For field electron emission (FE), an empirical equation for measured current
I
m
as a function of measured voltage
V
m
has the form
I
m
=
CV
m
k
exp[–
B
/
V
m
], where
B
is a constant and
C
and
k
are constants or vary weakly with
V
m
. Values for
k
can be extracted (i) from simulations based on some specific FE theory, and in principle (ii) from current–voltage measurements of sufficiently high quality. This paper shows that a comparison of theoretically derived and experimentally derived
k-
values could provide a sensitive and useful tool for comparing FE theory and experiment, and for choosing between alternative theories. Existing methods of extracting
k
-values from experimental or simulated current–voltage data are discussed, including a modernized ‘least residual’ method, and existing knowledge concerning
k
-values is summarized. Exploratory simulations are reported. Where an analytical result for
k
is independently known, this value is reliably extracted. More generally, extracted
k
-values are sensitive to details of the emission theory used, but also depend on assumed emitter shape; these two influences will need to be disentangled by future research, and a range of emitter shapes will need examination. Other procedural conclusions are reported. Some scientific issues that this new tool may eventually be able to help investigate are indicated.