🎯 Standard Error Calculator
Calculate the standard error of a sample mean from the sample standard deviation and sample size.
📊 Statistics📐 Formula included🧠 Practice questions✓ Free
Please enter valid values.
Formula and Explanation
Calculate the standard error of a sample mean from the sample standard deviation and sample size.
| Concept | Formula or rule |
|---|---|
| Standard Error Calculator | SE = s / √n |
How to Use This Calculator
- Enter the sample, counts, probabilities, or summary statistics requested above.
- Keep paired lists in the same order and separate values with commas.
- Select the correct test direction or sample/population option when available.
- Press Calculate and interpret the result together with the supporting statistics.
Worked Example
Example: A sample has standard deviation 12 and n = 64.
✓ SE = 12 ÷ √64 = 1.5
Where This Is Used
School & coursework
Check homework, understand formulas, and verify step-by-step statistics exercises.
Research
Explore estimates, uncertainty, distributions, and relationships before using full statistical software.
Business & data analysis
Summarize variation, compare groups, and communicate data-driven findings clearly.
Common Mistakes to Avoid
⚠️
Using variance instead of standard deviation
Take the square root of variance before using the formula.
Take the square root of variance before using the formula.
⚠️
Treating SE as data spread
SE describes uncertainty in the sample mean, not variation among individual observations.
SE describes uncertainty in the sample mean, not variation among individual observations.
⚠️
Ignoring sample independence
The formula assumes observations are sufficiently independent.
The formula assumes observations are sufficiently independent.
Practice Questions
1. SD 10 and n 25. Find SE.
Answer: 2
2. If n is quadrupled, what happens to SE?
Answer: It is cut in half.
3. SD 6 and n 36. Find SE.
Answer: 1
Frequently Asked Questions
What happens when sample size increases?▾
Standard error decreases in proportion to 1/√n.
Is standard error the same as standard deviation?▾
No. Standard deviation describes data spread; standard error describes precision of an estimate.
Can SE be zero?▾
Yes, if the sample standard deviation is zero.