  "Back-of-the-envelope" or "rule-of-thumb" calculations involving rough
estimates of quantities play a central scientific role in developing intuition
about the structure and behaviour of physical systems, for example in so-called
`Fermi problems' in the physical sciences. Such calculations can be used to
powerfully and quantitatively reason about biological systems, particularly at
the interface between physics and biology. However, substantial uncertainties
are often associated with values in cell biology, and performing calculations
without taking this uncertainty into account may limit the extent to which
results can be interpreted for a given problem. We present a means to
facilitate such calculations where uncertainties are explicitly tracked through
the line of reasoning, and introduce a `probabilistic calculator' called
Caladis, a web tool freely available at www.caladis.org, designed to perform
this tracking. This approach allows users to perform more statistically robust
calculations in cell biology despite having uncertain values, and to identify
which quantities need to be measured more precisely in order to make confident
statements, facilitating efficient experimental design. We illustrate the use
of our tool for tracking uncertainty in several example biological
calculations, showing that the results yield powerful and interpretable
statistics on the quantities of interest. We also demonstrate that the outcomes
of calculations may differ from point estimates when uncertainty is accurately
tracked. An integral link between Caladis and the Bionumbers repository of
biological quantities further facilitates the straightforward location,
selection, and use of a wealth of experimental data in cell biological
calculations.
