95% Confidence Interval Calculator
Choose a calculator type, enter your sample values, and get an instant 95% confidence interval.
What is a 95% confidence interval?
A 95% confidence interval (CI) is a range of values that is likely to contain the true population parameter, based on your sample data. In plain language: if you repeated the same study many times and built a confidence interval each time, about 95% of those intervals would contain the true value.
Confidence intervals are more informative than a single point estimate because they show uncertainty. Instead of saying “the mean is 72.5,” you can say “the mean is likely between 70.4 and 74.6.”
How this CI 95 calculator works
1) Mean confidence interval
For sample means, this calculator uses a two-sided 95% interval:
x̄ ± t* × (s / √n)
- x̄ = sample mean
- s = sample standard deviation
- n = sample size
- t* = 95% critical value from the t-distribution (df = n − 1)
This is the standard approach when population standard deviation is unknown, which is the most common real-world case.
2) Proportion confidence interval
For sample proportions, this tool uses the Wilson score interval, which is usually more reliable than the basic Wald approximation, especially for smaller sample sizes or proportions near 0 or 1.
- x = number of successes
- n = total trials
- p̂ = x/n = sample proportion
- 95% uses z = 1.96
When should you use a 95% CI?
A 95% confidence interval is useful when you want to estimate:
- Average outcomes (test scores, blood pressure, response time, spending)
- Rates and percentages (conversion rate, approval rate, defect rate)
- Uncertainty around survey or experiment results
It is often used in academic research, product analytics, A/B testing, quality control, and business reporting.
Quick interpretation guide
If your interval for a mean is [70.4, 74.6], you can report: “We estimate the true mean to lie between 70.4 and 74.6 with 95% confidence.”
If your proportion interval is [0.39, 0.58], that means the true percentage is likely between 39% and 58%.
Confidence intervals are not guarantees for one specific sample—they are a long-run reliability statement about the method.
Common mistakes to avoid
- Using a confidence interval to claim absolute certainty.
- Entering population standard deviation when you actually have sample SD.
- Using tiny, biased, or non-random samples and expecting valid inference.
- For proportions, using methods that break down with low counts (the Wilson method helps here).
FAQ
Is 95% the same as p < 0.05?
They are related but not identical. A 95% CI and a 5% significance level often tell a consistent story, but confidence intervals provide an effect-size range, not just a yes/no decision.
Can I use this for very small samples?
You can, but interpret cautiously. Small sample sizes can produce wide intervals and stronger sensitivity to assumptions.
Why is my interval so wide?
Wide intervals usually mean high variability, small sample size, or both. Increasing sample size reduces standard error and narrows the CI.
Final note
This ci 95 confidence interval calculator is designed for fast, practical estimates. For formal publication or high-stakes decisions, pair calculator results with a full statistical analysis and domain context.