Calculate your sample size

Find out how many people you need to respond to your survey for your sample size to be representative of a wider population.


What you need…

You’ll need to know the approximate size of the population you’ll be surveying, your confidence level for how representative responses will be, and also the margin of error for responses deviating from that of the wider population.

Sample size calculator FAQs

Everything you need to know about calculating sample size for your surveys and research.

What is sample size?

Sample size refers to the number of individuals selected from a larger population to represent it in a research study or survey. It determines the reliability and precision of the study’s findings, influencing the accuracy of conclusions drawn from the sample data.

Here’s some useful information about larger sample sizes and smaller samples:

Smaller sample sizes Larger sample sizes
Less precise Greater precision
Higher margin of error Lower margin of error
Less statistically significant More statistically significant
Limited generalization Enhanced generalization
More cost and time efficient Less cost and time efficient
Sample size

How do you calculate sampling size?

To calculate sample size, you typically follow these steps:

  1. Determine the Population Size: Identify the total number of individuals or elements in the population you’re studying.
  2. Choose the Confidence Level: Decide on the level of confidence you want in your study’s results. This is often expressed as a percentage, such as 95% or 99%.
  3. Select the Margin of Error: Determine the maximum acceptable difference between the sample estimate and the true population parameter. This is typically expressed as a percentage of the population parameter.
  4. Find the Z-score: Based on the chosen confidence level, find the corresponding Z-score from a standard normal distribution table.
  5. Plug Values into the Formula: Use the appropriate formula based on the study’s design and the parameter you’re estimating (e.g., mean, proportion). The formula will incorporate the population size, Z-score, and margin of error.
  6. Calculate the Sample Size: Perform the calculations using the formula to determine the required sample size.
  7. Round Up: Since you can’t have a fraction of an individual, round up the calculated sample size to the nearest whole number.

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Sample size formula

We see far too many confusing sample size formulas out there, so we’ve made ours as simple as possible.

Sample size formula = (Population size* (z-score)^2*0.5^2) / ((Population-1)*(Margin of error/100)^2+(z-score)^2*0.5^2)

For example, if you receive 1200 responses from a sample of 1500, you will have a response rate of 80.00%

What is population size?

Population size refers to the total number of individuals, elements, or units in the entire group or population that you are interested in studying.

It represents the entire pool from which a sample is drawn. In sample size calculations, knowing the population size is essential as it helps determine the required sample size to accurately represent the population.

What is margin of error?

The margin of error is a measure of the precision or uncertainty associated with the results obtained from a sample when estimating a population parameter.

It represents the maximum amount by which the sample result may differ from the true value of the population parameter.

Margin of error formula: Margin of error = Z * √ ((sample proportion * (1-sample proportion)) / sample size) * √ ((population size – sample size)/(population size-1))

Margin of error is typically expressed as a percentage and is influenced by factors such as sample size, variability within the population, and the chosen confidence level. A smaller margin of error indicates higher precision and confidence in the sample estimate.

Not sure what your margin of error is? Use our margin of error calculator.

What is confidence level?

The confidence level is the probability that the confidence interval, calculated from a sample, contains the true population parameter. It is expressed as a percentage and represents the level of certainty or reliability we have in our sample estimate.

For example, a 95% confidence level means that if we were to conduct the same study multiple times and calculate confidence intervals, we would expect about 95% of those intervals to contain the true population parameter.

Each confidence level is also associated with a z-score. The Z-score, also known as the standard score, is a statistical measurement that quantifies how many standard deviations a data point is from the mean of the dataset.

You can use our z-score table below to determine the score associated with each confidence level.

Confidence level z-score
80% 1.28
85% 1.44
90% 1.65
95% 1.96
99% 2.58
Z-score table

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