Indirect estimation of VO2max in athletes by ACSM’s equation: valid or not?


Hippokratia 2013, 17(2):136-140

Koutlianos N1, Dimitros E1, Metaxas T2, Deligiannis AS1, Kouidi E1
1Sports Medicine Laboratory, 2Laboratory of Ergophysiology-Ergometry, Department of Physical Education & Sport Science, Aristotle University of Thessaloniki, Thermi, Greece


Aim: The purpose of this study was to assess the indirect calculation of VO2max using ACSM’s equation for Bruce protocol in athletes of different sports and to compare with the directly measured; secondly to develop regression models predicting VO2 max in athletes.
Methods: Fiftyfive male athletes of national and international level (mean age 28.3 ± 5.6 yrs) performed graded exercise test with direct measurement of VO2 through ergospirometric device. Moreover, 3 equations were used for the indirect calculation of VO2max: a) VO2max= (0.2 · Speed) + (0.9 · Speed · Grade) + 3.5 (ACSM running equation), b) regression analysis model using enter method and c) stepwise method based on the measured data of VO2. Age, BMI, speed, grade and exercise time were used as independent variables.
Results: Regression analysis using enter method yielded the equation (R=.64, standard error of estimation [SEE] = 6.11): VO2max (ml·kg-1·min-1) = 58.443 – (0.215 · age) – (0.632 · BMI) – (68.639 · grade) + (1.579 · time) while stepwise method (R = .61, SEE = 6.18) led to: VO2max (ml·kg-1·min-1) = 33.971 – (0.291 · age) + (1.481 · time). The calculated values of VO2max from these regression models did not differ significantly from the measured VO2max (p>.05). On the contrary, VO2max calculated from the ACSM’s running equation was significantly higher from the actually measured value by 14.6% (p <.05).
Conclusions: In conclusion, it seems that ACSM’s equation is not capable of accurately predicting VO2max in athletes aged 18-37 years using Bruce protocol. Only theregression models were correlated moderately with the actually measured values of VO2max.

Key words: VO2max prediction, running equation, metabolic equivalent, exercise testing, cardiorespiratory fitness

Corresponding author: Dr Nikolaos Koutlianos, 75 Loutron Str, 57200 Lagadas, Greece, tel/fax: +302310992188, e-mail:


Maximal oxygen consumption (VO2max) is defined as the ability to transport and consume oxygen during exhausted work and is related to cardiorespiratory fitness1. The American College of Sports Medicine (ACSM) has published several metabolic equations for the indirect estimation of VO2max while walking, running, and stepping as well as for leg and arm ergometers2.

In the laboratory setting, the most accurate way to assess VO2max is undoubtedly via applying a maximal graded exercise test (GXT) performed to volitional exhaustion on a motorized treadmill or cycle ergometer while expired air is analyzed continuously by gas analyzers3,4. However, equipment costs and staff training limit direct measurement mainly to research and few clinical settings5. Thus, the need for an accurate prediction of the VO2 with the use of various equations is considered necessary. The equations can be performed according to: work information (speed, grade, work rate, step rate) or following calculations of appropriate work.

There are several exercise treadmill protocols for the prediction of VO2max. Current evidence suggests that in order to elicit the VO2max of apparently healthy individuals, continuous treadmill tests should generally last between 5 and 26 minutes. This is dependent on the basis that short tests are preceded and that treadmill grades do not exceed 15%6. The running equation of ACSM is only valid with steady state exercise and is designed for speeds greater than 5.0 mph (134 m·min-1)2.

