The Self-Employment tax calculation is: ((earnings * .9235) * .153)/2 — e.g. my earnings are 36,000. Tax bill is 2,543.32 and net earnings is $33,456.68.
If I have $12,000 in bills for the year, what's the formula to find out how much I'll need to earn to cover only those bills accounting for taxes taken out?
Your tax rate appears to be $7.06\%$ and you must multiply your net by $107.6\%$ to find the gross you need to earn to pay bills. For an unknown or changing tax rate, you can use the formula below. I have used your current tax rate on $\$12000$ to show how it works.
Let $g=gross\qquad n=net\qquad t=tax\space rate$
$\text{We know that }n=g-(gt)=g(1-t)\text{ so }$ $$\mathbf{g=\frac{n}{1-t}}=\frac{\$12000}{1-(0.9235*0.153/2)}=\$12912.22$$