Estimate an interval for the population mean from sample mean, standard deviation, sample size, and confidence level (normal z approximation). The results show margin of error and a number-line band on a fixed axis—wider SD or smaller n visibly widens the band.
How to use
- Enter sample mean and sample standard deviation (≥ 0).
- Enter n ≥ 2 and pick 90%, 95%, or 99% confidence.
- Read the interval, ± margin, and the band on the line; try sample presets to compare tighter vs wider intervals.
Example
Mean 100, SD 15, n = 25, 95% → margin about ±5.9; interval roughly 94.1–105.9 (see live output).
Same mean and SD with n = 8 → a wider margin and a wider band on the line.
Pair with the z-score calculator, sample size calculator, and standard deviation calculator.
Notes
Very small samples may need a t-based interval; this page uses common z critical values for quick estimates.
Frequently asked questions
What does a confidence interval mean?
At your chosen confidence level, the interval from sample stats is the usual mean ± margin range (z approximation)—a standard quick estimate, not a full Bayesian statement.
What formula is used?
Interval = sample mean ± z×(SD/√n) with tabulated z at 90%, 95%, or 99%.
Why does the number-line band change width?
Larger SD or smaller n widens the margin—the band on a fixed axis grows or shrinks visibly. Try the sample presets.
Which confidence level should I pick?
Higher confidence → wider intervals. 95% is common in reports; 99% is more conservative.
Is this OK for small samples?
Very small n may need a t interval. This page uses z for quick estimates.
Related tools?
Spread: standard deviation. One value: z-score. Surveys: sample size.
Population or sample SD?
Enter the sample SD from the same dataset as the mean and n.
Can I save my inputs?
Yes. Copy link below the form keeps your current inputs so you can share the scenario or save it for later.