Known population standard deviation and confidence levels of 90%, 95%, or 99%; not a t interval.
Confidence Interval Calculator
Enter your values below to get the result first, then scroll for the full explanation and guidance.
95% confidence interval
48.040036 to 51.959964Mean with known population standard deviation
95% confidence interval: 48.040036 to 51.959964 (Mean with known population standard deviation)
The interval is the sample mean plus or minus the selected normal critical value multiplied by sigma divided by the square root of n.
Confidence interval
The interval is the sample mean plus or minus the selected normal critical value multiplied by sigma divided by the square root of n.
Result snapshot
A quick visual read of the values behind this result.
Standard error1
Margin of error1.95996398
Recommended next checks
- →Use a t interval instead when the population standard deviation is unknown.
- Standard error
- 1
- Margin of error
- 1.95996398
Try different values to compare results.
Calculate a two-sided confidence interval for a population mean when the population standard deviation is known.
95% confidence interval
48.040036 to 51.959964Mean with known population standard deviation
95% confidence interval: 48.040036 to 51.959964 (Mean with known population standard deviation)
The interval is the sample mean plus or minus the selected normal critical value multiplied by sigma divided by the square root of n.
Confidence interval
The interval is the sample mean plus or minus the selected normal critical value multiplied by sigma divided by the square root of n.
Result snapshot
A quick visual read of the values behind this result.
Standard error1
Margin of error1.95996398
Recommended next checks
- →Use a t interval instead when the population standard deviation is unknown.
- Standard error
- 1
- Margin of error
- 1.95996398
Try different values to compare results.
Table of Contents
Table of Contents
About Confidence Interval Calculator
Confidence Interval Calculator helps you work through the main numbers for this topic quickly with a simple input flow and an instant result.
Use the calculator result as a practical starting point, then review the explanation and assumptions on the page if you want more context.
Calculation method
mean ± z critical value × population standard deviation / sqrt(n).
Formula explained
Calculation flow
This calculator is structured for fast UK-focused estimates with clear inputs, repeatable logic, and instant results.
Formula
Input values -> calculation engine -> instant result
How the result is built
1Enter the values requested in the form.
2The calculator applies the configured formula logic.
3The result updates instantly with a breakdown.
4Use the output to compare scenarios quickly.
Example
Example verified by the calculator's statistical inference reference cases.
Assumptions
- Known population standard deviation and confidence levels of 90%, 95%, or 99%; not a t interval.
Source basis
- UK-focused calculator flow
- Structured input validation
- Instant result breakdowns
FAQ
Common questions
Trust and notes
Assumptions and important notes
This calculator is designed to give a fast estimate using the method shown on the page. Results are most useful when your inputs are accurate and the tool matches your situation.
Use the result as guidance rather than a final diagnosis or professional decision. If the result could affect health, legal, financial, or compliance decisions, verify it with a qualified source where appropriate.
- Known population standard deviation and confidence levels of 90%, 95%, or 99%; not a t interval.
Method
UK calculator guidance
Last reviewed
April 17, 2026