## Reverse Engineering a 1RM Formula to find your training weight

In personal training you can use max-effort reps on an exercise with any weight to estimate a trainee’s one rep maximum (1RM, the most weight you could possibly lift one single time at full strength) for an exercise without the risk of having them actually go and try to lift the maximum weight they possibly can.

A CPT has a trainee lift as much weight as they can for 4-6 reps, working up until they reach a failure point, then use that max weight and the number of reps performed in a mathematic formula that can estimate a 1RM, which you then use to program workouts for that exercise.

This is similar to runners using conversion charts to figure out from a previous 5K or 10K time how fast you could run a mile, or how fast you could run a marathon, without you actually going out and try to do either. Weightlifting and endurance running of course come with different goals, but both use formulas and estimates to determine how to train.

There are a lot of 1RM formulas, and each certifying organization seems to recommend a different one. NFPT for example uses the Brzycki Formula. Meanwhile, NASM just gives you a chart, and that may have been calculated from just about anywhere.

To digress a moment, I personally use the Epley Formula. For what I’m about to describe, I have found it from experience more accurate for training purposes, as well as accurately gauging my actual one rep max. Various studies also indicate that it’s among the most accurate of the formulas.

I tell you all this because I actually used the weights I used during swolework not just to determine my 1RM for those weights, but also reverse engineered the formula to get a more specific answer for weight to use in exercises.

For example, at one point I was doing four 6 rep sets of lat pulldowns at 85 lbs, for me pretty heavy. I was giving close to max effort on these 6 reps each set, and I wanted to focus more on endurance with more reps, 12 reps to be exact. But I didn’t want to take the weight so far down that my strength wasn’t being challenged.

So first, I would use the Epley formula to estimate my 1RM, presuming that 85 lbs was the most weight I could lift in one 6 rep sitting.

Weight: w = 85
Reps: r = 6

1RM = w(1 + (r/30))
1 + (6/30) = 1.2

1RM = w * 1.2
1RM = 85 * 1.2 = 102 lbs

I can use this formula backwards by applying some algebra, understanding that any equation divided by itself equals 1.

If I divide both sides by (1 + (r/30)), I can isolate the weight w to one side, and basically create a reverse engineered formula where I can use my known 1RM and a selected number of repetitions to determine how much weight I need to use for that number of repetitions to get the maximum benefit from the workout.

1RM / (1 + (r/30)) = w

So, knowing I want to do 12 reps (r = 12), and knowing my 1RM = 102, I can determine the amount of lifting weight to use:

102 / (1 + (12/30)) = w

(12/30) = 0.40

102 / 1.40 = w

w = 72.9

I can’t get a lat pulldown machine to give me exactly 72.9 pounds of resistance (unless maybe I have one of those expensive Tonal machines), but I can get a multiple of 5, so I round down to 70 lbs. Sure, I could try rounding up to 75 lbs and see how that goes. But it’s probably safer to round down and get through a whole workout with relative ease before deciding to add that 5 lbs.

So then I do my 12 rep sets of lat pulldowns at 70 lbs weight, exercise from there, and get the max value out of that 4 sets. And in my experience, this weight ended up giving me exactly the right challenge for that portion of the workout.

Note: Sure, that’s in line with NASM’s 50-70% max recommendation for stabilization and endurance. But rather than using their wide range (51-72 lbs) and just randomly picking a weight within that, I get a firm answer that’s in line with the specific number of reps (12) I’m using. Let’s say I do 15 reps instead, r = 15.

102 / (1 + (15/30)) = w

(15/30) = 0.50

102 / 1.50 = w

w = 68

At 15 reps, it would be more appropriate for me to use 65 lbs. If I were to use the same weight, it might be too much, unless I rounded up to the nearest 5 lb increment from 68 for, say, the last 1-2 sets, e.g. I did the first 3 sets at 65 lbs, and the last set at 70 lbs, or maybe the first 2 sets at 70 lbs and then the last 2 sets at 65 lbs, etc.

In fact, a logical progression for me from sets of 12 endurance-themed reps at 70 lbs, instead of increasing the weight, would be to increase the number of reps to 15 at the same weight, and see if I can handle that. If I can, it might work out to bring the number of reps back to 12 while increasing the weight to 75 lbs.

## One thought on “Reverse Engineering a 1RM Formula to find your training weight”

1. A Home Endurance Workout Series Using 5-lb Dumbbells | Working Class Runner says:

[…] idea from my reverse engineered 1RM approach is that it’s possible to get a sufficiently challenging workout from very light […]