In the literature, the majority of studies have developed several regression models for the prediction of VO2max based on a variety of maximal treadmill exercise tests2,7,8. Additionally, the indirect estimation of multiple equivalents (METs) in the majority of the commercially available software of exercise test units is calculated from the ACSM running equation and it is applied in many cardiovascular centers and sports medicine labs even when using interval protocols on the treadmill. The degree of error in estimating aerobic capacity in the stress test setting is not well characterized and from our knowledge there is no study examining the accuracy of the ACSM running equation using the Bruce protocol in a specific population such as athletes although it is still widely used. The introduction of ventilatory expired gas analysis into traditional stress test procedures led to the direct measurement of VO2. Despite this, estimating than directly measuring VO2 remains a very common clinical standard in many stress-testing laboratories assessing exercise-trained subjects for cardiovascular screening. Thus, the aim of this study was to evaluate the accuracy of the indirect VO2max measurement using the ACSM’s running equation for the Bruce protocol in athletes of different sports in comparison with the directly estimated. Additionally, a secondary goal was the prediction of VO2max using models of regression analysis.

Materials and Methods


Study participants included 55 male athletes of different sports (soccer, n=15; basketball, n=13; cycling, n=7; volleyball, n=7; body-building, n=4; weightlifting, n=3; wrestling, n=3 and tae-kwon do, n=3). The physical and anthropometric characteristics of the subjects are listed in Table I. All subjects had a minimum of 3 training sessions per week and they were competing at national and international level. Before the study, subjects provided informed consent for their participation. The study protocol was in agreement with the guidelines of the Ethics Committee of the Aristotle University of Thessaloniki.

Pretesting Procedures

All subjects underwent a noninvasive cardiovascular screening, before exercise testing, in accordance with the recommended standards9. The height was measured to the nearest 0.5 cm using a stadiometer (KDS, Kyoto, Japan) and the weight to the nearest 0.1 kg on a medical-scale grade (Seca, Hamburg, Germany). All subjects were asked to avoid drinking any caffeinated and alcoholic beverages or using any ergogenic aids at least two days before the experimental session.

VO2max direct measurements

All participants performed a maximal exercise test using a Trackmaster treadmill. For the purpose of the study the treadmill was calibrated in order to ensure the accuracy of grade and speed. Subjects exercised to exhaustion using Bruce protocol. All athletes did not use the handrails. The electrocardiogram was monitored continuously during the test (CH-2000, Cambridge Heart Co., USA). The VO2max was measured via an ergospirometric device based on breath-by-breath gas analyzing system (Ultima Series, MedGraphics, USA). Prior to testing, a pneumotachograph was calibrated using a 3.0 L-syringe at various flow rates. Thereafter, oxygen and carbon dioxide analyzers were calibrated with known gas mixture according to the specifications of the manufacturer. The following exercise test criteria were used for the achievement of VO2max:

  1. Leveling off (plateau) of oxygen uptake with an increase of work rate10.
  2. Respiratory exchange ratio (VCO2/VO2) greater than 1.1011.
  3. Achievement of 90% of the age-adjusted estimate of maximal heart rate12.

In addition, the following parameters were recorded from the cardiorespiratory exercise test: the duration of the test, the maximal value of METsmax both by the ergospirometer and the exercise testing software unit using the Bruce protocol, the maximal pulmonary ventilation (VEmax), the maximal heart rate (HRmax), and the respiratory exchange ratio (RER).

VO2max indirect calculations

We hypothesized that other equations except from the ACSM’s metabolic equation might be accurate for the prediction of VO2max. Thus, overall the VO2max was calculated based on the following metabolic calculations:

  1. ACSM equation: VO2max = (0.2 · S) + (0.9 · S · G) + 3.5 (equation A)2

S: speed; G: grade

  1. VO2max was estimated using regression models using enter (equation B) and stepwise (equation C) methods.

Additionally, using the ACSM equation, the subjects had to complete at least one minute of each stage in order to be awarded with the full estimated metabolic equivalents value.

