Confidence Level Calculator
Working Backward From a Z-Score to a Confidence Level
Most confidence interval work starts with a target confidence level and looks up the corresponding Z critical value. This calculator runs that relationship in reverse: given a Z-score, it computes exactly what confidence level that score corresponds to on a two-tailed standard normal distribution — useful when a Z-score is already fixed and the resulting confidence needs to be reported.
The Formula
where Φ is the cumulative distribution function of the standard normal distribution — the area under the curve between −Z and Z is the two-tailed confidence level.
Reference Table: Z-Score to Confidence Level
| Z-Score | Confidence Level |
|---|---|
| 1.000 | 68.27% |
| 1.645 | 90.00% |
| 1.960 | 95.00% |
| 2.000 | 95.45% |
| 2.576 | 99.00% |
| 3.000 | 99.73% |
Values computed directly from the calculator's normal CDF formula; note these match the standard reference Z-scores used throughout statistics (1.645, 1.96, 2.576 for 90%, 95%, 99%).
Where This Calculation Matters
- Verifying reported statistics — checking that a stated confidence level matches the Z-score actually used in a calculation, a useful cross-check when reviewing someone else's analysis.
- Control chart design — process control limits are often set at a specific number of standard deviations (a Z-score), and this shows exactly what confidence that choice implies.
- Teaching the Z/confidence relationship — a direct way to see how the familiar 1.96 for "95% confidence" and 2.576 for "99% confidence" are derived, rather than memorized.
How to Use This Calculator
- Enter a Z-score (a non-negative number).
- Select Calculate to get the corresponding two-tailed confidence level as a percentage.
Related Calculations
To go the other direction — from a confidence level to a critical value — use the Critical Value Calculator. To build a full interval around a sample estimate, see the Confidence Interval Calculator.