Margin of Error Calculator

When you read a public opinion poll reporting that a candidate leads with 52% support with a margin of error of ±3 percentage points, that range is the margin of error (MOE). Because researchers cannot poll every single citizen, random sampling error inevitably occurs. The margin of error defines the boundaries of that uncertainty.

How Margin of Error Works

Margin of error establishes an upper and lower boundary—known as the confidence interval—around your survey estimate. For instance, if an employee satisfaction survey shows that 70% of staff feel valued with a margin of error of ±4% at a 95% confidence level, it means that if you repeated the survey 100 times under identical conditions, in 95 of those runs the true satisfaction level would fall between 66% and 74%.

The Law of Diminishing Returns in Sampling

A common misconception is that doubling your sample size will cut your margin of error in half. Because the sample size $ sits inside a square root in the formula, cutting the margin of error in half actually requires quadrupling your sample size:

• At = 100$, the margin of error is approximately ±9.8%.
• At = 400$, the margin of error drops to ±4.9%.
• To reach ±2.5%, you must survey roughly 1,600 people.
• To reach ±1.0%, you need nearly 10,000 participants.

This is why most national public opinion polls cap their samples around 1,000 to 1,500 participants—moving beyond this delivers tiny marginal improvements in precision at massive extra expense.

Confidence Level vs. Margin of Error

There is always a direct trade-off between how certain you want to be and how tight your interval is. If you increase your confidence level from 90% to 99% without adding more respondents, your margin of error expands. To be 99% sure your interval captures the truth, you must cast a wider net.