Margin of Error
Estimate margin of error and confidence interval for proportion-based survey results.
Survey Parameters
Calculator guide
Margin of Error Calculator
The margin of error calculator estimates a confidence interval for a proportion from a sample size, estimated proportion, and confidence level. It uses a standard normal approximation, so it is most useful as a basic planning or learning aid when the sample was collected in a suitable way.
How to use the calculator
- 1Enter the sample size as the number of observations and enter the estimated proportion between 0 and 1.
- 2Choose the confidence level offered by the tool, such as 90%, 95%, or 99%.
- 3Read the margin of error and implied interval. Check that the estimate stays within a valid probability range and that the sample design supports the assumptions.
Important details to understand
1.Start with the right inputs
Check every number, date, unit, and selected mode before calculating. A correct formula can still give a misleading answer when an input is missing, entered in the wrong unit, or based on a different time period.
2.Know what the calculation includes
The method below describes what this tool uses. Real situations can involve extra rules, costs, calendar conventions, or personal details that are not part of the form, so compare the assumptions with your actual question.
3.Read the unit and rounding
Look at the label as well as the displayed number. Rounding can change the last digits, and results in different units or time periods are not directly comparable until you convert them consistently.
4.Treat the result as a useful check
Use the output to understand a calculation, explore a scenario, or make an initial estimate. When a result affects a formal deadline, a health decision, a contract, or a large payment, confirm it with the relevant source or qualified professional.
How the calculation works
The tool uses the Wald approximation: standard error = √[p(1−p)/n], then margin of error = z×standard error. The selected confidence level determines z. The interval is the estimate plus or minus that margin, expressed as a percentage in the output.
A worked example
For an estimated proportion of 0.50 and a sample of 400 at 95% confidence, the standard error is 0.025 and the margin is about 1.96×0.025 = 0.049, or 4.9 percentage points.
When this calculator is useful
Learn how sample size and confidence level affect uncertainty, or make a rough survey planning estimate. A larger sample generally narrows this formula's margin when other inputs stay the same.
Planning ahead
Try a few realistic input values to see how a change in an amount, measurement, date, or rate affects the answer.
Learning the method
Follow the explanation and example to understand which inputs matter and how they are combined.
Checking your own work
Compare the result with a hand calculation, a worksheet, or a trusted source when you need an independent sense check.
Explaining a result
Keep the original inputs and units with the output so another person can understand what was calculated.
Tips for a more reliable answer
- Enter the values from the same source and keep units consistent throughout the calculation.
- Check that you selected the mode or option that matches the question you are trying to answer.
- Use the worked example to confirm you understand the inputs and the kind of result the tool returns.
- Save the inputs with the result so you can review or repeat the calculation later.
Limitations and assumptions
This estimate does not correct for non-random sampling, nonresponse bias, clustering, weighting, or finite population size. The Wald interval can perform poorly for small samples or proportions near 0 or 1. Consult a statistician for consequential survey reporting.
Every result depends on the information entered and the method described above. The calculator cannot confirm that the inputs are complete or that its assumptions match a particular provider, policy, location, body, or real-world situation.
Frequently asked questions
Does 95% confidence mean a 95% chance this one interval is correct?
In frequentist terms, the method would cover the true proportion in about 95% of repeated comparable samples under its assumptions.
Does margin of error include every kind of survey error?
No. It describes sampling variability under a model, not bias or measurement problems.
Can I use a small sample?
The formula can return a number, but small samples may make this approximation unreliable.
Why might my result differ from another calculator?
Tools can use different assumptions, units, date conventions, included costs, or rounding rules. Compare the inputs and method descriptions before deciding that one result is wrong.
What should I check if the answer looks wrong?
Review the selected mode, each entered value, the units, and any optional fields. Then compare a simple example with the method described in this guide.
Can I rely on the result for an official or high-impact decision?
Use the result as an estimate or explanation and check the limitations listed for this tool. Confirm important decisions with the relevant official source or a qualified professional.