Confidence Interval Calculator
Estimate the confidence interval for a population mean from your sample mean, standard deviation and size.
Confidence level
95% CI: 94.6323 to 105.3677
- 1
Standard error (SE)
σ ÷ √n = 15 ÷ √30 = 2.7386How much the sample mean is expected to vary from sample to sample. - 2
Margin of error
z × SE = 1.96 × 2.7386 = 5.3677
Formula
How this is calculated
The calculator takes four inputs: the sample mean x̄ (your best point estimate of the population mean), the standard deviation σ (how spread out the data is, in the same units as the mean), the sample size n (how many observations you collected), and a confidence level. From the level it picks a critical z-value from the standard normal distribution — 1.645 for 90%, 1.96 for 95%, and 2.576 for 99%.
It first computes the standard error of the mean, SE = σ / √n, which measures how much the sample mean is expected to vary from sample to sample. The margin of error is then z × SE, and the interval is x̄ ± margin, giving a lower and upper bound expressed in the same units as your data.
This z-method assumes the data are roughly normal (or n is large enough for the Central Limit Theorem to apply) and treats σ as known. For small samples with an estimated standard deviation, a t-distribution interval is more accurate, so the bounds here may be slightly too narrow in that case.
About this calculator
A confidence interval is a range of plausible values for a population parameter, calculated from a sample. A 95% confidence interval means that if you repeated the sampling process many times, about 95% of the intervals produced would contain the true population mean. The width of the interval reflects how much uncertainty there is in the estimate.
This calculator uses the z-based formula x̄ ± z × (σ / √n), where σ / √n is the standard error of the mean and z is the critical value for your chosen confidence level (1.645 for 90%, 1.96 for 95%, and 2.576 for 99%). Larger samples shrink the standard error and narrow the interval, while higher confidence levels widen it. The z-method assumes a known standard deviation and a reasonably large sample.
Frequently asked questions
It means that if you repeated your study many times, roughly 95% of the resulting intervals would capture the true population mean. It is not the probability that this particular interval contains the mean.
These are the critical z-scores from the standard normal distribution that leave 10%, 5% and 1% of the area in the two tails — corresponding to 90%, 95% and 99% confidence levels.
Increase your sample size, which reduces the standard error (σ / √n), or accept a lower confidence level. A larger sample is usually the most reliable way to tighten the interval.
Also known as
TG we-Calculate Editorial Team. (2026). Confidence Interval Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/confidence-interval-calculator
TG we-Calculate Editorial Team. "Confidence Interval Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/confidence-interval-calculator.
TG we-Calculate Editorial Team, "Confidence Interval Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/confidence-interval-calculator
@misc{wecalculate_confidence_interval_calculator, title = {Confidence Interval Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/confidence-interval-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?