How do you calculate confidence interval with either unknown σ^2 og known σ^2 ?

Confidence interval where σ^2/ population variance is known is calculated by taking Xbar-/+z-score(1,96,1,64 etc)*σ/sqrt of n. How to calculate Confidence interval where σ^2 depends on the sample size. If the sample is over 120 we can assume it is normal distributed. And the formula is xbar-/+z-score*s/sqrt of n. If the sample is under 120, we take xbar-/+ t* and multiply it with s/sqrt of n