Free Confidence Interval Calculator
Calculate confidence intervals for your sample data instantly. No signup required.
Results
Your Confidence Interval:
(, )
Margin of Error
±
Z-Score Used
How to Use This Calculator
- Enter your sample size (n) — the number of observations in your sample
- Enter your sample mean (x̄) — the average value of your sample data
- Enter your standard deviation (σ) — measures how spread out your data is
- Select your confidence level — 95% is most common for research
- Click Calculate to get your confidence interval
What is a Confidence Interval?
A confidence interval is a range of values that likely contains the true population parameter you're trying to estimate. When you collect sample data, you can't know the exact population mean, but a confidence interval gives you a range where the true mean probably falls.
For example, a 95% confidence interval means that if you repeated your sampling process 100 times, about 95 of those intervals would contain the true population mean.
The width of your confidence interval depends on three factors: your sample size (larger samples = narrower intervals), your data's variability (lower standard deviation = narrower intervals), and your chosen confidence level (higher confidence = wider intervals).
The Formula
CI = x̄ ± z × (σ / √n)
Where:
- x̄ = sample mean
- z = z-score for your confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%)
- σ = standard deviation
- n = sample size
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Frequently Asked Questions
What confidence level should I use?
95% is the most common choice in research and surveys. Use 99% when you need extra certainty (like medical research), or 90% when you can tolerate more uncertainty and want a narrower interval.
What sample size do I need for reliable results?
Generally, sample sizes of 30 or more work well when your data is roughly normally distributed. Larger samples give you narrower (more precise) confidence intervals.
What's the difference between confidence interval and margin of error?
The margin of error is half the width of the confidence interval. It's the "plus or minus" value you add and subtract from your sample mean to get the interval bounds.
Does this calculator use z-scores or t-scores?
This calculator uses z-scores, which are appropriate when you know the population standard deviation or have a sample size of 30 or more. For smaller samples with unknown population standard deviation, a t-score might be more appropriate.
How do I calculate standard deviation from my data?
Standard deviation measures the spread of your data. Most spreadsheet tools (Excel, Google Sheets) have built-in functions: use STDEV.S for sample standard deviation or STDEV.P for population standard deviation.
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