Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities

Mehmet Yavuz; Osman Dişçeken; Erhan Işıkdemir; Mücahit Işık; Hamit Cihan

doi:10.54141/psbd.1612949

Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities

Abstract

This study aimed to assess the validity of 15 formulas used to estimate one repetition maximum (1RM) bench press and deep squat strength in male and female university students who are recreationally active in sports. Forty-eight students (age = 22.4 ± 2 years, height = 169.8 ± 10.2 cm, weight = 66.5 ± 17.6 kg, BMI = 22.8 ± 4.3 kg/m2) from the Faculty of Sport Sciences participated. The participants’ 1RM values in the bench press and deep squat tests were compared with 15 different formulas. Levene’s test was used to test the homogeneity of variance, and a paired t-test was employed to evaluate the agreement of repeated paired measurements. Additionally, Bland-Altman plots, Intraclass Correlation Coefficient (ICC), and Concordance Correlation Coefficient (CCC) were utilized to assess the agreement of measurements. Results indicated that some formulas provided predictions close to the measured 1RM values, while others showed deviations. Specifically, in the bench press test, the P2 (Berger) and P6 (Kemmler) formulas provided more accurate predictions for female participants, while P5 (Cummings & Finn) and P10 (Mayhew) were successful for males. In the deep squat test, P3 (Brown) and P4 (Brzycki) provided the best predictions for females, while P1 (Adams) and P12 (O'Connor) showed high agreement for males. The findings suggest that selecting suitable formulas for 1RM estimation by gender and exercise type is essential for enhancing the effectiveness of strength training in sports sciences.

Keywords

Ethical Statement

This study was approved by Nevsehir Hacı Bektaş Veli University Scientific Research Ethics Committee on 06/09/2024 with the number 2400081856.

References

Adams, G. M. (1998). Exercise physiology: Laboratory manual (3. ed.). Mcgraw-Hill
Aksakallı, O., & Gelen, E. (2023). Yük-hız ilişkisi kullanılarak bir tekrarlı maksimum tahmini güvenilir midir? Farklı yöntemlerin karşılaştırılması. Spor Bilimleri Araştırmaları Dergisi, 8(1), 57-66. https://doi.org/https://doi.org/10.25307/jssr.1177374
Baker, D. G., & Newton, R. U. (2008). Comparison of lower body strength, power, acceleration, speed, agility, and sprint momentum to describe and compare playing rank among professional rugby league players. The Journal of Strength & Conditioning Research, 22(1), 153-158. https://doi.org/https://doi.org/10.1519/JSC.0b013e31815f9519
Balcı, Ş. S., & Özdemir, H. (2020). Genç yetişkinlerde setler arası dinlenme aralığı sürelerinin ve farklı yüklerin kuvvet egzersizi serilerindeki tekrar sayısına etkisi. Turkiye Klinikleri Journal of Sports Sciences, 12(1), 23-32. https://doi.org/https://doi.org/10.5336/sportsci.2019-71704
Berger, R. A. (1970). Relationship between dynamic strength and dynamic endurance. Research Quarterly. American Association for Health, Physical Education and Recreation, 41(1), 115-116. https://doi.org/https://doi.org/10.1080/10671188.1970.10614955
Braith, R. W., Graves, J. E., Leggett, S. H., & Pollock, M. L. (1993). Effect of training on the relationship between maximal and submaximal strength. Medicine & Science in sports & exercise, 25(1), 132-138. https://doi.org/https://doi.org/10.1249/00005768-199301000-00018
Brown, H. L. (1992). Lifetime fitness (3. ed.). Gorsceach Scarisbrick.
Brzycki, M. (1993). Strength testing—predicting a one-rep max from reps-to-fatigue. Journal of Physical Education, Recreation & Dance, 64(1), 88-90. https://doi.org/https://doi.org/10.1080/07303084.1993.10606684

