by Charles T. Ridgely
In parts 1 & 2 we discussed the proper way to test your 1RM and to Plot those values on a graph. This final post will help you finalize your 1 Rep Max values for each exercise.
You can use the best-fit line to determine your RMs for any weight. One way to do this is by looking at the values on the graph. For example, suppose you want to know how much weight you can lift for 10 reps (i.e., your 10RM). Draw a vertical line from the 10 Reps value on the Reps axis all the way up to the best-fit line. Then, draw a horizontal line from the point where your vertical line intercepts the best-fit line all the way over to the Weight axis. Looking at where the horizontal line crosses the Weight axis, you can easily see that your 10RM is about 152 lbs.
Another way to determine your RMs is by using an equation for the best-fit line. Such a line equation is
expressed in the general form:
This equation gives the weight (W) that you can lift in terms of the number of reps (R) that you can perform. In Eq. (1), W is a weight value you want to determine, R is the number of reps you want to perform with the weight, m is the slope of the line, and b is an intercept where the bestfit line crosses, or intercepts the Weight axis. The intercept b can be determined simply by looking at where the best-fit line crosses the Weight axis. In our example, the intercept b is about 192 lbs. The slope m of the line can be determined by using the equation:
The values {W1, R1} and {W2, R2} are respective weight and rep values of any two points that you select on the best-fit line. Because we have used only two RM values to draw the best-fit line, you can use the values again to determine the slope m. It should be noted, however, that had we used more than two RMs to draw the best-fit line, then those RM values could not be used to determine the slope m of the line, at least not unless they were actually positioned on the best-fit line. In general, you must select points that are positioned on the line; otherwise the accuracy of your calculations will be sacrificed. Using our 8RM and 13RM values, given above, the two points {W1, R1} and {W2, R2} become {160 lbs, 8 reps} and {140 lbs, 13 reps}, respectively. The slope m of the best-fit line is then determined as follows:
As you can see, the slope m is a negative number expressed in terms of lbs per rep. Note that it is okay to have a negative number for the slope m; it just means that the best-fit line slopes towards the Reps axis as it extends further to the right.
Now that we have values for the slope m and intercept b, we can put them into the equation for our best-fit line. Doing this gives
Notice that we have included the units lbs and reps in the equation. This helps us to keep track of the types of values that are included in the equation, and also reminds us that when we enter rep-values, the equation produces weight values.
You can determine your weights by plugging in some rep-values. One value that everyone likes to know is their 1RM. Let’s use Eq. (3) to determine your 1RM for the Bench Press by setting R equal to 1 rep. Doing this gives W = 188 lbs. Thus, in this example, you can lift about 188 lbs roughly one time. Now let’s set R equal to 10 reps. Carrying this out gives W = 152 lbs. Therefore, you can lift 152 lbs about 10 times.
Having an equation for each of your exercises is particularly useful for setting up your HST cycles. You can use these equations to quickly predict theoretical values for your 15RM, 10RM, and 5RM for each exercise you want to use in your HST cycle. Continuing with the example given above, we already know that your 10RM for the Bench Press is about 152 lbs, but we want to know your 15RM and 5RM, too. Setting R equal to 15 reps gives W = 132 lbs, and setting R equal to 5 gives W = 172 lbs. Therefore, your 15RM, 10RM, and 5RM are 132 lbs, 152 lbs, and 172 lbs, respectively.
Many printed and online Rep-Max calculators express the weights you are using as fractions or percentages of your 1RM; and indeed, there may be times when those values are more useful than the values given by Eq. (3). As mentioned above, however, many Rep-Max calculators are based on a large spectrum of lifters and thus may not be very accurate on an individual basis. In this section, we demonstrate ways to determine accurate, individualized fractions of your, or your clients’, 1RM.
