What does a 95% confidence interval mean?

If you repeated the study many times, 95% of the calculated confidence intervals would contain the true population mean. It does not mean there is a 95% chance the true mean is in this specific interval.

When should I use a Z vs T distribution?

Use Z when your sample size is large (n > 30) or when population SD is known. Use T for small samples with unknown population SD. This calculator uses Z-distribution.

How does sample size affect the interval?

Larger sample sizes produce narrower confidence intervals because the standard error (σ/√n) decreases. Doubling precision requires quadrupling the sample size.

What is standard error?

Standard error is the standard deviation of the sampling distribution of the mean. It measures how much the sample mean is expected to vary from the true population mean.

Can I use this for proportions?

This calculator is designed for means. For proportions, use the sample size calculator or a proportion-specific confidence interval formula: p ± Z×√(p(1−p)/n).

Math

↵ to calculate

Confidence Interval Calculator — 95% 99% CI Online

Calculate the confidence interval for a population mean given sample mean, standard deviation, sample size, and confidence level.

✨

How to use this calculator

👉 Fill in the boxes below and your answer appears instantly — no maths needed, we do it all for you! 🎉

👶

In plain English — what does this do?

🔢 This tool does the maths for you! Just type in your numbers, and it gives you the answer right away. No need to count on your fingers or use a pen and paper.

📌 Direct Answer & Summary

The confidence interval calculator computes the range of values within which the true population mean is likely to fall, based on sample data. It uses the Z-distribution for known population standard deviations and large samples.

Sample Mean (x̄)

Standard Deviation (σ)

Sample Size (n)

Confidence Level

What is Confidence Interval Calculator — 95% 99% CI Online?

How to use it

1️⃣ Enter the sample mean (the average of your data).
2️⃣ Enter the standard deviation of your sample.
3️⃣ Enter the sample size (number of observations).
4️⃣ Select your desired confidence level (90%, 95%, or 99%).
5️⃣ Click Calculate to get the confidence interval, margin of error, and standard error.

Formula

CI = x̄ ± Z × (σ/√n). Standard error = σ/√n. Margin of error = Z × SE. Z-values: 90%→1.645, 95%→1.96, 99%→2.576.

💡 See it in action — a real example

Sample mean = 50, SD = 10, n = 100, 95% confidence: SE = 10/√100 = 1.0. Margin = 1.96 × 1.0 = 1.96. CI = (48.04, 51.96).

❓ Common questions

What does a 95% confidence interval mean?: If you repeated the study many times, 95% of the calculated confidence intervals would contain the true population mean. It does not mean there is a 95% chance the true mean is in this specific interval.
When should I use a Z vs T distribution?: Use Z when your sample size is large (n > 30) or when population SD is known. Use T for small samples with unknown population SD. This calculator uses Z-distribution.
How does sample size affect the interval?: Larger sample sizes produce narrower confidence intervals because the standard error (σ/√n) decreases. Doubling precision requires quadrupling the sample size.
What is standard error?: Standard error is the standard deviation of the sampling distribution of the mean. It measures how much the sample mean is expected to vary from the true population mean.
Can I use this for proportions?: This calculator is designed for means. For proportions, use the sample size calculator or a proportion-specific confidence interval formula: p ± Z×√(p(1−p)/n).

⚡ Related Math Tools & Calculators

Sample Size Calculator P-Value Calculator Statistics Calculator