I've scoured the web to find an answer to this, as static strength is its own science, this is quite a difficult concept. I did find out there is a relationship to rate of force development, and explosive strength, since they all involve single contractions of the muscle. There are also multiple types of isometrics, such as overcoming isometrics and yielding isometrics, or even ballistic training. Your question seems to be aimed at yeilding isometrics(holding a weight). It's not a linear formula, for instance, if you plank for 5 minutes, 10 pounds on your back could reduce that to 2.5 minutes, or maybe 4 minutes, it depends on your static strength.
according to T-nation, a load of 50 to 80% for a duration of 20 to 60 seconds is best for hypertrophy. Everything is based off a 1-rep max, so planks might be hard to calculate but an isometic bench press, just take your 1-rep max, for instance, 250, and 50% would be 125lbs for 60 seconds, or 80% would be 200lbs for 20 seconds. so for 250 lbs 1 rep max, 125 for 60 seconds on the high end, 200 for 20 seconds on the low end. Try adding weight to a plank and see how much weight you can hold for 2 seconds, which is when "peak force of development" occurs, so you can definitely hold for 2 seconds.. you could use this as your 1 rep max, and use the same percantages, lets say you can do 100lb 2 sec max.. 50 lbs could be done for 60 seconds, or 80 lbs for 20 seconds. According to the research done by this article, https://www.t-nation.com/training/isometrics-for-mass, you should only do 20-60 seconds for maximal hypertrophy.. anything more is not beneficial, depending on your goals.
overcoming isometrics is trying to push weight that you impossibly cant move, but it stimulates muscle growth either way.. try pushing a car for 6 seconds.. you cant move it but you can gain muscle growth. This doesn't apply here but the weight doesn't matter.
To summarize, 50% of 1rm for 60 seconds or 80% for a 20 seconds. Anything more than 20-60 seconds is not hypertrophy but a combination of joint strength, tendon strength, explosiveness and speed. If you need an exact formula, I'm sure a skilled Health scientist/mathematician could use the rate of force formula against isometrics to calculate a length, but other than some estimations done by bodybuilders, there is not an EXACT formula for this, but really an estimation.