About Margin of Error Calculator
This margin of error calculator works out the plus-or-minus figure for a proportion from the sample size, the confidence level and the expected proportion, 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 margin of error is the half-width of the confidence interval. A poll that reports 52% with a margin of 3 points is saying the true value is probably between 49% and 55%. The page opens on 1,000 responses at 95% confidence, which gives about ±3.1 points.
Because the margin shrinks with the square root of n, quadrupling the sample halves it. The curve shows the confidence level the margin is based on, and the working shows each substitution.
How to use Margin of Error Calculator
- Choose what to calculate: survey size, margin of error, a mean, or an A/B test.
- For a survey, set the confidence level, the margin of error in percentage points and the expected proportion. Use 50% if you are unsure.
- If your population is small, type its size to apply the finite population correction.
- For an A/B test, enter the baseline rate, the change to detect, the power and the significance level.
- Read 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.
Margin of error for a proportion
The finite population factor applies only when the population N is known and the sample is a sizeable share of it.
E = z · √( p(1 − p) / n )
E_finite = E · √( (N − n) / (N − 1) )Worked examples
500 responses, 95%, p = 50% gives ±4.383 points
1,000 responses, 95%, p = 50% gives ±3.099 points
385 responses, 95%, p = 50% gives ±4.994 points
The ±5 points that the 385 rule is built on.
500 responses from a population of 1,000 gives ±3.101 points
The population correction cuts the margin when half the population answered.
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.
What is the margin of error?
It is the amount added to and subtracted from a sample result to give a confidence interval. It measures sampling error only, not bias from poor questions or non-response.
What proportion should I use?
Use the result you got if you are reporting a finding, or 50% for the worst case. The margin is largest at 50% and smaller for results near 0% or 100%.
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.
- Survey Sample Size CalculatorSet a confidence level, a margin of error and your population size to find how many responses to collect.
- 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.