One rep max formula - why do I get tired during warm-up

I'm doing a reverse on the one rep max formula. That is, if my one rep max in a certain exercise is 30 kg, then following the 1RM = m(30 + r)/30 formula, you get r = 30(RM - m)/m .

But this would also imply that in that case the maximum number of repeats with 4 kg should be 195 while with 2 kg it should be 420 reps. However, a warm-up with 28 reps with 2 kgs followed by 26 reps of 4 kgs renders me already tired. I can push the 30 kgs once, but I see no chance to ever do 195 reps with 4 kgs (let alone 420 with 2 kgs) after that.

What am I doing wrong? Where do my calculations go wrong? How can these numbers be improved?

• You make no mention of your training goal(s). Why are you concerned with 1 rep maximums? Jan 8 '14 at 17:46
• Basically I'm trying to do a strength training routine combined with endurance training (given that it's theoretically possible). Jan 8 '14 at 18:22
• I think you'd be better off designing a routine that works in phases. For example, the first part would have strength training as a goal, and, the second would have endurance training. IMO, combining the two with what you described will set you up for over training. Secondly, it's more important to have a specific goal. For example, gaining mass, getting stronger, etc. Decide what that should be. Jan 8 '14 at 18:28

2 Answers

Who ever said that one-rep max calculations were reversible? They're a very rough guide for estimating or predicting an appropriate one-rep max attempt. They're simply not designed to be inverted so that one can figure out the correct rep target for 2kg weights.

You would probably get better results basing your workout program on an existing, proven workout program instead of extrapolating from a highly specialized and approximate mathematical tool for powerlifting guesses.

• Sorry about the initial approach - I'm an engineer, not a trainer. I just thought I could figure out how these formulae work - and how they don't work. But thank you for confirming its irreversibility. Jan 9 '14 at 13:19
• @AndrásHummer Coming at it from a math/engineering perspective, it works when working towards a 1RM because the # reps in a 1RM is known, whereas in the reverse, both reps and weight are unknown, and so you get some wacky combinations like .00000001kg x 10 billion reps. Jan 9 '14 at 13:24
• This overview of set/rep schemes might be a better basis for workout goals. Also, this answer might help you understand the role of warm-up sets and how to plan them. :) Cheers Jan 9 '14 at 13:27
• Thank you, Dave. Two last questions: where do the rep numbers 5-5-5-2 come from in the warm up sets? Are they empiric or optimized numbers? Also, what is the difference threshold between two warm up weights where you decide to add a third one in between? Jan 9 '14 at 15:55
• @AndrásHummer 5-5-5-2 is based off of Rippetoe & Kilgore's recommendation in Starting Strength. (They actually recommend for most exercises something like 2 sets of 5 with the bar, then a few sets of 5 with increasing weight, then a set of 3 closer to the work-set weight, then a set of 2 very close (~20-50 pounds) to the work-set weight, then sets of 5.) You'll find that empirical or optimized numbers are few and far between and go by different standards in the lifting world. Jan 9 '14 at 15:59

There are some major limitations regarding 1RM formulas:

• They are designed with a certain demographic in mind. If you are outside that demographic, they may not be applicable. For example, the one you listed is designed for men in their 20s.
• They are designed to work within a certain rep range. For example, the one you listed becomes grossly inaccurate beyond 10 reps. The fewer reps involved, the more accurate they become.
• They are only an approximation. This is why they don't work outside of their designed parameters. It's better to think of it in terms of equivalent effort than it is to think that just because you lifting 100kg 10 times that you can automatically lift 133kg.

With those disclaimers out of the way, I can say without a doubt you are using the the formula incorrectly. The formulas become more useful when you understand about the different adaptations that happen with rep ranges. Granted, even the rep ranges are only useful to a point--but it helps to understand how to design your work around your goals:

• 1-3 reps: 90+% effort, used to test strength. Can also be used to primarily stimulate myophibrilar hypertrophy (more contractile protein pairs per muscle fiber) if used with 85-90% and more sets.
• 4-6 reps: 80-90% effort, used to build a balance of strength and size.
• 8-12 reps: 70-80% effort, used to primarily build size and commonly used by bodybuilders. Primarily stimulates sarcoplasmic hypertrophy (more energy system support for the muscle).
• 16+ reps: <70% effort, used to build muscular endurance.

Performing over 100 reps with any weight is a grueling exercise in endurance, and is very difficult. However, that effort does not translate to increasing your ability to do work. I.e. getting stronger or improving your energy systems.

Just as important: warmup should just be that. Getting your muscles warm enough to handle the work load. Performing massive sets with a weight only 2kg from the work weight is going to pre-fatigue the muscles so that you are robbing from what you can do at the work weight.