Margin of Error Calculator
Use the Margin of Error Calculator. Enter Sample proportion (%) and Sample size for a clear result, formula explanation, and practical planning checks.
Margin of Error measurements
Enter your values, then calculate.
Result
How to calculate margin of error
This calculator finds the margin of error for a survey or poll based on sample proportion and sample size — the range within which the true population value is expected to fall, at a 95% confidence level.
How the calculation works
Margin of error = 1.96 × √((p×(1−p))÷n) × 100, where p is the sample proportion (as a decimal) and n is sample size. The 1.96 multiplier corresponds to a 95% confidence level.
Example
A sample proportion of 50% from a sample of 1,000: 1.96×√(0.5×0.5÷1,000)×100 ≈ 1.96×0.0158×100 ≈ 3.1%.
Frequently asked questions
How is Result calculated?
Result = 1.96 × sqrt(([Sample proportion] ÷ 100) × (1 − [Sample proportion] ÷ 100) ÷ [Sample size]) × 100.
Is the Margin of Error Calculator free to use?
Yes — every calculator on Simple Calculator Tools is free, runs in your browser, and does not require an account.
Margin of Error Calculator
Margin of error = 1.96 × √((p×(1−p))÷n) × 100, where p is the sample proportion (as a decimal) and n is sample size. The 1.96 multiplier corresponds to a 95% confidence level.
Let's understand your margin of error result.
Calculate a result above and this guide will help you interpret it using this calculator's own formula and explanation.
Pro Tips for Margin of Error
- Margin of error is largest when the sample proportion is near 50% and shrinks as it approaches 0% or 100% — this is a mathematical property of the formula, not a data quality issue.
- Larger sample sizes reduce margin of error, but with diminishing returns — quadrupling sample size only halves the margin of error, since the formula depends on the square root of sample size.
Common Margin of Error Mistakes to Avoid
- Assuming margin of error is the same across every reported percentage in the same survey, when it actually varies slightly depending on how close each specific percentage is to 50%.
When to Use This Calculator
This calculator finds the margin of error for a survey or poll based on sample proportion and sample size — the range within which the true population value is expected to fall, at a 95% confidence level.