I frequently encounter situations where I want to perform a set of
similar calculations on different data. If it's a table, like new a
series of readings over time, I can set up a row for each entry and
copy the formulas down each time I add a new row.

But what if I want to replicate the entire sheet such as starting a
new series of readings? Is there some way to set up some kind of
"template" sheet that will be used for multiple derivative sheets?

Say I am keeping track of mileage and service for a car. I have a
sheet set up with rows and columns where I can enter gas purchases and
odometer readings.

If I buy a new car, can I set up a new sheet for the new car based on
the formulas for the old one?

And now for the $64,000 question, if I find a bug in a formula or make
a change, can I set it up so that all of the derivative sheets get
changed?

If I wrote a program, I could have the same calculation routine run
against a list of values. Is there something similar in Excel?