Sample Size Calculator
Find how many respondents your survey needs for a chosen confidence level and margin of error.
Details
How much the survey result may miss by.
Required sample size
385
Respondents needed (always rounded up)
This works out how many responses a survey needs to reach a given confidence level and margin of error.
Enter the confidence level and margin you want, and optionally the population size, and it returns the number of completed responses required.
How many people you need to survey
Sample size is how many people you need to survey for the result to be trustworthy. It is decided by two choices you make and, surprisingly, almost not at all by how many people exist.
Confidence level is how sure you want to be that your result is close to the truth, usually 95%. Margin of error is how close, usually ±5%. Together they fix the number.
The counter-intuitive part is that population size barely matters. Surveying a town of 20,000 or a country of 300 million needs roughly the same sample, which is exactly why national polls survey about a thousand people.
Because the margin is squared on the bottom, halving it quadruples the sample. Going from ±5% to ±2.5% takes you from 385 to about 1,537.
What to enter
- Confidence level
- How often the true value would fall inside your margin if you repeated the survey. 95% is the standard choice.
- Margin of error (e)
- How much wobble you will accept, as a plus-or-minus percentage. ±5% is common; ±3% is used for tighter political polling.
- Population proportion (p)
- Your expected split. Leave it at 50% unless you have prior data, because 50% needs the largest sample and is therefore the safe assumption.
- Population size (N)
- Optional. It only changes the answer meaningfully for small populations, and the reason is explained below.
Sample needed at 95% confidence
- ±10% margin
- About 97 responses. Rough, but enough for a quick internal read.
- ±5% margin
- About 385. The usual standard for general surveys.
- ±3% margin
- About 1,068. Typical for published political polling.
- ±1% margin
- About 9,604. Rarely worth the cost outside major national research.
- Small populations
- For a group of 10,000, the ±5% requirement drops slightly to about 370.
What this assumes
Responses are a genuinely random sample of the population. This assumption does far more work than the arithmetic does.
The figure is completed responses, not invitations sent. Plan for your response rate on top.
How to calculate the sample size you need
Pick your confidence and margin, then the formula does the rest.
- z
- 1.96 for 95% confidence, 2.576 for 99%
- p
- Expected proportion, 0.5 when unknown
- e
- Margin of error as a decimal, so 5% is 0.05
Choose a confidence level. 95% is standard and gives z = 1.96.
Choose a margin of error. ±5% is usual. Tighter margins cost sharply more responses.
Use p = 0.5 if unsure. It produces the largest sample, so it is the conservative choice.
Adjust for a small population. Only worth doing if your sample would be a large fraction of the whole group.
See a worked example: a survey at 95% confidence and ±5%
- Confidence
- 95%, so z = 1.96
- Margin
- ±5%, so e = 0.05
- Proportion
- 0.5, unknown
Top: 1.96² × 0.5 × 0.5 = 3.8416 × 0.25 = 0.9604.
Bottom: 0.05² = 0.0025.
0.9604 ÷ 0.0025 = 384.16, which rounds up to 385.
That 385 holds whether the population is 50,000 or 50 million. For a population of just 10,000 it falls slightly, to about 370.
385 completed responses
Frequently asked questions
Because a random sample's accuracy comes from how many people you asked, not what fraction of the group they represent. Once a population is large, adding more people to it changes almost nothing.
It is the reason a well-conducted poll of 1,000 can describe a country of 300 million. The finite population correction only bites when your sample would be a sizeable share of the whole group.
±5% is the general standard and needs about 385 responses. Published political polling usually wants ±3%, which needs about 1,068.
Because the margin is squared in the formula, precision gets expensive fast. Halving the margin quadruples the sample, so ±1% needs roughly 9,600.
Use 50%. It maximises the required sample, so you cannot end up short.
If you have solid prior data showing a lopsided split, using it reduces the sample needed. At an expected 90/10 split the requirement drops to about 139 at ±5%.
No, it is the number of completed responses. Invitations need to be far higher.
At a 20% response rate, needing 385 completions means contacting around 1,925 people. Budget for that from the start rather than discovering it halfway through fieldwork.
No, and this is the most important limitation. Sample size controls random error only. Bias is a separate problem that more responses make worse, not better.
A survey that only reaches people who answer the phone at 2pm on a weekday is unrepresentative whether it has 400 responses or 40,000. Who you ask matters more than how many.
Problems people actually run into
Treating a large sample as proof of accuracy
The famous cautionary case is a 1936 US election poll with over two million responses that called the result completely wrong, because the sample was drawn from car and telephone owners during the Depression.
A smaller, properly random sample beat it comfortably. Size addresses random error; it does nothing whatsoever about who was left out.
Quoting a margin of error on a subgroup
A survey of 1,000 has a margin of about ±3% overall, but the 80 respondents in one age band have a margin closer to ±11%.
Every time you slice the data, the effective sample shrinks and the margin widens. Reporting subgroup findings at the headline margin overstates their reliability substantially.
Results are estimates for general information only and are not professional financial, medical, or legal advice. Read our full disclaimer.
Last updated: September 4, 2026