What is a confidence interval?

A confidence interval is a range of values that, with a specified probability (the confidence level), contains the true population parameter. For example, a 95% CI means that if you repeated the study 100 times, about 95 of the resulting intervals would contain the true mean.

When is a Z-score used instead of a T-score?

A Z critical value is used when the sample size is 30 or larger (central limit theorem applies). For smaller samples the T-distribution is used, which has heavier tails to account for extra uncertainty from estimating population variance.

What does the margin of error represent?

The margin of error is the half-width of the confidence interval. It tells you how far the sample mean could be from the true population mean while still being consistent with your data at the chosen confidence level.

Does a higher confidence level always mean a better interval?

Not necessarily. A higher confidence level produces a wider interval, which is less precise. A 99% CI is more likely to contain the true value but gives a broader, less actionable range than a 95% CI. The right choice depends on the trade-off between certainty and precision you need.

What if I only have population standard deviation?

Enter it in the Standard Deviation field and select a sample size of 30 or more. The calculator will apply the Z-distribution, which is exact when the population standard deviation is known.

Confidence Interval Calculator

Name: Confidence Interval Calculator
Availability: InStock
Author: Nham Vu

Enter your sample data and confidence level to instantly compute the confidence interval and margin of error.

Sample Parameters

Sample Size (n)

Sample Mean (x̄)

Standard Deviation (s or σ)

Confidence Level

Enter your sample parameters on the left and click Calculate.

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Summary

Enter your sample data and confidence level to instantly compute the confidence interval and margin of error.

How it works

Enter the sample size (n), sample mean, and standard deviation.
Select your desired confidence level (90%, 95%, or 99%).
The calculator chooses Z or T critical value based on sample size.
Margin of error is computed as critical value times standard error.
The confidence interval is displayed as mean plus or minus the margin of error.

Use cases

Estimate population mean from survey or experiment data.
Validate statistical hypotheses in academic research.
Determine acceptable ranges for quality control measurements.
Calculate margin of error for poll results.
Assess precision of lab measurements and sensor readings.
Support data-driven decision making in business analytics.

Frequently Asked Questions

Last updated: 2026-06-10 · Reviewed by Nham Vu