Accuracy 1-RM Prediction Equations
32
Journal of Exercise Physiologyonline
(JEPonline)
Volume 13 Number 3 June 2010
Managing Editor
Tommy Boone, PhD, MPH
Editor-in-Chief
Jon K. Linderman, PhD
Review Board
Todd Astorino, PhD
Julien Baker, PhD
Tommy Boone, PhD
Larry Birnbaum, PhD
Eric Goulet, PhD
Robert Gotshall, PhD
Alexander Hutchison, PhD
M. Knight-Maloney, PhD
Len Kravitz, PhD
James Laskin, PhD
Derek Marks, PhD
Cristine Mermier, PhD
Chantal Vella, PhD
Ben Zhou, PhD
Official
Research Journal of
the American Society of
Exercise Physiologists
(ASEP)
ISSN 1097-9751
Sports Physiology
Accuracy of 1-RM Prediction Equations for the Bench Press and
Biceps Curl
MATTHEW HUTCHINS, RANDALL GEARHART JR
1Indiana
State University, Terre Haute IN, USA,2Ashland University,
Ashland OH, USA
ABSTRACT
Hutchins MD, Gearhart RF. Accuracy of 1-RM Prediction Equations for
the Bench Press and Biceps Curl. JEPonline 2010;13(3):32-39. Few
studies have examined the validity of 1-RM prediction methods with
smaller muscle groups. The researchers hypothesized that the prediction
methods would yield valid estimates of 1-RM and accuracy of the
prediction methods would not be affected by type of lift. Young (23.6
±3.5 yrs.), recreationally trained males (n=27) were recruited.
Experimental procedure: During trial 1, subjects completed 1-RM testing
for the bench press and biceps curl. During the second trial, subjects
completed repetitions to fatigue at a weight load equal to 85% of
measured 1-RM. One-repetition maximums and number of repetitions
performed at 85% measured 1-RM were recorded. Correlations between
measured and predicted 1-RMs demonstrated a moderate to strong
relationship (r = .81 - .97 bench press; r = .70 - .91 biceps curl). The
means of the predicted 1-RMs for the bench press were 94.2 ± 24.2 kg
and 94.9 ±24.5 kg. Both were lower than the mean of the measured 1RMs (95.5 ± 26.5 kg). The means of the predicted 1-RMs for the biceps
curl were 51.1 ±12.3 kg and 51.4 ± 12.4 kg. Both were higher than the
mean of the measured 1-RMs 49.4 ± 11.8 kg. These differences were
not significant. Error of prediction was between 5.4 and 6.8 kg for the
bench press and between 5.3 and 6.9 kg for the biceps curl. The Total
Error of Estimate was between 10.6% and 13.5% of the means.
Employing either prediction equation appears to be appropriate for
predicting bench press and biceps curl maximums.
Key Words: Resistance Training, Strength Testing, Dynamic Strength.
Accuracy 1-RM Prediction Equations
33
INTRODUCTION
Intensity for strength training is often based on a percentage of 1-repetition maximum (1-RM). The
most widely accepted method of determining a person’s 1-RM is a direct one in which the maximum
is actually achieved through a series of trials. This direct method is detailed by the American College
of Sports Medicine (10). The second means of obtaining 1-RM is an indirect method in which an
individual performs multiple repetitions at a specified weight load and those results are entered into
one of many prediction equations (1, 2, 3, 4, 5, 7, 8, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24). The 1-RM
is a critical variable for the purpose of prescribing exercise in various populations. Actual 1-RM testing
may not be appropriate with certain populations. These groups may benefit from the use of prediction
equations aimed at estimating maximal strength. The use of multiple repetitions to predict 1-RM is
beneficial. Most notably, the method is considered to be a safer method especially in the presence of
known injury (1). The current study examined the validity of the Berger (2, 3) and O’Conner et al. (20)
non-exercise specific 1-RM prediction methods for the bench press and biceps curl when compared
to the determined 1-RM. These equations were chosen because they are two of the more commonly
cited equations.
Knight (12) was one of the first to develop load specific exercise programs based on a person’s 1-RM.
