📊 Statistics & Probability
Margin of Error Calculator
Calculate margin of error for any survey or poll. Free MOE calculator with confidence level options.
What This Calculator Tells You
The margin of error tells you how far a survey or poll result could be from the true value for the whole population, purely because you asked a sample rather than everyone. When a poll says '52% ± 3%', the ± 3% is the margin of error.
Enter your sample proportion, sample size and confidence level to get the margin of error and the z-critical value behind it.
What to Enter
- Sample proportion (0–1) — the share who gave a particular answer, as a decimal (52% = 0.52). If you are planning a survey and do not know it yet, use 0.5 — it gives the largest, most cautious margin.
- Sample size — the number of completed responses.
- Confidence (%) — usually 95. Use 90 for a narrower range with less certainty, or 99 for more certainty.
Worked Examples
1. A national poll
52% support among 1,000 respondents at 95% confidence.
- Margin of error ±3.10% → true support likely between about 48.9% and 55.1%.
2. Quadrupling the sample halves the error
p = 0.5 at 95% confidence.
- 400 responses: ±4.90%.
- 1,600 responses: ±2.45%. Precision improves with the square root of sample size, so gains get expensive.
3. A customer survey at 90% confidence
30% of 250 customers want a feature.
- ±4.77% (z = 1.645).
How It’s Calculated
- z: Z-score (standard normal)
- p: Sample proportion / p-value
- n: Number of periods or sample size
How to Read Your Result
- ±3% or less is typical for professional polls with about 1,000 responses.
- ±5% is often acceptable for internal customer surveys.
- Overlapping ranges: if two results' margins overlap a lot, the difference may not be real.
- Subgroups have larger margins. 200 people out of a 1,000-person poll have a margin near ±7%.
Common Mistakes to Avoid
- Applying it to non-random samples. Opt-in website polls have unknown bias that no formula fixes.
- Entering 52 instead of 0.52 for the proportion.
- Ignoring non-response bias — the margin only covers random sampling error.
- Reading subgroup results with the overall margin.
When to Use This Calculator
- Report survey results with an honest range.
- Check whether a poll lead is meaningful.
- Plan how many responses a survey needs.
- Explain uncertainty in research findings to non-statisticians.
Frequently Asked Questions
What is the margin of error formula?
MOE = z × √(p(1 − p) ÷ n), where z is the critical value for your confidence level (1.96 for 95%), p the sample proportion and n the sample size.
What sample size gives a 5% margin of error?
About 385 responses at 95% confidence with p = 0.5. For ±3%, about 1,068. Use the sample size calculator to plan.
Does population size matter?
Only when the sample is a large share of the population (over about 5%). For large populations, the margin depends almost entirely on sample size.
What does 95% confidence mean?
If you repeated the survey many times, about 95% of the ranges built this way would contain the true population value.
Do you store the values I enter?
No. All calculations happen in your browser. Your data never leaves your device.
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