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Survey Sample Size Calculator

Set a confidence level, a margin of error and your population size to find how many responses to collect.

Calculate
Confidence level
Use 50 if you do not know. It gives the largest, safest sample.
Leave empty for a very large population. A small population needs a smaller sample.

Required sample size

278
Before population correction
384.146
Margin of error
±5 points
Expected proportion
50%
Critical value (z)
1.96

You need at least 278 completed responses for a margin of error of plus or minus 5 percentage points at 95% confidence (using p = 50%, the most cautious choice), from a population of 1000. Plan for non-response: divide 278 by your expected response rate to know how many people to invite.

Confidence level on the normal curve

Confidence level on the normal curveConfidence level on the normal curve. The central region is shaded. -4-3-2-101234z

The shaded middle is the confidence level. The critical value z at its edges scales the margin of error.

Step-by-step working

  1. 1Critical value
    zα/2 for 95%z_{\alpha/2}\ \text{for}\ 95\%zα/2​ for 95%
    ↓
    z=1.96z = 1.96z=1.96
  2. 2Sample size, large population
    n0=z2 p(1−p)E2n_0 = \dfrac{z^2\,p(1-p)}{E^2}n0​=E2z2p(1−p)​
    ↓
    n0=1.962×0.5(1−0.5)0.052=384.146n_0 = \dfrac{1.96^2\times 0.5(1-0.5)}{0.05^2} = 384.146n0​=0.0521.962×0.5(1−0.5)​=384.146
  3. 3Finite population correction
    n=n01+(n0−1)/Nn = \dfrac{n_0}{1 + (n_0 - 1)/N}n=1+(n0​−1)/Nn0​​
    ↓
    n=384.1461+(384.146−1)/1000n = \dfrac{384.146}{1 + (384.146 - 1)/1000}n=1+(384.146−1)/1000384.146​
  4. 4Round up
    n=⌈ ⋅ ⌉n = \lceil\,\cdot\,\rceiln=⌈⋅⌉
    ↓
    n=278n = 278n=278
  1. Tools
  2. Statistics
  3. Sample Size Calculator
  4. Survey Sample Size Calculator

About Survey Sample Size Calculator

This survey sample size calculator gives the number of completed responses you need to estimate a proportion within a chosen margin of error, with an optional finite population correction. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

The page opens on a population of 1,000 with a ±5 point margin at 95% confidence, which needs 278 responses rather than the 385 a very large population needs. Clear the population box to see the large-population answer.

The result is the number of completed answers. To plan invitations, divide it by your expected response rate. The table in the article lists the large-population sample size for common margins and confidence levels.

How to use Survey Sample Size Calculator

  1. 1Choose what to calculate: survey size, margin of error, a mean, or an A/B test.
  2. 2For a survey, set the confidence level, the margin of error in percentage points and the expected proportion. Use 50% if you are unsure.
  3. 3If your population is small, type its size to apply the finite population correction.
  4. 4For an A/B test, enter the baseline rate, the change to detect, the power and the significance level.
  5. 5Read the result, then open the working to copy the formula into your methods section.

Features

  • Survey sample size for a proportion at 90%, 95% or 99% confidence.
  • Margin of error for a given sample size, with finite population correction.
  • Sample size to estimate a mean from the standard deviation and the margin of error.
  • A/B test sample size per group from baseline rate, minimum detectable change, power and significance.
  • Finite population correction when the population is known and small.
  • A bell curve of the confidence level and step-by-step KaTeX working.

Survey sample size (Cochran)

Compute the large-population size, then shrink it for a known population N.

n0 = z² · p(1 − p) / E²
n = n0 / (1 + (n0 − 1) / N)

Worked examples

  • 95%, ±5 points, p = 50%, N = 1,000 → gives 278 responses

  • 95%, ±5 points, p = 50%, N = 10,000 → gives 370 responses

    Krejcie and Morgan (1970) list 278 and 370 for these two populations.

  • 95%, ±3 points, p = 50%, large population → gives 1068 responses

Privacy: how it works

  • All formulas run in your own browser tab. Nothing you type is sent to Ulkaa or to any other server.
  • There is no account and nothing is stored once you close the tab.

Tips

  • If you do not know the expected proportion, use 50%. It gives the largest sample and so a safe margin.
  • Smaller margins are expensive: moving from ±5 to ±2.5 points roughly quadruples the sample.
  • For an A/B test, decide the smallest change that would matter to the business. Detecting tiny lifts takes very large samples.
  • A population much larger than the sample barely changes the answer. The correction matters when the sample is more than about 5% of the population.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your numbers are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your numbers are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

How many survey responses do I need?

It depends on the margin of error, the confidence level and the population. For ±5 points at 95% in a large population it is 385, and for ±3 points it is 1,068.

Does the population size matter?

Only when it is small. Once the population is many times larger than the sample, the answer stops changing. For a population of 100,000 the answer is 383, close to the 385 for an unlimited population.

More Sample Size Calculator pages

  • Sample Size CalculatorFind how many responses a survey needs, the margin of error of a sample, or how many people an A/B test needs.
  • Margin of Error CalculatorType the sample size and get the margin of error for a survey result.
  • Sample Size for a Mean CalculatorEnter the standard deviation and the margin of error you can accept to find the number of observations.
  • A/B Test Sample Size CalculatorEnter your baseline conversion rate and the smallest lift you care about to find the sample per group.

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