Statistical Confidence Interval & Margin of Error Calculator

A Confidence Interval (CI) gives an estimated range of values which is likely to include an unknown population parameter. A 95% confidence level implies that if a study were repeated 100 times, 95 of the calculated intervals would contain the true population mean.

To use the Statistical Confidence Interval & Margin of Error Calculator, enter your Sample Mean (x̄), Sample Standard Deviation (s), Sample Size (n) and other values. The calculator instantly computes Confidence Interval Range, Margin of Error (ME) and more. Results update in real time as you change any input — no submit button needed.

How to Use This Calculator

Enter your Sample Mean (x̄) (e.g. 50.0), Sample Standard Deviation (s) (e.g. 10.0), Sample Size (n) (e.g. 100 in samples), and Confidence Level — choose from 90% Confidence Level (Z = 1.645), 95% Confidence Level (Z = 1.960), 99% Confidence Level (Z* = 2.576). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Standard Error SE = Sample Standard Deviation s ÷ √(Sample Size n)

Margin of Error ME = Critical Z-score × Standard Error SE

Confidence Interval = [ Sample Mean - ME , Sample Mean + ME ]

Worked Example

Sample Mean x̄ = 50.0, Standard Deviation s = 10.0, Sample Size n = 100 at 95% Confidence:

SE = 10.0 / √100 = 1.

00.

Margin of Error ME = 1.960 × 1.00 = 1.

960.

95% Confidence Interval = 48.040 to 51.960 (50.0 ± 1.96).

Understanding Your Result

Statistical results require context: a mean alone is misleading without knowing the standard deviation (spread). Normal distribution reference: 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, 99.7% within ±3 SD. For small sample sizes (n < 30), use t-distributions rather than z-scores. Statistical significance (p < 0.05) does not imply practical significance — effect size (Cohen's d, R², odds ratio) measures real-world importance. Correlation coefficient r: |r| < 0.3 weak, 0.3–0.7 moderate, > 0.7 strong.