His method was known as the Daily Adjustable Progressive Resistance Exercise (DAPRE) and was
used primarily for training persons on an individual basis and for patients recovering from injury.
Knight (12) was one of the first to determine that prediction of 1-RM from lesser loads offers added
safety for beginners and for those recovering from injury. This may prove beneficial for individuals
hesitant to lift a maximal weight or those who are medically restricted from maximal exertion (13). As
resistance training involves a variety of exercises performed for different muscle groups, it is critical to
examine the nature of prediction equations as they relate to the various exercises. Most previous
work has focused on core lifts or used exercise specific equations for smaller muscle groups (1, 7, 15,
17, 18, 19, 21). Core lifts are generally considered to be the bench press, deadlift, and squats.
Research suggests that exercise specific equations are more accurate than non-specific equations in
estimating 1-RM and that the accuracy of prediction decreases at higher repetitions (1, 5, 7, 15, 17,
18, 19, 24). Accuracy of prediction equations have also been shown to vary over different resistance
exercises, particularly when linked to the size of the muscle groups and the range of the movement
(4, 8, 10). As most resistance exercise sessions involve both core and accessory lifts, it is important
to examine the accuracy of prediction during both types of lifts. The cumbersome process of using
different prediction equations for each exercise makes this practice impractical. The examination of
predictability from a single equation increases the likelihood that such equation would be most useful
in the development of multi-RM testing procedures. This, combined with the ever increasing focus on
the resistance training component of physical activity, prompted the current investigation.
Several investigations have indicated that dynamic muscular strength can be accurately estimated
from multiple repetition testing with much of the research focusing on what are considered to be core
lifts (1, 2, 3, 4, 5, 7, 8, 9, 12, 17, 18, 19). However, research does show that prediction equations may
yield valid results with smaller muscle group lifts, especially when used with four to six RM loads (9,
24). Four to six- repetition maximum prediction equations improved the predictive accuracy of 1-RM
strength compared to seven to ten-repetition maximum prediction equations (8, 9, 21, 24). There is
general agreement that no more than ten repetitions should be used to estimate 1-RM regardless of
the type of lift (8, 9, 24). Therefore, for the purpose of multiple repetition testing, the present research
effort used a load equal to 85% of the measured 1-RM. Berger (3) indicates that a participant should
be able to perform six to eight repetitions at this load. Stated differently, it is assumed that there is a 2
– 2.5% decrease in a person’s 1-RM mass for each single increase in repetition maximal (3). This
difference could be much higher or lower depending upon previous training experience, learning
Accuracy 1-RM Prediction Equations
34
phenomenon associated with proper technique and even certain psychological influences. In an effort
to decrease the effects of learning phenomenon and training effects, recreationally trained males
were chosen to participate in the current study.
Research shows that only one in five Americans meet minimum recommended activity guidelines as
set forth by the Centers for Disease Control and Prevention (CDC) and the American Heart
Association (AHA) (6). Current recommendations state that adults should engage in moderateintensity aerobic physical activity on five or more days a week for a minimum of 30 minutes each day
or in vigorous-intensity aerobic physical activity three days a week for a minimum of 20 minutes each
day. Combinations of moderate and vigorous intensity activities can be combined to meet these
recommendations. Recommendations further state adults should perform activities that maintain or
increase muscular strength and endurance at least two days each week (6, 8, 10). These
recommendations are supported by the American College of Sports Medicine (ACSM) (9) and by the
CDC (6). As varying populations are being prescribed resistance exercise, this has led to a need to
better understand the accuracy of prediction equations with different muscle groups. Resistance
training using all major muscle groups has been shown to enhance the five health related
components of fitness when performed properly. These components are 1) body composition 2)
cardiorespiratory endurance 3) muscular strength 4) muscular endurance 5) muscular flexibility (9).
Accurate estimation of the 1-RM for each major muscle group is a key aspect of proper exercise
prescription and to the development of safe and effective resistance training programs.
