Z-Score Confidence Interval Calculator - LearnLinx Education & Math

Calculator

Calculate

Data value x (z-score)

Mean

Standard deviation

Sample size n (CI)

Critical z (CI) (1.96 ≈ 95%)

Reset

Result

Answer will appear here

Enter the values above and press Calculate to see the answer, step-by-step solution, and formula used.

How the result is calculated

z = (x − μ) / σ; CI = x̄ ± z × (s / √n)

Explanation

What this calculator does

Z-Score Confidence Interval Calculator helps you calculate the result using clear inputs, a formula, and practical examples.

How LearnLinx Calculates This Result

Formula

z = (x − μ) / σ; CI = x̄ ± z × (s / √n)

Enter your values and press Calculate to see each computation step with your numbers plugged into this formula.

Example

Enter your values, calculate the result, and review the formula used for the answer.

When to use it

Use it when you need a quick result for study, planning, documentation, or checking a manual calculation.

Common mistakes

Using population σ formulas with tiny samples without considering t-values.
Forgetting that CI needs sample size n.
Interpreting a CI as containing every individual data point.

Frequently asked questions

Z-score formula?

z = (x − mean) / SD.

Default CI z?

1.96 approximates a 95% normal confidence interval.

What formula does the Z-Score Confidence Interval Calculator use?

It uses: z = (x − μ) / σ; CI = x̄ ± z × (s / √n). The result page also shows a step-by-step breakdown of how your answer was calculated.

Is the Z-Score Confidence Interval Calculator free to use?

Yes. All LearnLinx calculators are completely free with no signup required. Signing in is optional and only adds a 60-day history of your calculations.