Statistical analyses

Statistical analyses were performed using the PASW statistics for Windows version 18 (SPSS Inc., Chicago, Illinois, USA). All data were expressed as mean values and standard deviation (SD). Age, BMI, speed, grade and exercise time were served as independent variables in multiple linear regression analysis, using both enter and stepwise methods to predict measured VO2max. Enter is a method in which all predictors are forced into the model simultaneously. This method relies on good theoretical reasons for including the chosen predictors, but the experimenter makes no decision about the order in which variables entered. In the stepwise method, decisions about the order in which predictors are entered into the model are based on a purely mathematical criterion. The computer then searches for the predictor that best predicts the outcome variable by selecting the predictor that has the highest simple correlation with the outcome. If this predictor significantly improves the ability of the model to predict the outcome, then this predictor is retained in the model and the computer searches for a second predictor. The criterion used for selecting this second predictor is that it is the variable that has the largest semi-partial correlation with the outcome13. Changes of variables within groups were evaluated by the Student’s t-test for paired data. For the estimation of the relationship between the measured and predicted values of VO2max, as calculated from the three equations, Pearson correlation was used. Level of significance was set at p<.05.


Athletes’ physical characteristics are reported in Table 1. The cardiorespiratory data during rest and maximal exercise test are presented in Table 2.

All the subjects ultimately completed at least one minute of the fifth stage ensuring that they reached a running speed at the end of the test since the running economy might be different between fast walking and running.

Multiple linear regression analysis using the enter method yielded the following prediction equation (B):

VO2max (ml·kg-1·min-1) = 58.443 – (0.215 · age) – (0.632 · BMI) – (68.639 · grade) + (1.579 · time) (R =.64, SEE = 6.11). The model was statistically significant (p<.05) explaining 40.7% (R2=.407) of the variance of measured VO2max. According to standardized β-weights (Table 3), age explained the largest amount of variance of VO2max.

Stepwise regression analysis generated the following equation (C): VO2max (ml·kg-1·min-1) = 33.971 – (0.291 · age) + (1.481 · time) (R=.61, SEE=6.18). Both age and exercise time, as predictor variables for VO2max, were statistically significant (p<.05) explaining the 36.8% (R2=.368) of the variance of VO2max. The unstandardized coefficients, t statistics, and beta coefficients for each independent variable are shown in Table III. There were no collinearities in both models of regression analysis since the values of the variance inflation factor (VIF) and the tolerance (1/VIF) for all the predictors in both methods were <4 and >0.2, respectively.

The differences between the values of VO2max, as they were calculated from the metabolic equations, are demonstrated in Table 4. Specifically, the calculated value of VO2max based on equation A was significantly higher compared to the actually measured VO2max by 14.6% (p<.05). Thus, the equation A was poorly, but nevertheless significantly correlated with the measured VO2max, while enter and stepwise regression equations were moderately correlated with the measured VO2max. Particularly, the correlation coefficients between the actually measured and the equation-based predicted values of VO2max were 0.27 (p=0.043) for equation A and 0.64 (p<0.001) and 0.61 (p<0.001) for equations B and C, respectively.


The main finding of the study was that the ACSM’s running equation overestimates the VO2max values when assessed in athletic population. On the contrary, the regression-based equations were significantly correlated with the actually measured VO2max.

Measurement of VO2max has ubiquitous outcomes in many fields of exercise science14,15. Thus, an increase of VO2max is the most important demonstration for a training effect14. In clinical settings, VO2max has also become the gold standard measure of cardiovascular fitness and exercise capacity16. Low cardiorespiratory fitness is a powerful and independent predictor of cardiac mortality in patients with chronic heart failure or hemodialysis patients17-19. On the contrary, an improvement of aerobic capacity following exercise training is associated with a lower risk of morbidity and mortality in these patients20,21.