The nature of the relationship between maximal and submaximal strength is a primary factor
influencing the prediction of 1-RM. Brzycki (5) argues that there is a distinct relationship between
anaerobic endurance and strength. Brzycki (5) goes on to state that it appears this relationship is not
quite linear beyond ten repetitions. It is also possible that individual muscle groups have different
relationships between maximal and submaximal strength. Therefore, the validity of prediction
equations with the bench press and biceps curl may be different. Another consideration is the effect
of increasing strength. Changes in muscular strength, in a given subject or population, has been
shown to have little effect on prediction of 1-RM using submaximal loads (4).
For comparison purposes, the current study tested the validity of two prediction methods with a small
muscle group as well as a large muscle group using non-exercise specific equations. It was
hypothesized that the prediction methods would yield valid estimates of 1-RM and accuracy of the
prediction methods would not be affected by type of lift.
METHODS
Subjects
Permission for the current investigation was approved by the Human Subjects Review Boards at
Indiana State University and at Southern Illinois University-Carbondale. Twenty-seven male
volunteers currently participating in recreational physical activity agreed to participate in this study.
Mean age of the group was 23.6 ± 3.5 years. Twenty-two of the subjects identified themselves as
Caucasian. Five subjects identified themselves as African-American. Subjects chosen for this study
reported that they were currently incorporating resistance training as part of their physical activity
regimen. Subjects additionally reported resistance training an average of 3.56 + 1.11 days per week.
Subjects were excluded if they had recently, or were currently using a personal trainer. The subjects
did not report skeletal muscle or cardiovascular complications during testing. Signed informed
consent and a medical history were obtained from each subject prior to participation. Subjects were
given instructions concerning test day procedures and what would be expected during each trial.
Subjects reported they had a “good night’s rest“, maintained adequate hydration, avoided alcohol and
Accuracy 1-RM Prediction Equations
35
tobacco prior to testing and avoided strenuous exercise the day of testing. This protocol was
observed for both days of testing.
Procedures
Upon arrival to the laboratory, subjects read and signed informed consent forms before any testing
took place. All questions were answered regarding the study procedures at this time. Height, weight,
and training history were recorded. A brief medical history was obtained at this time. The subjects
then underwent the first of two experimental trials beginning with 1-RM testing. The trials were
separated by at least 48 hr. apart, but not more than one week.
As part of the initial session, testing was performed to assess the 1-RM for both the bench press and
biceps curl exercises. A flat bench and an adjustable 45 degree curl bench were used for the
respective lifts. The protocol developed by the American College of Sports Medicine was followed
during this trial to determine 1-RM (9). Participants were allowed a light warm-up of 5 to 10 repetitions
at 40% to 60% of perceived maximum. Following a 1-minute rest period, the participants performed 3
to 5 repetitions at 60% to 80% of perceived maximum. Additional weight was added in small
increments until concentric failure occurred. 3 to 5 minutes rest occurred between attempts. To date
there is no standard for minimal rest interval between successive 1-RM attempts (24). Several studies
have used a two to three minute rest period (11, 22, 23). Other investigations indicate a rapid return
in maximal force production following a fatiguing task (22, 23). The practical applications are that rest
intervals, even relatively short ones, are not a major factor in the success of 1-RM attempts (23).
Subjects were encouraged to lift additional resistance to be sure the maximal muscle force was
achieved. Only when it was clear from their effort that no further resistance could be added was a
non-failure trial accepted. The 1-RM was determined to be the most resistance the subject could
concentrically lift once. Testing consisted of an average of 3 to 4 attempts with a maximum of 6
attempts. All lifts were conducted with an experienced spotter present.
Proper technique for the bench press was as follows. The subject lay horizontally on the back with
arms flexed at approximately a 90 degree angle at the elbow. The hands were placed in a horizontal
position and the width of the grip was set at shoulder width. Each subject started the lift at full
extension of the elbows. The barbell was lowered to the chest, held 1 sec. before the arms were fully
extended back to the starting position. Subjects were instructed that both portions must be completed
in a controlled fashion.
Proper technique for the biceps curl was as follows. Subjects were seated at a 45 degree curl bench.