Cummings, B., & Finn, K. J. (1998). Estimation of a one repetition maximum bench press for untrained women. The Journal of Strength & Conditioning Research, 12(4), 262-265.
Feigenbaum, M. S., & Pollock, M. L. (1999). Prescription of resistance training for health and disease. Medicine & Science in sports & exercise, 31(1), 38-45. https://doi.org/https://doi.org/10.1097/00005768-199901000-00008
Gordon, N. F., Kohl, H. W., Pollock, M. L., Vaandrager, H., Gibbons, L. W., & Blair, S. N. (1995). Cardiovascular safety of maximal strength testing in healthy adults. The American Journal of Cardiology, 76(11), 851-853. https://doi.org/https://doi.org/10.1016/s0002-9149(99)80245-8
Grgic, J., Lazinica, B., Schoenfeld, B. J., & Pedisic, Z. (2020). Test–retest reliability of the one-repetition maximum (1RM) strength assessment: a systematic review. Sports Medicine-Open, 6, 1-16. https://doi.org/https://doi.org/10.1186/s40798-020-00260-z
Hackett, D. A., Johnson, N. A., Halaki, M., & Chow, C.-M. (2012). A novel scale to assess resistance-exercise effort. Journal of Sports Sciences, 30(13), 1405-1413. https://doi.org/https://doi.org/10.1080/02640414.2012.710757
Hackett, D. A., Johnson, N. A., Halaki, M., & Chow, C. M. (2012). A novel scale to assess resistance-exercise effort. Journal of Sports Sciences, 30(13), 1405–1413. https://doi.org/10.1080/02640414.2012.710761
Haff, G. G., & Triplett, N. T. (2015). Essentials of strength training and conditioning (4. ed.). Human Kinetics.
Hart, C., Ward, T., & Mayhew, J. (1991). Anthropometric correlates of bench press performance following resistance training. Research in Sports Medicine: An International Journal, 2(2), 89-95. https://doi.org/https://doi.org/10.1080/15438629109511904
Hazır, T., Esatbeyoğlu, F., Ekinci, Y., & Kin İşler, A. (2019). Genç erkeklerde bir tekrar maksimal kuvvetin kestirilmesinde kullanılan formüllerin geçerliliği. Turkiye Klinikleri Journal of Sports Sciences, 11(3), 117-124. https://doi.org/https://doi.org/10.5336/sportsci.2019-70546
Işık, M., Akçakaya, M., & Şenel, Ö. (2020). Esneklik performansının kuvvet ile ilişkisi. Journal of Social and Humanities Sciences Research, 7(63), 3894-3904. https://doi.org/http://dx.doi.org/10.26450/jshsr.2252
Jaric, S. (2002). Muscle strength testing: use of normalisation for body size. Sports Medicine, 32, 615-631. https://doi.org/https://doi.org/10.2165/00007256-200232100-00002
Kemmler, W. K., Lauber, D., Wassermann, A., & Mayhew, J. L. (2006). Predicting maximal strength in trained postmenopausal woman. The Journal of Strength & Conditioning Research, 20(4), 838-842.
Knutzen, K. M., Brilla, L. R., & Caine, D. (1999). Validity of 1RM prediction equations for older adults. The Journal of Strength & Conditioning Research, 13(3), 242-246.
Koo, T. K., & Li, M. Y. (2016). A guideline of selecting and reporting intraclass correlation coefficients for reliability research. Journal of Chiropractic Medicine, 15(2), 155-163. https://doi.org/https://doi.org/10.1016/j.jcm.2016.02.012
Kraemer, W. J., & Ratamess, N. A. (2004). Fundamentals of resistance training: progression and exercise prescription. Medicine & Science in sports & exercise, 36(4), 674-688. https://doi.org/https://doi.org/10.1249/01.mss.0000121945.36635.61
Kravitz, L., Akalan, C., Nowicki, K., & Kinzey, S. J. (2003). Prediction of 1 repetition maximum in high-school power lifters. The Journal of Strength & Conditioning Research, 17(1), 167-172.
Lander, J. (1985). Maximum based on repetitions. National Strength and Conditioning Association, 6, 60–61.
Levinger, I., Goodman, C., Hare, D. L., Jerums, G., Toia, D., & Selig, S. (2009). The reliability of the 1RM strength test for untrained middle-aged individuals. Journal of Science and Medicine in Sport, 12(2), 310-316. https://doi.org/https://doi.org/10.1016/j.jsams.2007.10.007
Lopes, C. R., Aoki, M. S., Crisp, A. H., de Mattos, R. S., Lins, M. A., da Mota, G. R., Schoenfeld, B. J., & Marchetti, P. H. (2017). The effect of different resistance training load schemes on strength and body composition in trained men. Journal of Human Kinetics, 58, 177-186. https://doi.org/https://doi.org/10.1515/hukin-2017-0081
