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Margin of Error Calculator
Calculate the margin of error for surveys and polls, or find the sample size needed to achieve a desired margin of error at any confidence level.
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Use 50% if unknown — gives widest margin
Key Features — Margin of Error Calculator
Margin of error from sample size
Required sample size for target margin of error
Multiple confidence levels (80%–99.9%)
Adjustable population proportion
Custom Z-score input
Why Use This Tool — Margin of Error Calculator
Free Online Margin of error calculatorSurvey margin of error — for EveryoneFast & Easy Sample size calculatorPoll margin of error — 100% FreeFree Online Confidence interval margin of error
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Frequently Asked Questions — Margin of Error Calculator
What is margin of error?
Margin of error (MoE) quantifies the uncertainty in a survey or poll result. A poll showing 52% support with ±3% MoE means the true value is likely between 49% and 55%. The MoE is calculated as: MoE = z × √(p(1−p)/n), where z is the confidence-level z-score and n is the sample size.
Why use 50% as the proportion?
Using p = 50% (0.5) gives the most conservative (widest) margin of error, because p(1−p) is maximized at p=0.5. This is standard when you don't know the true proportion in advance, as it guarantees your sample size will be sufficient for any outcome.
What sample size do I need for a ±3% margin of error?
For a typical political poll: 95% confidence, 50% proportion, ±3% MoE → n = (1.96² × 0.25) / 0.03² = 1,067 respondents. This is why most national polls survey 1,000–1,200 people. For ±2% you need about 2,401 respondents; for ±5% only 385.