Confidence Interval Calculator
Complete the confidence interval or margin of error for normally distributed sample means
Confidence Interval Calculator
Easily calculate confidence intervals for population means using our free Confidence Interval Calculator. Supports multiple confidence levels and Z‑values for accurate statistical analysis.
What is the Confidence Interval?
A confidence interval is a statistical measure that provides a range of estimates within which an unknown parameter (such as the population mean) is likely to fall.
It is calculated using observed (sample) data at a chosen confidence level (for example, 95%), which reflects the reliability of the estimation process — not the exact probability that the computed interval contains the true value.
Understanding Confidence Level
If 100 confidence intervals are computed at a 95% confidence level, we expect 95 of them to contain the true parameter value.
However, for any single confidence interval, it either contains the true value or it does not — we cannot assign a probability to that specific case.
Examples of Confidence Intervals
- 20.6 ± 0.887
- 20.6 ± 4.3%
- [19.713 – 21.487]
Formula for Confidence Interval (Known Standard Deviation)
Confidence Interval:
X̄ ± Z × σ⁄√n
- X̄ = Sample mean
- Z = Z-value for chosen confidence level
- σ = Population standard deviation
- n = Sample size
Example Calculation
Given:
X̄ = 22.8
Z = 1.960
σ = 2.7
n = 100
Calculation:
22.8 ± 1.960 × 2.7⁄√100
= 22.8 ± 1.960 × 0.27
= 22.8 ± 0.5292
Z-values for Common Confidence Levels
| Confidence Level | Z Value |
|---|---|
| 70% | 1.036 |
| 75% | 1.150 |
| 80% | 1.282 |
| 85% | 1.440 |
| 90% | 1.645 |
| 95% | 1.960 |
| 98% | 2.326 |
| 99% | 2.576 |
| 99.5% | 2.807 |
| 99.9% | 3.291 |
| 99.99% | 3.891 |
| 99.999% | 4.417 |
Related Calculators:
Z‑Score and Probability Calculator, Permutation and Combination CalculatorExternal Resources:
Confidence interval Calculator on Calculator.net