and lets you set any margin of error from 1% to 10%. If you know the population size, enter it for a finite population correction - this is especially important for smaller populations where the required sample size can be significantly reduced. For very large or unknown populations, the calculator uses the standard infinite population formula.

Understanding these inputs is key to designing effective research. A higher confidence level means you need more respondents. A smaller margin of error also increases the required sample size. This tool shows you the trade-offs clearly, helping you balance statistical rigor with practical constraints like budget and timeline. Whether you are conducting market research, academic studies, quality assurance testing, or public opinion polling, this calculator ensures your sample is large enough to draw valid conclusions.

Formula / How It Works

n = (z^2 x p x (1-p)) / e^2 | Finite correction: n_adj = n / (1 + (n-1)/N) | z(95%) = 1.96, z(99%) = 2.576

Frequently Asked Questions

The confidence level represents how certain you want to be that the true population value falls within your margin of error. A 95% confidence level means that if you repeated the survey 100 times, approximately 95 of those results would contain the true population value. Common levels are 90%, 95%, and 99%. Higher confidence requires larger sample sizes.
Margin of error is the range of values above and below a survey result within which the true population value is likely to fall. A margin of error of plus or minus 3% on a result of 60% means the true value is likely between 57% and 63%. Smaller margins of error provide more precise results but require larger samples.
Yes, but mainly for smaller populations. For populations above about 20,000, the required sample size barely changes with population size. For a population of 500, you might need 217 responses for 95% confidence with 5% margin of error. For a population of 1,000,000, you would need about 384 - not much more. This is because of the finite population correction factor.
For an infinite population: n = (z^2 x p x (1-p)) / e^2, where z is the z-score for your confidence level (1.96 for 95%), p is the expected proportion (0.5 for maximum variability), and e is the margin of error. For a finite population N: n_adjusted = n / (1 + (n - 1) / N).
Response rates vary widely by method. Email surveys typically get 10-30%, phone surveys 10-50%, and in-person surveys 50-80%. Plan to invite more people than your required sample size. If you need 400 responses and expect a 25% response rate, you should send the survey to at least 1,600 people.

Related Tools

Normal Distribution Calculator

Calculate z-scores, percentiles, and probabilities with an interactive bell curve visualization.

Statistics and Data

Standard Deviation Calculator

Calculate mean, variance, and standard deviation for both population and sample data sets instantly.

Statistics and Data

Probability Calculator

Calculate basic, conditional, and Bayesian probability with visual aids and step-by-step solutions.

Statistics and Data

Percentage Calculator

Calculate percentages, percentage change, difference, increase, and decrease instantly.

Math and Numbers

Mean Median Mode Calculator

Find the mean, median, mode, and range of any data set with a frequency table and distribution display.

Statistics and Data

Grade Calculator

Calculate weighted course grades with customizable assignment categories, points, and what-if grade scenarios.

Education and Academic