Free sample size calculator for surveys and polls. Enter population size, confidence level, margin of error and response distribution for the minimum responses you need.
Your results will appear here.
Enter your values and press Calculate.
Enter your population size (use 100,000 or more when it is unknown or very large), pick a confidence level, and set your margin of error and expected response distribution. The calculator converts your confidence level to its z-score, then uses Cochran's formula to calculate the base sample size and shrinks it with the finite population correction when your population is small. Every result is rounded up, since you cannot survey a fraction of a person.
This calculator uses Cochran's formula, the standard sample size formula for surveys that estimate a proportion (a percentage, such as the share of customers who are satisfied). The formula is n = Z² * p(1-p) / E². Z is the z-score for your confidence level: 1.645 for 90%, 1.96 for 95% and 2.576 for 99%. The variable p is the expected response distribution as a decimal (50% becomes 0.5), and E is the margin of error as a decimal (5% becomes 0.05).
Worked example: at 95% confidence with a 5% margin of error and p = 0.5, the calculation is n = 1.96² * 0.5 * 0.5 / 0.05² = 0.9604 / 0.0025 = 384.16, rounded up to 385 responses. That is where the famous 385 minimum survey sample comes from.
Step 1: enter your population size, the total group your survey represents. If the population is unknown or very large, enter 100,000 or more; the result barely changes beyond that point.
Step 2: pick a confidence level. 95% is the research standard; 90% needs fewer responses and 99% needs many more.
Step 3: set your margin of error. 5% is the usual choice for general surveys; use 3% or less for higher-stakes research.
Step 4: set the response distribution. If you have no prior estimate, keep 50%, the safe default.
Read the minimum sample size as a target to reach or beat, never as an exact number to stop at early.
The confidence level is how sure you want to be that your results reflect the true population value. A 95% confidence level means that if you repeated the survey 100 times, about 95 of those surveys would land within your margin of error of the true value.
Choose 95% for most surveys: it is the standard that academic journals, regulators and professional researchers accept. Choose 90% when resources are tight and the stakes are low, since it needs a smaller sample (271 vs 385 at a 5% margin of error). Choose 99% for high-stakes decisions such as medical or safety research, accepting that it needs about 73% more responses than 95% at the same margin of error (664 vs 385 at 5%).
Each confidence level maps to a z-score used in the formula: 90% uses 1.645, 95% uses 1.96 and 99% uses 2.576.
The margin of error is the range above and below your result inside which the true population value is likely to fall. If 60% of respondents prefer an option with a 5% margin of error, the true value is likely between 55% and 65%.
The margin of error sits under a square in the formula's denominator, so precision is expensive: halving the margin of error quadruples the required sample. At 95% confidence, a 5% margin of error needs 385 responses, a 3% margin needs 1,068 and a 1% margin needs 9,604.
For most decisions, 5% is acceptable and is the standard for public opinion polling. Use 3% for higher-precision research, 10% for quick internal pulse surveys where a smaller sample keeps costs down, and reserve 1% for national censuses or decisions where tiny differences matter.
For very large populations, size barely matters: a national poll needs about 1,000 respondents whether the country has 10 million or 300 million people. That is why the population field can stay at 100,000 when the true size is unknown.
When the population is small, the finite population correction shrinks the required sample, because sampling a large share of a small group gives you more information per response. The correction is n = n0 / (1 + (n0-1) / N), where n0 is the unadjusted sample size and N is the population.
The effect is meaningful below about 10,000 people. Starting from the classic 385 (95% confidence, 5% margin of error): a population of 10,000 needs 370, a population of 5,000 needs 357, a population of 2,000 needs 323, a population of 1,000 needs 278 and a population of 500 needs only 218. If the calculation ever returns a sample close to your full population, survey everyone instead: that is called a census.
The response distribution (also called the population proportion) is the share of people you expect to give a particular answer. In the formula it appears as p(1-p), and that product reaches its maximum of 0.25 exactly when p = 0.5. A larger product means a larger sample size, so 50% produces the biggest, most conservative answer.
Keep the default 50% whenever you have no reliable prior estimate. It guarantees the sample is large enough no matter how the answers actually split. Only use a different value when real evidence supports it: a pilot study or earlier survey showing 70% adoption lets you use 70% and plan a smaller sample. Never shrink the sample on a guess, because if the true split is closer to 50/50 than you assumed, your actual margin of error will be wider than planned.
Plan for non-response. The calculator gives you completed responses, but not everyone you invite will answer. If you need 385 completes and expect a 40% response rate, invite 385 / 0.40 = 963 people. Divide the required sample by your expected response rate to get the number of invitations to send.
Give subgroups their own calculations. If you want to compare results between groups (for example, new vs returning customers), each group must individually reach the minimum sample size. You cannot fix an underpowered subgroup after data collection ends, so build the quotas into the plan.
Always round up. A result of 384.16 means 385 responses, because 384 would leave the margin of error slightly wider than promised. The calculator rounds every result up for this reason.
For most general surveys, a good starting point is the standard answer of 385 responses: 95% confidence, a 5% margin of error and a 50% response distribution for a large population. If you want tighter precision, 95% confidence with a 3% margin of error needs 1,068 responses. Enter your own numbers above for the exact minimum your study needs.
Choose 95% for most surveys; it is the accepted standard in academic research, clinical studies and professional polling. Choose 90% when your budget is limited and the stakes are low (it needs about 30% fewer responses). Choose 99% for high-stakes medical, safety or regulatory decisions, accepting that it needs roughly 73% more responses than 95% at the same margin of error.
Plus or minus 5% is the standard for general surveys and public polling. Use 3% for higher-precision research, 1% for censuses or decisions where small differences matter, and 10% for quick internal surveys where speed and cost matter more than precision. Remember that halving the margin of error quadruples the sample size, so only demand tight margins when the decision justifies the cost.
Because 50% produces the largest, safest sample size. The formula multiplies p by (1-p), and that product peaks at p = 0.5. Any other value gives a smaller sample, which is only honest if real prior data supports it. When you do not know the true split, 50% guarantees the sample covers every possible outcome.
Barely, once the population is large: above about 100,000 people the finite population correction changes the answer by less than half a percent, which is why national polls need only around 1,000 respondents regardless of country size. Below about 10,000 people the correction matters: a population of 5,000 needs 357 instead of 385, and a population of 500 needs only 218, at 95% confidence with a 5% margin of error.
Yes. If you plan to compare groups, such as age bands or customer segments, each group must reach the minimum sample size on its own. A total sample of 385 split across four equal groups gives each group fewer than 100 responses, which cannot support the same confidence level and margin of error. Plan subgroup quotas before you start collecting data.
Yes. The calculator tells you how many completed responses you need, not how many people to contact. Divide the required sample by your expected response rate: 385 completes at a 40% response rate means sending 963 invitations. Skipping this step is one of the most common causes of underpowered surveys.
Because you cannot survey a fraction of a person, and rounding down would break the promise. A result of 384.16 needs 385 responses: collecting only 384 would leave the margin of error slightly wider than the one you planned for. The ceiling is the smallest whole sample that truly meets your requirements.
Sample size is simply how many responses your study collected. Minimum sample size is the smallest number that still meets your chosen confidence level and margin of error. This calculator returns the minimum; collecting more than the minimum is fine and only improves precision.
Survey everyone. When the population is very small, the finite population correction can return a number at or near the full population, which means sampling offers no real saving over a census. In that case, contacting every member of the population is the correct design.
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