# Confidence Interval Calculator

Free confidence interval calculator. Compute 90%, 95%, or 99% confidence intervals for a population mean from sample mean, standard deviation, and sample.

## What this calculates

Calculate confidence intervals for a population mean using your sample statistics. Choose from 90%, 95%, or 99% confidence levels to determine the range within which the true mean likely falls.

## Inputs

- **Sample Mean (x̄)** — The average value of your sample data.
- **Standard Deviation (σ or s)** — min 0.0001 — The standard deviation of the sample or population.
- **Sample Size (n)** — min 1 — The number of observations in the sample.
- **Confidence Level** — options: 90%, 95%, 99% — The desired confidence level for the interval.

## Outputs

- **Lower Bound** — The lower limit of the confidence interval.
- **Upper Bound** — The upper limit of the confidence interval.
- **Margin of Error** — The margin of error (half-width of the interval).
- **Standard Error** — The standard error of the mean (σ/√n).
- **Interpretation** — formatted as text — How to interpret the confidence interval.

## Details

A confidence interval gives a range of values that is likely to contain the true population parameter.

Formula

CI = x̄ ± z × (σ / √n)

Where:

- x̄ = sample mean

- z = z-score for the chosen confidence level

- σ = standard deviation

- n = sample size

Common z-scores

- 90% confidence: z = 1.645

- 95% confidence: z = 1.96

- 99% confidence: z = 2.576

A wider interval provides more confidence but less precision. Increasing the sample size narrows the interval without sacrificing confidence.

## Frequently Asked Questions

**Q: What does a 95% confidence interval mean?**

A: A 95% confidence interval means that if you were to take 100 different samples and compute a confidence interval for each one, approximately 95 of those intervals would contain the true population mean. It does NOT mean there is a 95% probability the true mean is in this specific interval.

**Q: When should I use a z-score vs. a t-score?**

A: Use a z-score when the population standard deviation is known or when the sample size is large (n >= 30). Use a t-score when the population standard deviation is unknown and the sample size is small. This calculator uses z-scores, which is appropriate for large samples.

**Q: How can I make my confidence interval narrower?**

A: You can narrow a confidence interval by: (1) increasing the sample size, (2) lowering the confidence level (e.g., from 99% to 95%), or (3) reducing variability in the data (lower standard deviation).

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Source: https://vastcalc.com/calculators/statistics/confidence-interval
Category: Statistics
Last updated: 2026-04-21