## 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). Your 1RM is the most weight you could possibly lift one single time at full strength for an exercise. Calculating this with lighter lifting removes the risk of trying to lift the maximum weight you possibly can.

A CPT has a trainee lift as much weight as they can for 4-6 reps. You start at a reasonable weight and progress until they reach a failure point. You then enter that max weight and the number of reps performed in a mathematic formula that can estimate a 1RM. You then use this number 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 a marathon, without having to first do either. Weightlifting and endurance running of course have different goals. But both use formulas and estimates to determine training intensity.

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 could have been calculated from just about anywhere. I personally use the Epley Formula. For what I’m about to describe, I have found Epley from experience more accurate for training purposes. It has accurately gauged my true 1RM. Various studies also indicate that it’s among the most accurate of the formulas.

I used the weights I trained with during swolework not just to determine my 1RM for those exercises, but also reverse engineered the 1RM formula to determine weight to use in sets.

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

To start I used the Epley formula to estimate my 1RM for lat pulldowns. I presumed 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. This basically creates a reverse engineered formula where I enter my known 1RM and a set number of repetitions to determine what weight and number of repetitions can produce the maximum benefit from the workout.

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

Knowing I want to do 12 reps (r = 12), knowing my 1RM = 102, I can determine the optimal weight:

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. But I can get a multiple of 5, so I round down to 70 lbs. I could try rounding up to 75 lbs and see how that goes. It’s probably safer to round down and get through a whole workout at 70 before deciding to add that 5 lbs.

So I do my 12 rep sets of lat pulldowns at 70 lbs weight. This likely gives me the max strength endurance value out of that 4 sets. In my experience, this weight gave me exactly the challenge I wanted for that exercise.

Note: 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 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’s best for me to use 65 lbs. If I were to use the same 70 lbs, it might be too much. I could round up to the nearest 5 lb increment from 68 for, say, the last 1-2 sets. So I could do the first 3 sets at 65 lbs, and the last set at 70 lbs. I could do the first 2 sets at 70 lbs, the last 2 sets at 65 lbs. There’s other ways you could probably come up with.

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

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