Statistics • 90/95/99% Levels
Confidence Interval Calculator
Calculate confidence intervals for population mean.
(94.63, 105.37)95% confidence interval for population mean
Calculate confidence intervals for population mean.
Enter a sample mean, standard deviation, sample size, and confidence level (90%, 95%, or 99%), and this calculator returns the confidence interval — the range in which the true population mean is likely to fall, along with the margin of error.
Confidence Interval = Sample Mean ± (Z-score × (Standard Deviation / √Sample Size))
The Z-score corresponds to your chosen confidence level: 1.645 for 90%, 1.96 for 95%, and 2.576 for 99%. A wider interval (higher confidence level, smaller sample, or larger standard deviation) reflects more uncertainty about the true population value; a narrower interval reflects a more precise estimate.
A 95% confidence interval means that if you repeated the same sampling process many times, about 95% of the resulting intervals would contain the true population mean — it does not mean there's a 95% chance the true mean falls in this one specific interval.
It means that if the sampling process were repeated many times, about 95% of the intervals calculated that way would contain the true population parameter. It is a statement about the reliability of the method, not a probability about this one interval.
The margin of error includes standard deviation divided by the square root of the sample size, so as sample size grows, that term shrinks — more data gives a more precise estimate of the population mean.
95% is the most common default in research and reporting. Use 99% when the cost of being wrong is high and you want a wider safety margin; use 90% when you want a tighter estimate and can tolerate more risk of missing the true value.