There is such a formula for both forcing and feedback, but the forcing formula starts with unknown assumptions,
and the feedback formula does not work with the observed data for high levels of ECS.
This are detailed by ACS,
Climate Sensitivity - American Chemical Society
They then go on to show,
Without explaining where the 5.35 come from, (It is from the assumed 2XCO2 forcing of 3.71 Wm-2).
3.71/ln(2)=5.35
CO2 forcing alone is of little concern, which even at the assumed level, would produce a 2XCO2 warming of 1.1C,
it is the feedbacks that would push warming to dangerous levels.
The feedbacks for a predicted 2CO2 ECS of 3C, are simple.
The input is the 1.1C of forcing warming, and the output is 3 C after equalization,
so 3/1.1=2.72. For an ECS of 3C to be real, past warming perturbations, would have to be multiplied by 2.72,
and still match observed warming.
Herein lies the problem, for the decade average ending in 1950, the Harcrut4 data set had warming of .288 C,
Total warming (decade average ending in 2018) was .89C, leaving a difference of .602C.
The forcing of all the greenhouse over that time (CO2-eq) based on NOAA,
NOAA/ESRL Global Monitoring Division - THE NOAA ANNUAL GREENHOUSE GAS INDEX (AGGI)
was (5.35 X ln(496/337) X .3)=.620C.
The forcing plus the earlier warming perturbation, is almost equal to the observed warming!
There is simply no room for any amplified feedbacks, even after 70 years of equalization.
But for fun, let's calculate how much feedback an ECS of 3C should show.
James Hansen wrote that 60% of equalization should be complete within 25 to 50 years,
so .288 X 2.72 X.6=.47C! We clearly do not have room in the observed record for an additional .47C.