Measure survey uncertainty with flexible statistical inputs. Build clearer intervals, compare sample sizes, visualize precision trends, and export results quickly.
This page uses a single-column layout. The input grid adapts by screen size.
The chart shows how margin of error changes with sample size.
These examples help compare sample size effects under the current assumptions.
| Sample Size | Point Estimate | Margin of Error | Confidence Interval |
|---|---|---|---|
| 100 | 50.00% | 9.80% | 40.20% to 59.80% |
| 250 | 50.00% | 6.20% | 43.80% to 56.20% |
| 400 | 50.00% | 4.90% | 45.10% to 54.90% |
| 800 | 50.00% | 3.46% | 46.54% to 53.46% |
| 1200 | 50.00% | 2.83% | 47.17% to 52.83% |
For proportions: MOE = z × √(p(1-p)/n) × FPC × √DEFF
For means: MOE = z × (σ/√n) × FPC × √DEFF
Where: z is the critical value from the confidence level.
p is the observed sample proportion.
σ is the known or assumed standard deviation.
n is the sample size.
FPC = √((N-n)/(N-1)) when population size N is finite.
DEFF adjusts uncertainty for complex sample designs.
Choose whether you are estimating a proportion or a mean.
Enter your sample size and confidence level.
Add population size only when finite correction matters.
Use design effect above 1 for complex surveys.
For proportions, enter the observed proportion from 0 to 1.
For means, enter the sample mean and standard deviation.
Submit the form to view the margin, interval, and chart.
Download results as CSV or PDF when needed.
Margin of error measures expected sampling uncertainty around an estimate. Smaller values indicate more precision. It is commonly reported with surveys, polls, and experiments.
Larger samples reduce standard error. That reduction narrows the confidence interval and lowers margin of error. The improvement slows as sample size becomes very large.
Use proportion mode for yes-no outcomes, conversion rates, approval shares, defect rates, or any result expressed as a fraction or percentage.
Use mean mode for averages like income, response time, score, or weight. You need a sample mean and a known or assumed standard deviation.
Finite population correction reduces margin of error when a sample is a meaningful fraction of the total population. It matters more when sampling without replacement.
Design effect adjusts the variance for clustered, weighted, or stratified survey designs. A value above 1 increases uncertainty compared with simple random sampling.
Not always. Higher confidence gives wider intervals. Lower confidence gives tighter intervals. Choose the level that matches the decision risk and reporting standard.
This page focuses on margin of error from a given sample. However, you can compare graph points and examples to judge how much larger a sample may help.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.