Confidence Interval Calculator
Get your confidence Interval calculated instantly, for free.
The Confidence Interval Calculator takes a sample mean, standard deviation and sample size and instantly calculates a statistical confidence interval. No signup, no spreadsheet formulas — just enter your numbers and get an accurate result.
Manual calculations are easy to get wrong, especially with percentages, dates or fees involving multiple steps. This calculator handles the math precisely so you can focus on the decision the number is informing.
How to Use the Confidence Interval Calculator
- Enter the required values
- Click Calculate
- Review your result instantly
Best Practices
- Double-check input units (currency, dates, percentages) match what's expected
- Use the result as a planning estimate — confirm exact figures with official statements where money is involved
- Bookmark this tool for quick repeated calculations
This tool is free to use with no signup required.
Frequently Asked Questions
What is a confidence interval?
A confidence interval is a range of values, calculated from sample data, that is likely to contain the true population parameter (like a mean) with a specified level of confidence, such as 95%.
What does a 95% confidence level actually mean?
It means that if you repeated the sampling process many times, approximately 95% of the calculated intervals would contain the true population parameter — it does not mean there's a 95% chance the true value is in this specific interval.
What inputs do I need to calculate a confidence interval?
Typically the sample mean, sample size, standard deviation (or standard error), and desired confidence level (commonly 90%, 95%, or 99%).
Why does a larger sample size produce a narrower confidence interval?
Larger samples provide more precise estimates of the population parameter, reducing the standard error and therefore narrowing the range needed to achieve the same confidence level.
Is this tool free to use?
Yes, completely free with no signup, no limits and no software to install.
Is my data saved anywhere?
No — calculations run in your browser and the values you enter are not stored or sent to a server.
What confidence level should I use: 90%, 95%, or 99%?
95% is the most common default in research and business analysis, offering a balance between precision and reliability — 99% gives a wider, more conservative interval, while 90% gives a narrower one.
Does this work for proportions as well as means?
Confidence intervals can be calculated for both means and proportions, though they use slightly different formulas — check which calculation mode this tool supports.
Is this useful for A/B testing analysis?
Yes — confidence intervals are commonly used in A/B testing to assess whether an observed difference between variants is statistically meaningful.
What's the difference between confidence interval and margin of error?
The margin of error is the ± range added to a point estimate, while the confidence interval is the full range (point estimate minus and plus the margin of error) — they're closely related expressions of the same uncertainty.
The Confidence Interval Calculator works out a range of plausible values for a population parameter (a mean or proportion) based on sample data and your chosen confidence level — typically 90%, 95%, or 99%.
What a Confidence Interval Actually Means
A 95% confidence interval does not mean "there's a 95% probability the true value falls in this range" — a common misinterpretation even among people who use statistics regularly. It means that if you repeated the same sampling process many times and built a confidence interval each time, about 95% of those intervals would contain the true population value. The true value either is or isn't in any single interval you calculate; the 95% describes the reliability of the method across repeated sampling, not the probability for one specific interval.
Why Sample Size Changes Interval Width
Larger samples produce narrower confidence intervals for the same confidence level, since more data reduces the uncertainty in your estimate of the true population value. This is why polling organizations report both a result and a margin of error tied to their sample size — a poll of 200 people carries a much wider margin of error than one of 2,000, even reporting the identical percentage result. If you need a narrower, more precise interval, increasing sample size is the direct lever; increasing confidence level alone actually widens the interval, not narrows it.
Confidence Level vs. Interval Width: A Tradeoff
Raising the confidence level (say, from 95% to 99%) makes the interval wider, not narrower, because being more certain the true value falls within the range requires casting a wider net. There's no way to simultaneously increase confidence and narrow the interval without also increasing sample size — the three factors (confidence level, sample size, interval width) are mathematically linked, and improving one without changing sample size means trading off against another.
When to Use z-Distribution vs. t-Distribution
For large samples (generally n > 30) with a known or well-estimated population standard deviation, the z-distribution is appropriate. For smaller samples, or when the population standard deviation is unknown and estimated from the sample itself, the t-distribution is the statistically correct choice, since it accounts for the additional uncertainty from a smaller dataset with wider tails than the normal distribution. Using z instead of t on a small sample tends to produce an interval that's falsely narrow relative to the actual uncertainty involved.
