Margin of Error Calculator
Margin of Error Calculator
Enter your survey's sample size, the proportion you observed (or 0.5 if unknown, for the most conservative estimate), and your confidence level. This calculates the margin of error — how far the true population value could plausibly be from your survey's result.
Using 0.5 for the observed proportion when it's unknown isn't an arbitrary default — it's the value that produces the largest possible margin of error for a given sample size, making it the safest, most conservative assumption when you genuinely don't have a prior estimate to work from. This tool answers the opposite question from the related Sample Size Calculator: this one tells you the precision you already have from a completed survey, while Sample Size tells you how large a survey you'd need to run in advance to hit a specific target margin of error.
- Formula: margin of error = z × √(p × (1 − p) ÷ n), where z is the critical value for your confidence level, p is the observed proportion, and n is the sample size.
- The opposite question from Sample Size: this tool tells you the precision you already have from a completed survey, while the Sample Size Calculator tells you how many people you'd need before running one.
- Larger samples shrink the margin of error, but with diminishing returns: because n is under a square root, quadrupling your sample size only halves your margin of error.
What does a ±5% margin of error actually mean in a poll?
If a poll shows 52% support with a ±5% margin of error, the true population support is estimated to fall somewhere between 47% and 57% at the stated confidence level — the reported 52% is a point estimate, not a certainty.
Why use 0.5 as the proportion if I don't know the actual result yet?
The term p × (1 − p) is largest (and so gives the widest, most conservative margin of error) when p = 0.5, making it the safe assumption before you have real data to plug in.
Margin of Error Calculator
Enter your survey's sample size, the proportion you observed (or 0.5 if unknown, for the most conservative estimate), and your confidence level. This calculates the margin of error — how far the true population value could plausibly be from your survey's result.
Using 0.5 for the observed proportion when it's unknown isn't an arbitrary default — it's the value that produces the largest possible margin of error for a given sample size, making it the safest, most conservative assumption when you genuinely don't have a prior estimate to work from. This tool answers the opposite question from the related Sample Size Calculator: this one tells you the precision you already have from a completed survey, while Sample Size tells you how large a survey you'd need to run in advance to hit a specific target margin of error.
- Formula: margin of error = z × √(p × (1 − p) ÷ n), where z is the critical value for your confidence level, p is the observed proportion, and n is the sample size.
- The opposite question from Sample Size: this tool tells you the precision you already have from a completed survey, while the Sample Size Calculator tells you how many people you'd need before running one.
- Larger samples shrink the margin of error, but with diminishing returns: because n is under a square root, quadrupling your sample size only halves your margin of error.
What does a ±5% margin of error actually mean in a poll?
If a poll shows 52% support with a ±5% margin of error, the true population support is estimated to fall somewhere between 47% and 57% at the stated confidence level — the reported 52% is a point estimate, not a certainty.
Why use 0.5 as the proportion if I don't know the actual result yet?
The term p × (1 − p) is largest (and so gives the widest, most conservative margin of error) when p = 0.5, making it the safe assumption before you have real data to plug in.