The height was set so that the top of the curl bench was at mid-sternal level. Seat height allowed for
both feet to be planted on the ground and for the back to remain straight. A spotter assisted the
subject to a starting position at the top part of the lift. At this point, the bar was just below the chin
with elbows flexed at approximately a 90 degree angle. The bar was then lowered by slowly
extending the elbows to a point of 180 degree elbow extension. The concentric portion of the
contraction consisted of raising the bar back to the starting position. Subjects were instructed to
complete the lift in a controlled fashion with the back remaining straight and without the weights being
swung or bounced. A repetition was counted when the protocol was met.
The second day of testing consisted of an experimental trial at 85% of the previously measured 1RM. After an appropriate warm-up consisting of 3-5 repetitions at 60.4% to 80.7% 1-RM, a weight
load equal 85% ± 1.3% of the previously obtained 1-RM was loaded onto the bar. The subject was
asked to complete one set of repetitions to concentric failure. The number of repetitions recorded was
equal to the number of concentric lifts completed with proper technique as determined by the
Accuracy 1-RM Prediction Equations
36
researcher. The Berger (2,3) and the O’Conner et al. (20) prediction methods were then used to
determine predicted 1-RMs. The Berger and O’Conner equations are listed below.
Statistical Analyses
All data were analyzed using Statistical Package for the Social Sciences (SPSS) version 11 (IBM
Company, Chicago, IL). Data are presented as means and standard deviations. Alpha was set at .05
which was accepted as significant. Differences in measured and predicted 1-RMs were determined
using one-way ANOVA with actual resistance or predicted 1-RM as the dependent variable. The two
assumptions of the ANOVA were met. The analysis showed that the data had a normal distribution
and the variances were not significantly different (p > 0.05). Correlations between measured and
predicted 1-RMs were determined using Pearson’s Product Moment analysis. The Total Error of
Estimate was also determined to analyze the magnitude of the prediction error. The equation for Total
Error of Estimate is listed below (16).
RESULTS
Descriptive data for the two groups are found in Table 1.Bench press was not different (p > 0.05;
actual p = .982) between the measured 1-RM and the two predicted 1-RMs. Data are presented in
terms of means and standard deviations. The Total Error of Table 1. Descriptive data of the
Estimate was lower for the O’Conner et al. equation (20) than the subjects (n=27).
Berger equation (2, 3) during the bench press. Mean number of Paramter
Mean+SD
repetitions completed at 85% measured 1-RM was 8.6 (Table 2).
Biceps curl was not different (p > .05; actual p = .824) between the
measured 1-RM and the two predicted 1-RMs. Data are presented
in terms of means and standard deviations. The Total Error of
Estimate was lower for the O’Conner et al. equation (20) than the
Berger equation (2, 3) during the biceps curl exercise. The Total
Error of Estimate was lower for the O’Conner et al. equation (19).
Mean number of repetitions completed at 85% measured 1-RM
was 9.3 (Table 3).
Age (years)
Height (cm)
Weight (kg)
23.6±3.5
180.3±8.2
83.1±19.6
Training Volume
(days/week)
3.56±1.1
Training
Experience
(years)
4.74±2.1
DISCUSSION
The primary finding of the current investigation was that the prediction methods were equally effective
in predicting bench press and biceps curl 1-RMs. There are numerous equations used to predict 1RMs. The current study focused on two well known prediction equations. The equations chosen were
the Berger equation (2, 3) and an equation from O’Conner et al. (20). The correlations (.84 - .98) and
the lack of significant differences and similar error rates between measured and predicted 1-RMs
strongly suggest that these equations produce valid estimates of 1-RMs, even when used with
smaller muscle groups. In addition, these data suggest that exercise specific equations are not
needed to yield accurate estimates of 1-RM when either of the two aforementioned equations is used.
This finding is important in that using a single equation allows for a reduction in testing time and
Accuracy 1-RM Prediction Equations
37
makes 1-RM testing simpler and more practical. Other research efforts suggest that the equations are
capable of yielding valid estimates for lower body exercises (13) and can be used with machine lifts
or with free weights (15). The prediction method showed little bias in whether the measured 1-RM is
over or underestimated.
