Existing metric for personal productivity hours needed per life hour?

It seems to me this seminal paper has looked at the question

Gary Becker - A Theory of the Allocation of Time

You can use economic intuition to establish the value of one hour of work in terms of one hour of life. Suppose you have a consumer/worker that has to choose how much time to devote to work or leisure. His total daily hours allotment is

$24=h+ell$

where $h$ is the number of hours worked and $ell$ is the number of hours of leisure. He values leisure according to some utility function $u(cdot)$ and his total utility also depends on the amount of goods $x$ consumed

$U(x,ell)=x+u(ell)$

he earns a hourly wage $w$. He spends all of his income in this single consumption good, which we assume has a nominal price of 1$. Therefore he has the following budget constraint

$x=wh$

Then, if the consumer/worker is choosing optimally how much to work the margin, it must be true that, on the margin, one hour of leisure has the same value as one hour of work

$dfrac{partial u}{partialell}=w$

In other words, he must be indifferent on the margin between working 1 more minute or using it for leisure.

To know the value of every hour of leisure we need to know of course the function $u(cdot)$. But at least on the margin, if you want to know what's the value of one unit of time not spent on work - there you have it: it's the hourly wage rate.

Becker suggested you could use that intuition to include leisure and household production in GDP. You should weight all hours not spent on work by their respective wage rate.

With regards to your initial question: how many hours of "life" do you gain for every hour of work? It should be 1, otherwise you're not choosing your leisure time optimally.

R.I.P. Gary Becker, Nobel Prize in Economics. I had the privilege of attending his last Price Theory course at UChicago before he died. He lectured on this.