What This Calculator Measures

Estimate confidence interval coverage based on confidence level and sample size.

By combining practical inputs into a structured model, this calculator helps you move from vague estimation to clear planning actions you can execute consistently.

This calculator estimates CI width and coverage based on sample size and variance.

How to Use This Well

Set confidence level and sample size.
Enter estimated standard deviation.
Add margin target and coverage goal.
Review CI width and coverage.
Adjust sample size if needed.

Formula Breakdown

Margin = z × (σ ÷ √n)

z: confidence multiplier.

σ: standard deviation.

n: sample size.

Worked Example

95% confidence with σ=12 and n=200.
Margin ≈ 1.96 × 0.85 = 1.7.
CI width ≈ 3.4.

Interpretation Guide

Range	Meaning	Action
0–2	Tight CI.	High precision.
2–5	Moderate CI.	Usable precision.
5–10	Wide CI.	Increase sample.
10+	Very wide.	Refine inputs.

Optimization Playbook

Increase sample: reduce margin.
Lower variance: narrower CI.
Adjust confidence: balance precision.
Track coverage: ensure target met.

Scenario Planning

Baseline: current sample size.
Higher confidence: increase to 98%.
More samples: add 100 samples.
Decision rule: keep margin under target.

Common Mistakes to Avoid

Using the wrong variance estimate.
Ignoring distribution choice.
Overstating confidence without sample size.
Skipping margin checks.

Implementation Checklist

Estimate variance realistically.
Set confidence target.
Check margin vs goal.
Adjust sample plan.

Measurement Notes

Treat this calculator as a directional planning instrument. Output quality improves when your inputs are anchored to recent real data instead of one-off assumptions.

Run multiple scenarios, document what changed, and keep the decision tied to trends, not a single result snapshot.

Confidence Interval Coverage Calculator

Quick Facts

Your Results

Coverage Ready