Sample Size Calculator for a Mean
How many responses do you need to estimate an average? Enter the expected standard deviation and the margin of error you can accept.
How to enter your data: This calculator uses three simple boxes, not a pasted list. Type one number for the expected standard deviation, type one number for the margin of error (the plus-or-minus amount you can accept), and choose a confidence level from the dropdown (95% is the usual choice). Keep both numbers in the same unit as the thing you are measuring, for example points on a 1 to 10 score.
The Sample Size Calculator for a Mean tells you how many responses you need to collect so that a survey average, such as an average rating, average waiting time, or average spend, is accurate enough to trust. You enter how spread out you expect the answers to be, how close to the true average you want to land, and how sure you want to be. It gives back one number: the smallest number of responses you should gather.
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Where it is used
- HR staff: An HR officer works out how many employees to survey so the average staff happiness score, marked out of 10, can be trusted.
- Teachers: A teacher checks how many pupils to test so the class average mark is a reliable figure and not just luck.
- Small-business owners: A cafe owner finds how many customers to ask so the average spend per visit is accurate before making stock decisions.
Estimating a mean vs a proportion
When your key metric is an average (such as a mean satisfaction score) rather than a percentage, sample size depends on how variable the responses are. A larger expected standard deviation requires a larger sample.
When should you use it?
Use this before you send out a survey when the thing you care about is an average, not a percentage. Good examples are an average satisfaction score, an average waiting time, an average spend, or an average test mark. The calculator tells you the smallest number of responses to collect so that average is worth trusting. If your main question is a yes or no, or a share such as "what percent said yes", use the plain sample size calculator instead. Run this while planning, so you know your target before you start collecting.
What does the result mean?
The result is a single number: the fewest completed responses you need to collect. Reach that number and your survey's average should land within the margin of error you asked for, as often as your confidence level promises. For example, at 95% confidence you can expect the true average to sit inside your margin about 95 times out of 100. There is no single "correct" number, because it changes with your inputs. A 95% confidence level is the widely used standard, so most people leave it there.
Mistakes to avoid
Do not guess the standard deviation wildly, because it strongly changes the answer; base it on a small trial run or past data. Keep every number in the same unit, so if scores run 1 to 10, enter the spread and margin in points, not percentages. Do not set the margin of error to zero or a tiny value, as that demands a huge sample. Remember the result is a minimum, so expect some people not to reply and invite a few extra. Finally, do not use this tool for percentages; use the proportion sample size calculator for those.
How to use this calculator
- In the Expected standard deviation box, type how much you think the answers will vary, for example 2 for scores out of 10.
- In the Margin of error box, type how close to the true average you need to be, for example 0.5 points.
- Pick your confidence level from the dropdown; 95% is the usual choice.
- Read the Required sample size, which is the fewest responses you need to collect.
Worked example
Say a company measures staff happiness on a 1 to 10 scale. From a quick trial, scores vary by about 2 points (the standard deviation), and the team wants the average to be within 0.5 points of the true figure, at 95% confidence. Entering a standard deviation of 2, a margin of error of 0.5, and 95% confidence gives a required sample size of 62 responses.
Frequently asked questions
What do I type in the Expected standard deviation box?
Enter one number showing how much you expect the answers to vary. A bigger number means answers are spread out; a smaller number means they sit close to the average.
Where do I get the standard deviation if I have never run this survey?
Do a small trial with a handful of people and put those answers into our Standard Deviation Calculator, or borrow a figure from a past survey or a similar published study. A rough estimate is fine to start with.
What should I put for the margin of error?
This is how close you want your average to the true average, in the same units you are measuring. For scores out of 10 you might accept plus or minus 0.5 points. A smaller margin is more precise but needs more responses.
Which confidence level should I choose?
95% is the common default and is fine for most surveys. A higher level like 99% means you want to be more certain and needs more responses; a lower level like 90% needs fewer but is less sure.
What does the final number tell me?
It is the smallest number of completed responses you should collect. Gather at least that many and your average should be accurate within your margin of error. It is a minimum, so collecting a few extra is wise.
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