We study the dependence of the primordial nuclear abundances as a function of the electromagnetic fine-structure constant $$\alpha $$
α
, keeping all other fundamental constants fixed. We update the leading nuclear reaction rates, in particular the electromagnetic contribution to the neutron-proton mass difference pertinent to $$\beta $$
β
-decays, and go beyond certain approximations made in the literature. In particular, we include the temperature-dependence of the leading nuclear reactions rates and assess the systematic uncertainties by using four different publicly available codes for Big Bang nucleosynthesis. Disregarding the unsolved so-called lithium-problem, we find that the current values for the observationally based $${}^{2}\text {H}$$
2
H
and $${}^{4}\text {He}$$
4
He
abundances restrict the fractional change in the fine-structure constant to less than $$2\%$$
2
%
, which is a tighter bound than found in earlier works on the subject.