Sample Size Calculator

About the Sample Size Calculator

Determines how many responses you need for a survey to achieve a given margin of error at a chosen confidence level, with an optional finite-population correction.

How to use this calculator

1. Choose your confidence level, then get the matching z value, such as 1.96 for 95%.
2. Enter an estimated proportion p, or use 0.5 if you do not know it because that gives the largest required sample.
3. Enter your desired margin of error e as a decimal, such as 0.04 for 4%.
4. Compute n with the formula, then round up to the next whole person because you cannot survey a fraction of a person.

The formula explained

The formula computes the minimum sample size needed to estimate a population proportion with a chosen margin of error, assuming a normal approximation. The value of p controls how variable the population is, and the margin of error sets how precise you want the estimate to be.

• n = required sample size
• z = z score for the chosen confidence level
• p = estimated population proportion
• e = desired margin of error, written as a decimal

Step by step method

1. Identify the confidence level and write down its z value.
2. Choose p, often 0.5 if no prior estimate is available.
3. Plug z, p, and e into \(n = \frac{z^2 p(1-p)}{e^2}\).
4. Round the result up to the next whole number.

Worked example

Problem. How many people should you survey to estimate a proportion with 95% confidence, a margin of error of 4%, and no prior estimate for p?

1. Use 95% confidence, so \(z = 1.96\). Set \(p = 0.5\) and \(e = 0.04\).
2. Substitute into the formula: \(n = \frac{1.96^2 \cdot 0.5(1-0.5)}{0.04^2} = \frac{3.8416 \cdot 0.25}{0.0016}\).
3. Compute \(n = 600.25\), then round up to 601.

Tips and common mistakes

• Always enter the margin of error as a decimal, so 5% becomes 0.05, not 5.
• If you do not know p, use 0.5, because it gives the safest, largest sample size estimate.

Frequently asked questions