The Total Error of Estimate suggests that while they are valid, the equations are not without some
error. The current findings are consistent with the work of others (1, 8, 11). The equation with the
lowest Total Error of Estimate
Table 2. Measured and Predicted 1RM in the Bench Press
for both the bench press and the
Total Error
Total Error
Equation
Mean±SD
r=
biceps curl was the O’Conner et
(kg)
(%)
al. equation (20). The fact that
Measured
95.5±26.5
the error rates for the biceps curl
Berger
94.2±24.2
.97
6.8
7.2
show nearly a twofold difference
O’Conner et al.
94.9±24.5
.98
5.4
5.7
in
the
amount
of
error
associated with prediction is
most likely because the equations were initially designed and tested with large muscle groups.
One limitation of the current study was the use of only two upper body lifts. Future investigations
could test a variety of both upper and lower body lifts. Also, the current study selected recreationally
trained male subjects. Potential differences may be noted if training status and gender are not
controlled. Additional research should be conducted with different participant groups and varying
percentages of 1-RM loads.
In summary, non-exercise specific 1-RM prediction equations produced valid estimates of muscular
strength for the bench press and Table 3. Measured and Predicted 1RM in the Biceps Curl
biceps curl. There was a
Total Error
Total Error
Mean±SD
r=
relatively higher rate of error Equation
(kg)
(%)
when the equations were used Measured
49.4±11.8
to predict 1-RM with a small Berger
51.1±12.3
.84
6.9
13.5
muscle group lift in the current O’Conner et al.
51.4±12.4
.91
5.3
10.6
study. Our results are in
agreement with others regarding this concept (8, 21, 24). At 85% 1-RM, the equations suggest that
seven to eight repetitions can be performed.
CONCLUSIONS
The present results may have implications for the teacher, clinician or personal trainer. With more
emphasis being placed on concepts such as “New Physical Education” and recommendations from
the CDC, AHA, and ACSM for inclusion of resistance training as part of physical activity programs,
the need for safe, accurate measures of 1-RM is important. Validation of the Berger (2, 3) and
O’Connor et al. (20) equations indicates that a single prediction equation may be used in developing
individualized resistance programs for students, clients, etc. ACSM (9) states that one can use a 6RM, for example, as a measure of muscular fitness. If a subject is following a 10- to 12-RM weight
training program, muscular fitness can be tracked over time without the need to measure the
subjects’ 1-RM (9). The use of prediction equations may be safer for older populations and with those
recovering from injury. For some purposes, a measured 1-RM may be warranted, but the prediction
method allows for an accurate estimate without the need to elicit maximal muscle tension.
Accuracy 1-RM Prediction Equations
38
Address for correspondence: Hutchins, MD, PhD Department of Health, Safety, and Environmental
Health Sciences, Indiana State University, Terre Haute, IN, USA, 47803. Phone (812)237-3108; FAX:
(812)237-8607.; Email. matt.hutchins@indstate.edu.
REFERENCES
1.
Abadie, B, Altorfer, G, and, Schuler, P. Does a regression equation to predict maximal
strength in untrained lifters remain valid when subjects are technique trained? J Strength
Cond Res 1999;13:259-263.
2.
Berger, RA. Optimum repetitions for the development of strength. Res Q 1962;33:334-339.
3.
Berger, RA. Relationships between dynamic strength and dynamic endurance. Res Q
1970;41:115-116.
4.
Brechue, W. F., and Mayhew, J. L. Upper-body work capacity and 1RM prediction are
unaltered by increasing muscular strength in college football players. J Strength Cond Res
2009;23:2477-2486.
5.
Brzycki, M. Predicting a one rep max from reps-to-fatigue. JOPERD 1993;64:88-90.
6.
Centers for Disease Control and Prevention (2005). National Center for Health Statistics:
About Healthy People 2010. Available at: URL: http://www.cdc.gov/nchs.htm. Accessed 1
February 2008.
7.
