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Formulas And Coefficients That Predict Your 1-Rep Maximum

by Casey Butt

The nature of human strength being what it is, it is undoubtably true that you can do more reps with a light weight than you can with a heavy one. If you can do 200 lbs. for one rep then you can probably do 120 lbs. for twenty reps (or more), or 165 lbs. for seven reps or so. Maybe you could get 180 for three or four. This line of thought then, presents a question: If you know how many reps you can do with a certain weight, can you predict your 1-rep maximum (1RM)?

The answer is, to a certain degree of accuracy, yes. In fact, there are several equations and sets of coefficients that allow you to do just that. They all essentially work like this: You multiply the amount of weight you can handle for a given number of reps by a certain coefficient that corresponds to that number of reps. For example, if I can overhead press 135 for 8 then I would multiply 135 x 1.242 (the coefficient corresponding to 8 reps) for an estimation of my 1-rep maximum in the overhead press of 168 lbs. Is this accurate? Well, naturally, its not 100% accurate for everyone (or maybe anyone), but it does give most people some idea of their 1-rep capabilities.

All of the multitude of 1RM estimation equations and coefficients were arrived at by testing a group of people and analyzing the results. The people in the groups performed reps to failure (well, one rep before failure is what was actually counted) with a certain percentage of their 1RM. The average maximum percentage of their 1RM that people could use for a given number of reps allows a coefficient to be calculated that estimates 1RM. For instance, if, on average, people could perform 7 reps with 83.3% of their 1RM then for you to apply this data to yourself you would divide whatever weight you could use for 7 reps by 0.833. Say you maxed out at 150 lbs. for 7 reps; to estimate your 1RM you would divide 150 by 0.833 to get 180 lbs. In practice, the reciprocal of the percentage is usually taken, so that you would multiply by 1.2 rather than divide by 0.833 (150 x 1.2 = 180). Of course, the inherent innaccuracy here arises from the fact that you are assuming that you are the 'average' person. Nonetheless, these coefficients can have their value.

Some schemes are given as individual coefficients, and some are given as formulas. Some years ago, Matt Brzycki (Coordinator of Health Fitness, Strength and Conditioning Programs at Princeton University) fitted the graph of his data (to around the 10-rep mark) and obtained a formula which has become quite popular.

The Brzycki Formula

This formula (actually, I have somewhat rewritten it for convenience) first appeared in a paper entitled Strength testing: Predicting a 1-rep max from reps-to-fatigue in a 1993 issue of the Journal of Health, Physical Education, Recreation and Dance. It is as follows:



This formula is reasonably accurate, for many people (depending on their weight training habits - more on this later), for up to around ten reps. Calculating it out as coefficients for each rep count gives us:

reps performed multiplication coefficient
1
1.000
2
1.029
3
1.059
4
1.091
5
1.125
6
1.161
7
1.200
8
1.242
9
1.286
10
1.330

So, as yet again another example, if you could use 200 lbs. for five reps then you would get around 200 x 1.125 = 225 lbs. for one.

The Epley Formula

Another such formula for estimating 1RM was presented by Boyd Epley in 1985. It looks like this:



The predictions from this formula are a bit more accurate for someone who does a lot of low-rep training or has a high proportion of fast twitch fibers in the muscle groups being tested. Again, after 10 reps or so its accuracy starts breaking down. Calculating it out as coefficients for each rep count gives us:

reps performed multiplication coefficient
1
1.000
2
1.066
3
1.099
4
1.132
5
1.165
6
1.198
7
1.231
8
1.264
9
1.297
10
1.330

As you can see, these differ somewhat from the Bryzcki Formula coefficients. How do you now which ones are closer to your own capabilities? Well, you'll have to establish your actual max and compare the predictions to that. Of course, you can always use them both and take the two predictions as upper and lower bounds of your estimate.

As a comparative example, 200 lbs. for five reps would give you a 1RM estimate of 200 x 1.165 = 233 lbs. with the Epley Formula - the Brzycki Formula predicts a 1RM of 225 lbs.

The Lander Formula

Yet another formula for estimating 1RM was presented in a paper entitled Maximums based on reps by J. Lander in a 1985 National Strength Conditioning Journal. It looks like this:



The predictions from this formula fall somewhere between the predictions given by the Brzycki and Epley formulas. Calculating it out as coefficients for each rep count gives us:

reps performed multiplication coefficient
1
1.000
2
1.042
3
1.072
4
1.104
5
1.137
6
1.173
7
1.211
8
1.251
9
1.294
10
1.341

The National Strength And Conditioning Association (NSCA) Coefficients

Some years back, the NSCA also published some sets of 1RM estimation coefficients. They took it a step further, however, and determined different coefficients for different lifts. Here are their coefficients for the Squat, Bench Press and Deadlift.

reps performed squat coefficient bench coefficient deadlift coefficient
1
1.000
1.000
1.000
2
1.0475
1.035
1.065
3
1.13
1.08
1.13
4
1.1575
1.115
1.147
5
1.2
1.15
1.164
6
1.242
1.18
1.181
7
1.284
1.22
1.198
8
1.326
1.255
1.22
9
1.368
1.29
1.232
10
1.41
1.325
1.24

These are a step further in the right direction as they address these lifts specifically. However, they are most appropriate for lifters, such as powerlifters, who train specifically for 1RM attempts.

