Sample Size Calculator

How to Use the Sample Size Calculator

Select your desired confidence level from the dropdown (90%, 95%, or 99%), enter the margin of error as a percentage, and optionally adjust the population proportion. The calculator instantly returns the required sample size and the corresponding Z-score. Results update in real time, so you can experiment with different parameters to see how they affect the number of respondents you need.

Determining the right sample size before collecting data is one of the most important steps in any survey or research study. A sample that is too small produces unreliable results, while one that is too large wastes time and resources. This calculator takes the guesswork out of the process by applying the standard statistical formula used by researchers worldwide.

Understanding the Sample Size Formula

The formula for calculating sample size for a proportion is n = (Z² × p × (1 − p)) / E², where Z is the Z-score for the chosen confidence level, p is the estimated population proportion (expressed as a decimal), and E is the margin of error (also as a decimal). This formula assumes an infinite population. For finite populations, apply the finite population correction: n_adj = n / (1 + (n − 1) / N), where N is the population size.

Confidence Level and Z-Score

The confidence level tells you how certain you can be that the true value lies within your margin of error. A 95% confidence level uses a Z-score of 1.96, meaning you are capturing 95% of the normal distribution. Increasing to 99% (Z = 2.576) provides more certainty but requires a larger sample. Dropping to 90% (Z = 1.645) reduces the required sample size at the cost of less certainty. In most social science and market research, 95% is the standard choice.

Practical Tips for Researchers

Always round the sample size up to the next whole number to maintain at least the stated confidence level. If you expect survey non-response, inflate the sample size accordingly. A common practice is to multiply by 1 / (expected response rate). For example, if you need 385 responses and expect a 70% response rate, send the survey to at least 385 / 0.70 = 550 people. Using 50% as the population proportion is the safest default when you have no prior data.

Frequently Asked Questions

How do you calculate sample size?

Sample size is calculated using the formula n = (Z² × p × (1 − p)) / E², where Z is the Z-score for your confidence level, p is the estimated population proportion, and E is the desired margin of error. For a 95% confidence level with 5% margin of error and 50% proportion, the sample size is 385.

What is a confidence level?

The confidence level represents the probability that the true population parameter falls within the margin of error of your sample result. A 95% confidence level means that if you repeated the survey 100 times, approximately 95 of those samples would contain the true population value.

What is margin of error?

Margin of error is the range within which the true population value is expected to fall. A margin of error of 5% means your results could be up to 5 percentage points above or below the reported figure. Smaller margins of error require larger sample sizes but produce more precise results.

What is the Z-score used for in sample size calculations?

The Z-score corresponds to the confidence level and represents the number of standard deviations from the mean in a normal distribution. For 90% confidence the Z-score is 1.645, for 95% it is 1.96, and for 99% it is 2.576.

Why use 50% as the default population proportion?

A proportion of 50% (0.5) maximises the expression p × (1 − p), which produces the largest possible sample size. This is the most conservative estimate and guarantees the sample is large enough regardless of the actual proportion.