In a previous study, Foster et al22, had suggested that individual characteristics may present significant impact on the estimation of VO2. Even though the ACSM’s equation was developed using highly fit male subjects or based on estimates23,24, our data suggest that its use for predicting VO2max in a group of athletes aged 18-37 yrs participating in various sport disciplines leads to inaccurate results. Particularly, ACSM’s running equation overestimates the VO2max values by 14.6% when assessed in athletes. Also, other studies have criticized the use of the ACSM’s equation in adults25. This overestimation of the ACSM’s equation in predicting VO2max is most likely due, in part to its intended use for estimation during steady state exercise, which makes it inappropriate for use with graded stress testing of any age group5,26. Furthermore, many studies have shown that trained and elite athletes exhibit better running economy than untrained and amateur or recreational athletes, respectively27. These differences in running economy and energy expenditure have been attributed to several biomechanical, metabolic and neuromuscular factors such as metabolic adaptations of the muscular cell, the ability of the muscles to store and release elastic energy and more efficient mechanics such as improved running technique, leading to less expended energy on braking forces and minimized vertical oscillation28.

Physical activity levels may be an independent predictor of VO2max in healthy adults, following sex and age in order of significance7. In absence of specific physical activity recordings in our study and comparisons between sex, the age was found to be a significant predictor of VO2max in both enter and stepwise regression equations. In the present study, the age factor was more effective than BMI, grade and exercise time using the enter method and more effective than exercise time when using stepwise method, while BMI, speed and grade were excluded from this model analysis. Peterson et al5, observed a 0.20 increase in R2 when adding gender, age, BMI and activity levels to a model that originally included just the “traditional” test variables of treadmill: grade and speed.

Age is considered to be an important variable when estimating VO2max across a wide chronological range14. George et al29 used a maximal graded exercise test to predict VO2max in 18-65 aged adults and they concluded that the age seems to be more effective at predicting VO2 max than gender and BMI, but not as effective as treadmill speed and grade.

Peterson et al14, also reported that there was a lack of significance for the exercise time as a predictor of VO2max, due to the used Pieper protocol, suggesting that protocols utilizing large metabolic increments such as the Bruce protocol would make test duration a significant predictor of VO2max. This observation is confirmed by our results using stepwise regression equation. Nevertheless, exercise time was not a strong predictor of VO2max when using enter method in regression analysis.

The most common maximal GXT for the treadmill still remains the Bruce protocol that provides excellent accuracy and a standardized testing procedure for all participants7. The Bruce protocol has advantages and disadvantages and probably is not appropriate for predicting VO2max in all populations due to the abrupt increase in exercise intensities which make it difficult for many individuals to complete28. Bruce et al7,8, studied inherent physiologic differences between healthy, sedentary and diseased populations. In each population, a unique relationship of work load with VO2 existed. On the other hand, the Bruce protocol requires all participants to advance from one stage to the next at the same speed and grade making it comparable between participants based on the same exercise intensity requirements. Also, total exercise time can be used by clinicians as a measured variable to accurately classify participants according to cardiorespiratory fitness or cardiovascular risk1.

The limitations of the study mainly concern the size of the sample since a small number of athletes from eight different sport disciplines were recruited. Thus, it would have been advantageous to have included a randomly matched cohort of athletes from many different sports in order to quantify the VO2max discrepancy under the also known limitation of the aggressive nature in workload adjustment of the Bruce protocol. Furthermore, the training characteristics might differ between the athletes’ sport clubs in terms of frequency and intensity of the training load even in the same sport.


Our results indicated that the widely used ACSM’s running equation performing the Bruce protocol in many sport centers is not accurately predicting VO2maxin athletes aged 18 – 37 years. Thus, it is verified that direct measurement of VO2maxin athletes should be preferred instead. Cardiopulmonary exercise testing is the only way to directly measure VO2, but despite this, the estimation of exercise capacity based on equations will undoubtedly continue mainly due to cost effectiveness issues. In case of indirect estimation of maximal aerobic capacity, regression models in specific populations of different age and physical fitness with standard treadmill velocities and grades would be most efficient in predicting VO2max. Further studies are encouraged to develop and examine precise regression models that accurately estimate VO2max.

Conflicts of interest

None declared.


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