For any exercise that you perform, the weight that you lift can be viewed as a fractional value of the maximum weight that you can lift one time. This fractional value can be expressed simply as whatever weight you are using divided by your 1RM weight:
where W is the weight you are using and WM is your 1RM weight. Next, we return to Eq. (1) and notice that when we set R = 1 to represent your 1RM weight, we obtain
where we have again used WM to represent your 1RM weight. Upon substituting Eq. (5) into the denominator of Eq. (4) to eliminate WM, we arrive at
This equation expresses the weights you use as fractions of your 1RM.
Let’s use Eq. (6) in an example. Suppose you’ve been bench pressing 160 lbs for 8 reps, and you want to express this weight as a fraction of your 1RM. Referring to Eq. (3), recall that the intercept b is 192 lbs and the slope m is – 4 lbs/rep. Putting these values into Eq. (6) gives
Setting W = 160 lbs then leads to
Thus, in this example, 160 lbs is about 85% of your 1RM for the Bench Press.
Just as you can express your weights as fractions of your 1RM, you can also express fractions of your 1RM as weights. This is useful in those instances when you need to convert a particular fraction of your 1RM into a weight value. For example, say you want to work with 65% of your 1RM on a light Bench Press day. So how much weight should you pile onto the bar? To find out, first solve Eq. (6) for the weight W:
This equation converts fractions of your 1RM into weight values. Now, we already know from Eq. (7) that (b + m) =188 lbs. Using this and setting f = 0.65 then gives
Therefore, if you want to work with 65% of your 1RM for the Bench Press, you should pile about 122 lbs onto the bar.
Equations (7-8) provide simple conversions between weight values and fractions of your 1RM. But now we need to obtain an equation that expresses fractions of your 1RM in terms of the number of repetitions you can perform. This is most simply done by equating the right-hand side of Eq. (8) with the right-hand side of Eq. (1):
Solving this expression for the fraction f then gives
This equation gives you a fraction of your 1RM when you enter a number of repetitions that you can perform.
Equation (10) is best understood by using an example. Returning again to our Bench Press example, we note that the intercept b is 192 lbs and the slope m is – 4 lbs/rep, and that (b + m) = 188 lbs. Plugging these values into Eq. (10) and performing some minor simplification leads to
Upon further simplification, we then arrive at the expression
This equation gives you fractions of your 1RM for the Bench Press when you enter numbers of repetitions that you can perform.
Let’s use Eq. (12) to determine what the fraction of your 1RM is when you can perform 8 reps with a particular weight. Setting R = 8 reps and performing the computation leads directly to
Therefore, according to this example, you can bench press about 85% of your 1RM for 8 reps.
HST and many other fitness programs require you to determine your RM weights for each exercise that you plan to use in your training cycle. Typically, you’d have to spend an extra week testing your RMs, take a wild guess, or use Rep-Max calculators. Although estimating your RMs is easy and takes very little time, a drawback is that Rep-Max calculators generally are based on the performance of many different lifters. Because of this, these calculators do a poor job of predicting accurate RMs on an individual basis.
A far more accurate approach has been presented herein. Whether you need to know your own RMs, or those of your clients, the methods demonstrated herein enable you to provide an individually tailored analysis for any lifter, at any time, for any exercise. One thing to keep in mind, however, is that as your performance changes over time, the data you use to determine your RMs will have to be updated accordingly.
This concludes our detailed 3 part series on determining your 1 Rep Max and Percentage of 1 RM for any exercise performed. We realize that this is very complex fitness information that the average bodybuilder doesn’t have time to calculate each and every time they perform an exercise. That’s why we’ve made it easy by creating the SimGym fitness app for iPhones and iPod Touch devices…The only proven approach to monitoring gym results based on the true 1 RM methodology. We use these advanced techniques to allow you to accurately measure your workouts and exercises in the gym. At only $2.99 on the iTunes App Store, you’ll definitely get everything you bargain for. Also, check out our website where you can monitor your logs and see your progress over time. Very soon, we are going to be launching a marketplace to purchase workout programs tailored for individual fitness goals, so stay tuned!
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- Dan Collins