The Value Of These Coefficients

Aside from giving you an idea of your 1RM without you actually having to test for it - and possibly exposing yourself to the risk of injury - these coefficients can be used in several other ways. The following are some purposes that I have found them useful for.

  1. Determining the fiber composition and/or neuromuscular efficiency of your muscles and muscle groups.
  2. Judging progress when using different weight and rep schemes across different workouts.
  3. Determining the seriousness of any "weak links" in your strength.

Determining the fiber composition and/or neuromuscular efficiency of your muscles and muscle groups: If these coefficients estimate from your 8-rep maximum that you should be able to lift 200 for one, but you can only handle 180, then you know that you either have fewer than average type IIB fibers in that muscle or muscle group (at least as compared to the people in the group that was used to establish the coefficients) or that your neuromuscular system is not efficient enough to fire them optimally when performing low reps. If you regularly train with lower reps (1-5) but your 1RM is still less than these coefficients predict then you probably have fewer than average type IIB fibers, as this type of training stimulates the neuromuscular system to optimize itself for heavy lifting. If you don't regularly train with lower reps, then you really don't have a basis for deciding which case applies to you (or possibly both).

Of course, if your 1RM is actually much higher than these coefficients predict it could mean that you have a higher percentage of type IIB fibers in that muscle group(s) than average, but you must keep in mind that if you regularly train with low reps your 1RM may possibly be higher than predicted because of a highly adapted (efficient) neuromuscular system for this type of lifting.

Judging progress when using different weight and rep schemes across different workouts: These coefficients allow you to compare what you did last week with what you did this week, even if you used a different weight for a different number of reps. This, I believe, can be an extremely valuable aspect of these coefficients - if you heed the inherent shortcomings of them. Progressive resistance, so that you are getting stronger each workout, is the cardinal rule of weight training, yet it amazes me how many people don't take it seriously. Occasionally I'll ask someone if they progessed since last week and they'll tell me that they don't know. They may say that they did 195 lbs. for 8 reps last week and 183 lbs. for 10 reps this week, and that they have no means for comparing the two performances. This is where 1RM estimation coefficients have some value. Using the Brzycki Coefficients 195 x 1.242 = 242.2, whereas 183 x 1.330 = 243.4. This represents an improvement.

Now, this is by no means absolute - these numbers are very rough indeed. If you really had to push for the 183 for 10 (barely making the tenth rep), but you more easily got 195 x 8 (although you don't believe that you could have gotten another rep), then it is quite possible that you could have gotten 183 for 10 last week, and this week's workout does not represent a strength improvement at all. This clearly points out an inaccuracy when accepting these 1RM estimations without any scrutiny. In addition, the fiber composition of the muscle group being worked must also be taken into account (see above). But, in a very broad sense, they can give you a way of keeping track of your progress. Comparing workouts a few months apart would be such an instance. If the above two workouts took place two months apart instead of one week it would be much clearer that your strength did not increase appreciably, considering the extended period of time. In this case you can safely assume that either you're doing something wrong or that you're nearing your genetic potential.

Determining the seriousness of any "weak links" in your strength: If, for instance, you can squat 315 lbs. for 10 (which using the NSCA coefficients predicts a 1RM in the squat of 444 lbs.) yet you can actually only Squat 355 for one because your lower back gives out, then you know that you have a significant disparity between your hip and leg strength and your lower back strength. In this case, some serious lower back strengthening is in order. Pertaining to the Squat, this is the situation that I have frequently found myself in. It's one thing for the lower back to maintain its proper degree of arch under 315 lbs., but quite another for it to maintain that same arch under a 444 lb. load. Of course, once again, the fiber type composition of the muscle group being tested must be taken into account.

Note On The Olympic-Style Lifts

Because of the reliance of the Olympic-style lifts on technique and neuromuscular efficiency, these coefficients don't apply very well to the Olympic-style lifts. These coefficients were not taken using highly trained Olympic Weightlifters.

The Final Word

The final word is that these coefficients are not the final word ...but they can have their place. The three cases above are probably the most significant uses for them (aside from actually predicting your 1RM). If you chose to utilize them for the purposes that I have outlined above I caution you that you must know your own body's capabilities intimately. In these instances, beginners just don't have the experience to draw useful conclusions from the predictions that these coefficients make. I hope this information is of use to you.

By the way, back on the The WeighTrainer Main Page there's a link to a calculator on this site which calculates the Brzycki, Epley and Lander Formulas and useful variations of them. You may want to take a look.



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