How to Use the Confidence Interval Calculator

What is a Confidence Interval Calculator?

A Confidence Interval Calculator is a statistical tool that estimates the range in which the true population mean is likely to fall, based on sample data. It's widely used in research, science, business, and data analysis to infer the reliability of a sample estimate.

---

How to Use the Calculator (Step-by-Step)

Step 1: Enter the Sample Mean (x̄)
This is the average value from your data sample. For example, if you surveyed 100 people and the average income was $52,000, you would enter 52000.

Step 2: Enter the Standard Deviation (σ)
This is a measure of spread in your data — how much the data varies from the mean. If you don't know it, you can estimate it or use the sample standard deviation.

Step 3: Enter the Sample Size (n)
How many observations or data points are in your sample? Enter that number.

Step 4: Select Confidence Level
Choose how confident you want to be in the result. The most common levels are:

• 90% — More narrow, but less confidence
• 95% — Standard in most studies
• 99% — Very high confidence, but wider range

Step 5: Click “Calculate Confidence Interval.”
The calculator will display the interval as:
(Lower Bound, Upper Bound)

---

Example Use Case

Imagine you're testing average delivery time for your logistics company.

• Sample Mean = 4.2 days
• Standard Deviation = 1.1 days
• Sample Size = 64
• Confidence Level = 95%

The calculator might show:
(3.97, 4.43)
→ This means you're 95% confident that the true average delivery time is between 3.97 and 4.43 days.

---

Confidence Interval Calculator – FAQ

What does a confidence interval tell me?

It shows the range where the true population mean likely lies based on your sample, with a certain level of confidence (e.g., 95%).

---

What's the difference between 90%, 95%, and 99% confidence levels?

• 90%: Narrower interval, but only 90% confident
• 95%: Balanced choice, most common
• 99%: Very wide interval but higher certainty

---

Can I use this calculator if my sample size is small?

Yes, but for very small samples (<30), use a t-distribution instead of a z-distribution, which this calculator currently assumes.

---

Do I need population standard deviation (σ)?

Yes — this version assumes it's known. For an unknown population standard deviation, you'd use the sample standard deviation (s) and a t-score.

---

Is this calculator suitable for proportions?

No — this calculator is for means. For proportions (like % of people who voted), you need a different formula.