night/ calendar counter

Does jotform have a counter, that can count the nights on a calendar automatically?

I am not sure if I have understood your requirement correctly. Please note that you can add "Form Calculation" widget to calculate the number of days between two date fields.

Please take a look at following demo form where you need to select the date and it will calculate the number of days from the current date: https://form.jotform.com/91733635133960

Will this not fit into your requirement? If not, please explain the issue a bit more in detail and we will take a look.

We will wait for your response.