Margin of Error Calculator
What precision did your sample actually buy? Compute the ± on any survey result.
Free · No signup · By the analysts at Blackridge Research · Updated 2026-07-18
Inputs
Results
What this means
Adjust the inputs to calculate.
About the Margin of Error Calculator
Margin of error tells you how much your sample results might differ from the true population value.
It answers: what precision did your sample actually buy?
Formula
ME = z × √(p(1-p)/n)
- ME
- — Margin of Error
- z
- — Z-score for confidence level
- p
- — Sample proportion
- n
- — Sample size
How to use this calculator
- 1
Enter your sample size
The number of responses you collected.
- 2
Enter your population size
Optional: enter your total population for finite population correction.
- 3
Choose your confidence level
Common choices: 90%, 95%, or 99%.
- 4
Enter sample proportion
The percentage from your sample (use 50% for maximum margin of error).
Example calculations
Customer satisfaction survey
You surveyed 500 customers and found 65% satisfaction. What's the margin of error at 95% confidence?
ME = 1.96 × √(0.65×0.35/500) = ±4.2%
- Margin of error:
- ±4.2%
- Confidence interval:
- 60.8% — 69.2%
- Lower bound:
- 60.8%
- Upper bound:
- 69.2%
The true satisfaction rate is between 60.8% and 69.2% with 95% confidence.
Interpreting your results
A smaller margin of error means more precise results. To reduce margin of error, increase your sample size.
The confidence interval gives you the range where the true population value is likely to fall.
A margin of error of ±5% or less is generally considered acceptable for business decisions.
Need the market data behind this calculator?
The Margin of Error Calculator is only as good as its inputs. Blackridge Research publishes syndicated market reports with vetted market sizes, growth rates, and competitive landscapes across 40+ industries — and builds custom studies when the shelf report doesn't exist.
Industry applications
Business
- Survey reporting: present results with their margin of error.
- Decision making: understand the precision of data driving decisions.
- Quality control: assess the precision of quality measurements.
Construction
- Quality surveys: report quality assessment results with margin of error.
- Safety surveys: understand the precision of safety culture measurements.
Research
- Research reporting: present margin of error with all survey findings.
- Data interpretation: assess whether observed differences are meaningful.
Common mistakes to avoid
-
✗ Ignoring margin of error in reporting
Always report the margin of error with survey results.
-
✗ Confusing margin of error with sample size
Sample size alone doesn't determine precision — the proportion matters too.
Frequently asked questions
›What is a good margin of error?
±5% is generally considered acceptable. ±3% is excellent.
›How can I reduce margin of error?
Increase your sample size or use a lower confidence level.
Glossary
- Margin of error:
- The range within which the true population value is likely to fall.
- Confidence interval:
- The range of values that likely contains the true population value.
- Confidence level:
- The probability that the confidence interval contains the true population value.
Explore more free tools
Sample Size Calculator
How many survey responses do you need? Cochran's formula with finite population correction.
Confidence Interval Calculator
Build the interval around a proportion or a mean — the range the truth plausibly occupies.
Survey Response Rate Calculator
Measure response and completion rates, and size the outreach a target sample requires.
Survey Duration Calculator
Estimate how many days of fieldwork a target sample will take at your outreach pace.