Chapman, PP, Whitehead, JR, and Binkert, RH. The 225-lb reps-to fatigue test as a
submaximal estimate of 1-RM bench press performance in college football players. J Strength
Cond Res 1998;12:258-261.
8.
Dohoney, P, Chromiak, JA, Lemire,et al. Prediction of one repetition maximum (1-RM) strength
from a 4-6 RM and a 7-10 RM submaximal strength test in healthy young adult males.
JEPonline 2002;5(3):54-56.
9.
Franklin, BA, Whaley, MH, Howley, ET, et al. ACSM Guidelines for Exercise Testing and
Prescription. 6th Editition. Philadelphia, PA: Wolters Kluwe Company, 2010. pp. 81-83.
10.
Haskell, WL, Lee, IM, Pate, RR, Powell, KE, Blair, SN, Franklin, BA, Macera, CA, Heath, GW,
Thompson, PD, and Bauman, A. Physical activity and public health: Updated
recommendations for adults from the American College of Sports Medicine and the American
Heart Association. Med Sci Sports Exerc 2007;39:1423-1434.
11.
Hitchcock, HC. Recovery of short term power after dynamic exercise. J Appl Physiol
1989;67:677-681.
12.
Knight, K. Knee rehabilitation by the daily progressive resistive exercise technique. Am J
Sports Med 1979;7:336-337.
Accuracy 1-RM Prediction Equations
39
13.
Knutzen, KM, Brilla, LR, and Caine, D. Validity of 1 RM prediction equations for older adults. J
Strength Cond Res 1999;13:242-246.
14.
Kravitz, L., Akalan, C., Nowicki, K., and Kinzey, S. J. Prediciton of 1 repetition maximum in
high-school power lifters. J Strength Cond Res 2003;17:167-172.
15.
Lesuer, DA, Mccormick, JH, Mayhew, JL, et al. The accuracy of prediction equations for
estimating 1-RM performance in the bench press, squat, and deadlift. J Strength Cond Res
1997;11:211-213.
16.
Lowry,
R.
Correlation
and
Regression.
Available
http://faculty.vassar.edu/lowry/corr_stats.html. Accessed 1 May 2009.
17.
Mayhew, JL, Ware, JS, Bemben, MG, et al. The NFL-225 test as a measure of bench press
strength in college football players. J Strength Cond Res 1999;13:130-134.
18.
Mayhew, JL, Ware, JS, Cannon, K, et al. Validation of the NFL-225 test for predicting 1-RM
bench press performance in college football players. J Sports Med Phys Fitness
2002;42:304-309.
19.
Morales, J and Sobonya, S. Use of submaximal repetition tests for predicting 1 RM strength in
class athletes. J Strength Cond Res 1996;10:186-189.
20.
O’Conner, B, Simmons, J and O’shea, P. Weight Training Today. St. Paul, MN: West
Publishers, 1989.
21.
Reynolds, JM, Gordon, TJ, and Roberts, RA. Prediction of one repetition maximum strength
from multiple repetition maximum testing and anthropometry. J Strength Cond Res
2006;20:584-593.
22.
Sahlin, K, and Ren, JM. Relationships of contraction capacity to metabolic changes during
recovery from a fatiguing contraction. J Appl Phys 1989;67:648-654.
23.
Weir, JP, Wagner, LL, and Housh, TJ. The effect of rest interval length on repeated maximal
bench presses. J Strength Cond Res 1994;8:58-61.
24.
Whisenant, M. J., Panton, L. B., East, W. B., and Broeder, C. E. Validation of submaximal
prediction equations in estimating equations for the 1 repetition maximum bench press test on
a group of collegiate football players. J Strength Cond Res 2003;17:221-227.
25.
Wood, TM, Maddalozzo, GM, and Harter, RA. Accuracy of seven equations for predicting 1RM performance of apparently healthy, sedentary older adults. Meas Phys Edu Exerc Sci
2002;6:67-94.
at:
URL:
Disclaimer
The opinions expressed in JEPonline are those of the authors and are not attributable to JEPonline,
the editorial staff or ASEP.