Macht, J. W., Abel, M. G., Mullineaux, D. R., & Yates, J. W. (2016). Development of 1RM prediction equations for bench press in moderately trained men. The Journal of Strength & Conditioning Research, 30(10), 2901-2906. https://doi.org/https://doi.org/10.1519/JSC.0000000000001385
Mayhew, J., Ball, T., & Bowen, J. (1992). Prediction of bench press lifting ability from submaximal repetitions before and after training. Research in Sports Medicine: An International Journal, 3(3), 195-201. https://doi.org/https://doi.org/10.1080/15438629209511946
Mayhew, J., Kerksick, C. D., Lentz, D., Ware, J. S., & Mayhew, D. L. (2004). Using repetitions to fatigue to predict one-repetition maximum bench press in male high school athletes. Pediatric Exercise Science, 16(3), 265-276. https://doi.org/https://doi.org/10.1123/pes.16.3.265
Mayhew, J. L., Ball, T. E., Arnold, M. D., & Bowen, J. C. (1992b). Relative muscular endurance performance as a predictor of bench press strength in college men and women. The Journal of Strength & Conditioning Research, 6(4), 200-206.
Mayhew, J. L., Johnson, B. D., LaMonte, M. J., Lauber, D., & Kemmler, W. (2008). Accuracy of prediction equations for determining one repetition maximum bench press in women before and after resistance training. The Journal of Strength & Conditioning Research, 22(5), 1570-1577. https://doi.org/https://doi.org/10.1519/JSC.0b013e31817b02ad
Mayhew, J. L., Prinster, J., Ware, J., Zimmer, D., Arabas, J., & Bemben, M. (1995). Muscular endurance repetitions to predict bench press strength in men of different training levels. The Journal of sports medicine and physical fitness, 35(2), 108-113.
McBurnie, A. J., Allen, K. P., Garry, M., Martin, M., Jones, P. A., Comfort, P., & McMahon, J. J. (2019). The benefits and limitations of predicting one repetition maximum using the load-velocity relationship. Strength & Conditioning Journal, 41(6), 28-40. https://doi.org/https://doi.org/10.1519/SSC.0000000000000496
Mitter, B., Csapo, R., Bauer, P., & Tschan, H. (2022). Reproducibility of strength performance and strength-endurance profiles: A test-retest study. Plos One, 17(5), e0268074. https://doi.org/https://doi.org/10.1371/journal.pone.0268074
Naclerio, F., Faigenbaum, A. D., Larumbe-Zabala, E., Perez-Bibao, T., Kang, J., Ratamess, N. A., & Triplett, N. T. (2013). Effects of different resistance training volumes on strength and power in team sport athletes. The Journal of Strength & Conditioning Research, 27(7), 1832-1840. https://doi.org/https://doi.org/10.1519/JSC.0b013e3182736d10
O’Connor, B., Simmons, J., & O’Shea, P. (1989). Weight training today (1. st ed.). West Publishing.
Pamart, N., Drigny, J., Azambourg, H., Remilly, M., Macquart, M., Lefèvre, A., Lahjaily, K., Parienti, J. J., Rocamora, A., & Guermont, H. (2023). Effects of a 20-week high-intensity strength training program on muscle strength gain and cardiac adaptation in untrained men: preliminary results of a prospective longitudinal study. JMIR Formative Research, 7, e47876. https://doi.org/https://doi.org/10.2196/47876
Picerno, P., Iannetta, D., Comotto, S., Donati, M., Pecoraro, F., Zok, M., Tollis, G., Figura, M., Varalda, C., Di Muzio, D., Patrizio, F., & Piacentini, M. F. (2016). 1RM prediction: a novel methodology based on the force–velocity and load–velocity relationships. European Journal of Applied Physiology, 116(10), 2035–2043.
Pioske, J. N., Boyd, M. L., Pohlman, R. L., & McAllister, M. J. (2025). Cross-validation of equations for estimating 1-repetition maximum bench press from repetitions to failure in recreationally active men. Journal of Strength and Conditioning Research, 39(2), 560–566. https://doi.org/10.1519/JSC.0000000000004893
Ratamess, N. A., Falvo, M. J., Mangine, G. T., Hoffman, J. R., Faigenbaum, A. D., & Kang, J. (2007). The effect of rest interval length on metabolic responses to the bench press exercise. European Journal of Applied Physiology, 100(1), 1–17. https://doi.org/10.1007/s00421-007-0394-y
