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Survey sample size calculator

Find how many responses you need for a given margin of error, or how precise the answers you already have are. Includes the correction for small groups like your client list.

What do you want to find?
Confidence level

How far the result may be from the true value, e.g. 5 means ± 5 points.

Leave 50 if you don't know. It gives the largest, safest sample.

Everyone you could survey, e.g. your 800 customers. Leave empty for a very large group.

From your past surveys, to see how many people to invite.

Responses needed

385

Without population correction
385
Confidence
95%
Margin of error
± 5.0%

Assumes a simple random sample. People who choose to answer can differ from those who don't, and no formula fixes that. Nothing you type leaves your browser.

The formula

n₀ = z² × p × (1 − p) ÷ e², where z depends on the confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the proportion you expect and e is the margin of error as a decimal. At 95% confidence, p = 0.5 and e = 0.05: 1.96² × 0.25 ÷ 0.0025 = 384.2, so 385 responses.

Finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N), where N is the size of the group. It matters when you survey a group you can count, like your clients or your newsletter list. For 1,000 people the 385 drops to 278; for 200 people, to 132.

What the inputs mean

  • Confidence level: how sure you want to be that the true value is inside your margin. 95% is the usual choice.
  • Margin of error: the ± around your result. If 60% of answers say yes with a ± 5 margin, the true share is likely between 55% and 65%.
  • Expected proportion: your guess of the answer. 50% is the safe default because it needs the most responses.
  • Population: everyone you could survey. Leave it empty if it's large (tens of thousands or more): the correction barely changes the result.

What no formula fixes

The math assumes everyone had the same chance to answer. If only your happiest clients reply, 385 responses won't give you a ± 5 picture of all clients. Send the survey to everyone in the group, remind once, and keep it short. For a satisfaction survey, the NPS calculator turns the answers into a score with its own margin of error.

IN SHORT

For a large population, the sample size is z² × p × (1 − p) ÷ e², where z is 1.96 at 95% confidence, p is the expected proportion (use 50% if unsure) and e is the margin of error. At 95% and ± 5% that's 385 responses. For a small group, divide by 1 + (n − 1) ÷ N: with 1,000 customers you need 278. The calculator also turns a number of answers back into a margin of error.

Prices and limits as of .

Questions

How do you calculate sample size for a survey?
n = z² × p × (1 − p) ÷ e². Use z = 1.645 for 90% confidence, 1.96 for 95% and 2.576 for 99%. With p = 0.5 and e = 0.05 at 95%, n = 384.2, rounded up to 385.
What is the finite population correction?
When the group you survey is small, each answer covers a bigger share of it, so you need fewer. The corrected size is n ÷ (1 + (n − 1) ÷ N). For 500 clients at 95% and ± 5% you need 218, not 385.
Why use 50% as the expected proportion?
p × (1 − p) is largest at 50%, so it gives the biggest, safest sample. Use a different value only if a past survey tells you roughly what to expect.
What margin of error should I use?
± 5 points at 95% confidence is the usual default. Use ± 3 if small differences matter to your decision, or ± 10 for a quick check with a small audience.
How do I calculate the margin of error from my sample size?
e = z × √(p × (1 − p) ÷ n). With 400 answers at 95% and p = 0.5, e is about ± 4.9 points. Switch the calculator to Margin of error to see it for your numbers.
How many people should I invite?
Divide the responses you need by your expected response rate. If you need 218 answers and about 25% of people reply, invite 872. Enter your response rate to see it.

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