Confidence Interval for a Correlation Calculator
Find the confidence interval for a correlation coefficient. Enter the correlation, the sample size and the confidence level.
Learn how to calculate it yourselfEnter your values
Results update as you type.
Confidence interval
Calculate it yourself
Find a 95% confidence interval for a correlation of 0.50 based on 30 paired observations.
Follow this worked example, then repeat the steps with your own numbers.
Transform the correlation to the Fisher scale
z = ½ ln[(1 + 0.50)/(1 − 0.50)] ≈ 0.54931.Calculate the standard error and margin
SE = 1/√(30 − 3) ≈ 0.19245. For 95% confidence, margin = 1.96 × SE ≈ 0.37720.Find limits on the transformed scale
Lower z ≈ 0.17210; upper z ≈ 0.92651.Transform both limits back to correlations
r = [exp(2z) − 1] ÷ [exp(2z) + 1]. The interval is approximately 0.170 to 0.729.
Use a normal-table critical value for other confidence levels. This Fisher approximation requires n > 3 and a correlation strictly between −1 and 1.
Check your answer in the calculatorUse your PaperSurvey.io results
Use the reported correlation and paired-response count as inputs to this confidence-interval calculator.
Why a correlation needs an interval
A correlation from a sample is only an estimate of the true correlation in the population. The confidence interval shows the range of values that are consistent with your data, so you can tell a precise estimate from a shaky one. Smaller samples give wider intervals.
How it is calculated
The interval is built with the Fisher r-to-z transformation, which makes the sampling distribution roughly symmetric, then the endpoints are converted back to the correlation scale. This is why the interval around r is not symmetric, especially for correlations far from zero.
Frequently asked questions
What if the interval includes zero?
If the interval spans zero, the correlation is not statistically significant at that confidence level: the data are consistent with no relationship.
Get Started with PaperSurvey.io Software
Start your 14-day free trial now, no credit card required.