Reynolds, J. M., Gordon, T. J., & Robergs, R. A. (2006). Prediction of one repetition maximum strength from multiple repetition maximum testing and anthropometry. Journal of Strength and Conditioning Research, 20(3), 584–592. https://doi.org/10.1519/R-15304.1
Ribeiro, A., Silva, J. A. da, Nascimento, M., Martinho, D., dos Santos, L., de Salles, B., Mayhew, J., & Cyrino, E. S. (2024). Accuracy of 1RM Prediction Equations Before and After Resistance Training in Three Different Lifts. International Journal of Strength and Conditioning, 4(1).
Ribeiro Neto, F., Guanais, P., Dornelas, E., Coutinho, A., & Costa, R. G. (2017). Validity of one-repetition maximum predictive equations in men with spinal cord injury. Spinal Cord, 55(10), 950-956. https://doi.org/https://doi.org/10.1038/sc.2017.49
Ruf, L., Chéry, C., & Taylor, K. (2017). Validity and Reliability of the Load-Velocity Relationship to Predict the 1RM in Deadlift. Journal of Strength and Conditioning Research, 31(11), 2897–2904.
Sarabia, J., Moya-Ramón, M., Hernández-Davó, J., Fernandez-Fernandez, J., & Sabido, R. (2017). The effects of training with loads that maximise power output and individualised repetitions vs. traditional power training. Plos One, 12(10), e0186601. https://doi.org/https://doi.org/10.1371/journal.pone.0186601
Schoenfeld, B. J., Contreras, B., Krieger, J., Grgic, J., Delcastillo, K., Belliard, R., & Alto, A. (2019). Resistance training volume enhances muscle hypertrophy but not strength in trained men. Medicine & Science in sports & exercise, 51(1), 94. https://doi.org/https://doi.org/10.1249/MSS.0000000000001764
Schoenfeld, B. J., Peterson, M. D., Ogborn, D., Contreras, B., & Sonmez, G. T. (2015). Effects of low-vs. high-load resistance training on muscle strength and hypertrophy in well-trained men. The Journal of Strength & Conditioning Research, 29(10), 2954-2963. https://doi.org/https://doi.org/10.1519/JSC.0000000000000958
Seo, D.-i., Kim, E., Fahs, C. A., Rossow, L., Young, K., Ferguson, S. L., Thiebaud, R., Sherk, V. D., Loenneke, J. P., & Kim, D. (2012). Reliability of the one-repetition maximum test based on muscle group and gender. Journal of Sports Science & Medicine, 11(2), 221. Shaw, C. E., McCully, K. K., & Posner, J. D. (1995). Injuries during the one repetition maximum assessment in the elderly. Journal of Cardiopulmonary Rehabilitation and Prevention, 15(4), 283-287. https://doi.org/https://doi.org/10.1097/00008483-199507000-00005
Software, M. (2024). MedCalc Statistical Software (Version 20). MedCalc Software Ltd. . Retrieved October 28, 2024 from https://www.medcalc.org
Team, R. C. (2024). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing. Retrieved October 28, 2024 from https://www.r-project.org/
Tan, S., Wang, J., & Liu, S. (2015). Establishment of the Prediction Equations of 1RM Skeletal Muscle Strength in 60- to 75-Year-Old Chinese Men and Women. Journal of Aging and Physical Activity, 23(4), 600–646.
Tucker, J. E., Pujol, T. J., Elder, C. L., Nahikian-Nelms, M. L., Barnes, J. T., & Langenfeld, M. E. (2006). One-repetition maximum prediction equation for traditional college-age novice females: 1808: Board# 181 2: 00 PM–3: 00 PM. Medicine & Science in sports & exercise, 38(5), 293.
Wathen, D. (1994). Load assignment (2 ed., Vol. 435). Human Kinetics.
Welday, J. (1988). Should you check for strength with periodic max lifts. Scholasric Coach, 57(9), 49-68.
Willardson, J. M. (2006). A brief review: Factors affecting the length of the rest interval between resistance exercise sets. The Journal of Strength & Conditioning Research, 20(4), 978–984. https://doi.org/10.1519/R-19325.1
Yüksel, O., Erzeybek, M. S., Şentürk, A., & Akın, S. (2019). Süper slow motion kuvvet antrenmanlarının kadın voleybolcuların bench press peak power ve 6 sn–30 sn wattbike peak power değerlerine etkisinin incelenmesi. Uluslararası Spor Bilimleri Öğrenci Çalışmaları, 1(1), 50-57.

