# Confidence interval calculator

> Estimate intervals with explicit distribution and sample assumptions.

[Open tool](https://www.toolcabana.com/tk/confidence-interval-calculator) · [Statistics and analysis](https://www.toolcabana.com/tk/category/statistics-and-analysis)

Tool ID: confidence-interval-calculator. Requested language: tk. Description language: en. Complete guide translation: no; untranslated sections use English.

## Overview (en)

The Confidence interval calculator takes a sample mean, a known population standard deviation, a sample size and a confidence level from 50 to 99.99% and returns the lower bound, upper bound, margin of error and z value. It computes a normal z interval, mean ± z × σ / √n. It is not a t interval for a standard deviation estimated from the sample.

## Supported tasks (en)

Calculates a normal z interval for a mean with known population standard deviation. This is not a t interval for an estimated sample deviation.

## Steps (en)

1. Enter the requested values in the settings panel.
2. Adjust the basic settings, then open Advanced mode for export and fine-tuning options. Custom settings stay active when the panel is closed.
3. Run confidence interval calculator, review the output, then use the available copy or download controls.

## Settings

- Sample mean (en; key: mean; type: number); minimum: -1000000000000; maximum: 1000000000000
- Known population standard deviation (en; key: sd; type: number); minimum: 0; maximum: 1000000000000
- Sample size (en; key: size; type: number); minimum: 1; maximum: 10000000
- Confidence (%) (en; key: confidence; type: number); minimum: 50; maximum: 99.99

## Limitations (en)

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Privacy and connections (en)

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

## Questions (en)

### What is the formula for a confidence interval for a mean?

The margin of error is z × σ / √n, and the interval is the sample mean minus and plus that margin. With a mean of 50, σ of 10, n of 100 and 95% confidence, z is about 1.96, so the interval is roughly 48.04 to 51.96.

### When should I use a t interval instead?

Use a t interval when the population standard deviation is unknown and estimated from your sample, especially with small samples. This calculator always uses the normal z critical value, which assumes σ is known and gives narrower intervals than a t interval would.

### How does the confidence level change the interval?

Higher confidence uses a larger z critical value, which widens the interval. The calculator finds z from the standard normal distribution at 0.5 + confidence/200, so 90%, 95% and 99% give about 1.645, 1.960 and 2.576.

### Where is my input processed?

This operation processes its source in your browser. Copy and download are explicit actions; source input is not saved in an account or history.

### What are the input limits?

Local bounded calculations. Numeric inputs must be finite and within the visible ranges. Lists and tables have operation-specific limits. Models, estimates and supplied rates must be checked against your intended use.

## Related tools

- [Descriptive statistics calculator](https://www.toolcabana.com/tk/descriptive-statistics-calculator)
- [Linear regression calculator](https://www.toolcabana.com/tk/linear-regression-calculator)
- [Sample size calculator](https://www.toolcabana.com/tk/sample-size-calculator)
- [Probability distribution explorer](https://www.toolcabana.com/tk/probability-distribution-explorer)