Standard Error Calculator
Calculate standard error of the mean, confidence intervals, and margin of error
Input Method
Summary Statistics
Use summary statistics when you already have the mean, standard deviation, and sample size.
Confidence Level (Optional)
Select confidence level to calculate margin of error and confidence interval.
Standard Error Results
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Standard Error of the Mean (SEM)
Sample Size (n)
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Sample Mean (x̄)
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Standard Deviation (s)
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Margin of Error
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Confidence Interval
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The standard error measures the precision of the sample mean estimate.
Standard Error Formula
SEM = s / √n
Where:
s = sample standard deviation
n = sample size
Interpretation
- Smaller SE = More precise estimate
- Larger n = Smaller SE
- Less variability = Smaller SE
- SE decreases as √n increases
Confidence Intervals
- 95% CI = x̄ ± 1.96 × SE
- 90% CI = x̄ ± 1.645 × SE
- 99% CI = x̄ ± 2.576 × SE
- CI width increases with confidence level
When to Use
- Hypothesis testing
- Confidence intervals
- Sample size planning
- Comparing means
- Research papers