Details

Primary Language

English

Subjects

Sports Training

Journal Section

Research Article

Authors

Mehmet Yavuz
0000-0001-6096-2197
Türkiye

Osman Dişçeken
0000-0003-2500-4932
Türkiye

Erhan Işıkdemir ^*
0000-0002-4443-2222
Türkiye

Mücahit Işık
0000-0002-9172-0104
Türkiye

Hamit Cihan
0000-0002-7704-1316
Türkiye

Publication Date

August 30, 2025

Submission Date

January 6, 2025

Acceptance Date

August 5, 2025

Published in Issue

Year 2025 Volume: 16 Number: 2

DOI

https://doi.org/10.54141/psbd.1612949

IZ

https://izlik.org/JA34LE59EK

Cite

RIS / Bibtex

APA

Yavuz, M., Dişçeken, O., Işıkdemir, E., Işık, M., & Cihan, H. (2025). Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities. Pamukkale Journal of Sport Sciences, 16(2), 490-514. https://doi.org/10.54141/psbd.1612949

AMA

1.Yavuz M, Dişçeken O, Işıkdemir E, Işık M, Cihan H. Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities. Pamukkale J Sport Sci. 2025;16(2):490-514. doi:10.54141/psbd.1612949

Chicago

Yavuz, Mehmet, Osman Dişçeken, Erhan Işıkdemir, Mücahit Işık, and Hamit Cihan. 2025. “Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities”. Pamukkale Journal of Sport Sciences 16 (2): 490-514. https://doi.org/10.54141/psbd.1612949.

EndNote

Yavuz M, Dişçeken O, Işıkdemir E, Işık M, Cihan H (August 1, 2025) Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities. Pamukkale Journal of Sport Sciences 16 2 490–514.

IEEE

[1]M. Yavuz, O. Dişçeken, E. Işıkdemir, M. Işık, and H. Cihan, “Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities”, Pamukkale J Sport Sci, vol. 16, no. 2, pp. 490–514, Aug. 2025, doi: 10.54141/psbd.1612949.

ISNAD

Yavuz, Mehmet - Dişçeken, Osman - Işıkdemir, Erhan - Işık, Mücahit - Cihan, Hamit. “Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities”. Pamukkale Journal of Sport Sciences 16/2 (August 1, 2025): 490-514. https://doi.org/10.54141/psbd.1612949.

JAMA

1.Yavuz M, Dişçeken O, Işıkdemir E, Işık M, Cihan H. Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities. Pamukkale J Sport Sci. 2025;16:490–514.

MLA

Yavuz, Mehmet, et al. “Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities”. Pamukkale Journal of Sport Sciences, vol. 16, no. 2, Aug. 2025, pp. 490-14, doi:10.54141/psbd.1612949.

Vancouver

1.Mehmet Yavuz, Osman Dişçeken, Erhan Işıkdemir, Mücahit Işık, Hamit Cihan. Validity of Formulas Used to Estimate One Repetition Maximum Strength of Upper and Lower Extremities. Pamukkale J Sport Sci. 2025 Aug. 1;16(2):490-514. doi:10.54141/psbd.1612949