You don't name the physicists you're talking about, but some type of calculating aid has been around for ages.
Prosthaphaeresis was a method of doing multiplication and division using trig tables. A lot of effort was put into making the trig tables, but once created, provided a fairly effective way of doing multiplication and division. It was around in Newton's time.
In fact, by time Newton was born, a better method was invented. John Napier invented logarithms, followed by Henry Briggs inventing base 10 logs. Multiplication and division were even easier using log tables instead of trig tables.
In fact, you could put the logarithmic scales on rulers and do quite a few calculations much easier. Isaac Newton came up with a way to http://web.mat.bham.ac.uk/C.J.Sangwin/Sliderules/Newtonpoly.pdf using logarithmic scales.
That was just a novel way of using the
slide rule invented by William Oughtred. As a better way of fastening the scales together with a sliding scale were designed, you had a device that's more effective than most digital calculators. You have to go to the good graphing calculators (such as a TI-89), before your digital calculators are more capable than a good slide rule.
Albert Einstein's favorite slide rule was a Nestler 23R (this was also Werner Von Braun's favorite slide rule - in fact it was the favorite of most scientists or engineers that grew up in Germany).
I'm torn as to my favorite. I like the feel of the bamboo on my Post Versalog 1460 and it's actually my favorite for most general type problems. My Pickett N4-ES is better for electrical engineering problems. My avatar is a close up of part of my pocket Pickett N600-T, a little 6 inch slide rule.
So, unless you're talking about someone like Archimedes, they probably used a calculator.
The reason different slide rules are better for different types of problems has to do with the fact that you lose accuracy and speed everytime you have to copy down a number from the slide rule. Setting up a problem so you minimize slide movements and minimize having to take a reading makes for better calculations, so the placement of different scales on the body or slide to solve the problems most often encountered makes a difference. That's the other advantage of a digital calculator. You don't need one caculator for chemistry (a Post 1491, for example) and a different one for physics (a Post 1460, for example).
Of course, only needing one calculator for all of your calculations is kind of boring. What kind of collection is that?
