Sample Size Calculator
Find out how many responses you need to collect. Set your confidence level and the margin of error you can tolerate to get the required sample size.
How to enter your data: This tool uses three separate boxes, not a list to paste. Type the population size in the first box, or leave it blank if the group is very large or unknown. Then pick a confidence level from the dropdown and type the margin of error as a percentage. The required sample size updates on its own as you change the boxes, so there is nothing to submit.
The Sample Size Calculator tells you how many completed survey responses you need before you can trust the results. You choose how sure you want to be, called the confidence level, and how much give or take you can accept in the answers, called the margin of error. It then gives you a single target number of responses to collect, so you avoid gathering too few to be reliable, or far more than you actually need.
Built into PaperSurvey.io
Skip the copy-paste. Scan your paper or web surveys and PaperSurvey computes these metrics automatically on your real data, ready to export to Excel, SPSS and R.
Where it is used
- Teachers and school staff: A teacher works out how many parents need to reply to a school survey before the results fairly stand in for all families.
- Small-business owners: A cafe owner finds how many customers must fill in a feedback card before it is safe to act on what they say.
- Event organisers: A conference organiser checks how many attendees to survey so the satisfaction scores reflect the whole crowd, not just a vocal few.
How many survey responses do you need?
The right sample size depends on how confident you want to be and how precise you need the results to be. This calculator uses Cochran’s formula with a finite population correction, the same approach used across academic and market research.
Remember your response rate
The number here is the number of completed responses you need. To know how many people to invite, divide it by your expected response rate. Paper surveys typically achieve far higher response rates than email, so you need to reach fewer people to hit the same sample size.
When should you use it?
Use it while you are still planning, before you start collecting responses. It answers the simple question of how many replies are enough, so you do not gather too few and end up with shaky results, or waste effort chasing far more than you need. It suits any survey where the answers are meant to stand in for a larger group, such as customers, students, staff or event guests. If you already have your responses and want to check how solid they are, use the margin of error calculator instead.
What does the result mean?
The big number is how many completed responses you should aim to collect. Reaching it means your results are precise enough for the confidence level and margin of error you picked. A very common standard is 95 percent confidence with a margin of error of plus or minus 5 percent, which for a large group works out at roughly 385 responses. A smaller margin of error raises the number of responses needed, while a larger one lowers it. Remember, the number counts finished replies, not how many people you invite.
Mistakes to avoid
Do not treat the number as how many people to invite. Some people never reply, so you should invite more than the target. For example, if you expect half to respond, invite about double. Do not set the margin of error to a tiny value like plus or minus 1 percent without a real reason, as it can demand thousands of responses. Do not guess the population. Use the real size of the group you care about, or leave it blank if it is very large or unknown.
How to use this calculator
- Type your population size in the first box, or leave it blank if the group is very large or unknown.
- Choose a confidence level from the dropdown, where 95 percent is the standard, safe choice.
- Type the margin of error you can accept as a percentage, for example 5 for plus or minus 5 percent.
- Read the required sample size, which updates on its own, as the number of completed responses to aim for.
Worked example
A shop owner wants to survey customers with 95 percent confidence and a margin of error of plus or minus 5 percent, and leaves the population blank because there are many customers. The calculator shows about 385, so the owner should aim for 385 completed responses. If only about half of customers usually reply, the owner should hand out or send around 770 forms to reach that target.
Frequently asked questions
Why does the population size barely change the result for large populations?
Above roughly 20,000 people the required sample size levels off. Precision depends far more on the number of responses than on the size of the population.
What response distribution should I use?
This calculator uses 50%, which requires the largest sample and is the safest choice when you do not know how answers will split.
What do I type in the population box?
Put the total size of the group you want to learn about, such as your number of customers, students or staff. If that group is very large, or you are not sure, just leave the box blank.
What is the confidence level?
It is how sure you want to be that your results reflect the whole group. 95 percent is the usual choice and roughly means you would land close to the true figure 95 times out of 100 if you repeated the survey.
What is the margin of error?
It is how much give or take you accept in the results. A margin of plus or minus 5 percent means a result of 60 percent could really be anywhere from 55 to 65 percent. Smaller margins need more responses.
What does the result number tell me?
It is the number of completed responses you should aim to collect. Reach it and your results will be about as precise as the settings you chose.
How many people should I invite to hit that number?
Divide the number by the share you expect to reply. If you expect half to answer, invite about twice the target. Paper surveys handed out in person usually get far more replies than email.
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