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[Phys-L] Uncertainty Calculator



Hi Folks --

I cobbled up an Uncertainty Calculator. Given some input variables
with error bars, it calculates the output variable and its error bars.

https://www.av8n.com/physics/uncertainty-calculator.html

It runs in the browser. You don't need to install anything or
download anything. It should work on all platforms, including
smartphones, laptops, desktops, et cetera.

It has two modes. It starts in basic mode. I tried to keep this
as clean and simple as possible, so that high-school students could
use it without getting confused or intimidated.

Basic mode uses Crank Three Times to calculate the results. This
is a calculation that anybody could do using a pocket calculator.
Crank Three Times is simpler and in every way better than the
calculus-based rules for «propagation of error bars» (PoEB). In
situations where the calculation doesn't make sense, C3T will give
you a warning, whereas other methods such as PoEB would give wrong
answers without warning. As always, «sig figs» has all the same
problems as PoEB, and more besides.

The calculator can handle any mathematical formula that you are
likely to encounter in an introductory physics course. All the
usual mathematical operators and functions are available.

It can handle multi-step calculations. It correctly handles
correlations that arise in the course of the calculation, as they
so often do. The usual PoEB methods have no clue about this.

On the same page as the calculator you can find a few hundred words
of explanation, including several live demos.

===============

Meanwhile, there is also Monte Carlo mode. This does a more elaborate
calculation and displays more information.
https://www.av8n.com/physics/uncertainty-calculator.html?mc

This upholds the rule of thumb that says No Fancy C3T. If basic C3T
is not good enough, you should be doing Monte Carlo.

MC is not something you would normally do using a pocket calculator.
Whereas C3T turns the crank three times, MC turns the crank 10,000
times.

Eventually it would be nice to add a /plot/ of the probability density
distribution. This should be straightforward, but I haven't gotten
around to doing it.

==============

There are other online Uncertainty Calculators out there. However,
the others all seem to rely on «propagation of error bars», which
is more laborious, less powerful, and less reliable. I will never
in a million years understand why anybody would bother with that.