Introduction

The report of the twentieth congress of the Communist Party of China states that ‘we must insist on safeguarding and improving people’s livelihoods in the course of development, encouraging common endeavors to create a better life, and constantly realizing the people’s aspirations for a better life’1. Seeking happiness for the people has always been the party’s original heart and mission. In 2020, during his fifth visit to the Beijing Winter Olympics organizing work, he said that “from a strong sports country to a healthy China, the people’s health, the people’s physical fitness, and the people’s happiness are all in the same vein”2. As an important reserve of talent for the future development of the country, the mental health of college students is of great concern to society. However, surveys show that some college students currently have mental health problems, and effective measures are urgently needed to improve them. The two-factor theory model states that subjective well-being is a significant determinant of mental health3. According to the New Era Resident Psychosocial Survey Report (2023), college students’ subjective well-being scores are low4. Numerous studies have confirmed that physical activity is an effective intervention to induce positive emotions and enhance participants’ subjective well-being. However, the mechanism of physical activity’s influence on college students’ subjective well-being needs to be studied in depth. Subjective well-being is an emotional and subjective overall evaluation of people’s quality of life and life satisfaction5. As an important part of positive psychology as well as psychological quality, subjective well-being is a comprehensive psychological indicator of the quality of life of individuals and society6. James Lange’s theory states that emotion is the perception of physiological changes in the body, and physical exercise causes a series of physiological changes in the body, such as increased heart rate, shortness of breath, etc., which are transmitted to the brain through the nervous system, thus triggering a positive emotional experience, which in turn improves subjective well-being7. The role of physical exercise on subjective well-being has been supported by many results. For example, physical activity can make sports participants have a pleasurable and hedonistic experience, improve self-esteem, life satisfaction and health benefits, and thus enhance subjective well-being8. Long-term participation in physical activity can effectively enhance subjective well-being, and variables such as personality traits and physical self-esteem mediate the relationship between physical activity behavior and subjective well-being9. Some scholars believe that physical activity can not only directly improve the subjective well-being of college students, but also affect subjective well-being through mediating variables such as self-esteem, interpersonal relationships, mental toughness and stress perception10,11,12,13. Accordingly, research hypothesis H1 is proposed: physical activity can positively predict college students’ subjective well-being.

Stress perception is that ‘individuals have the exploitable potential to recover quickly from adversity, failure, positive practices, and increasing responsibilities’14. Neuroplasticity theory suggests that the brain has the ability to change neural connections and their function through experience and learning. Physical exercise promotes neuroplasticity in the brain and enhances stress resistance, as well as strengthens neuronal connections in the prefrontal cortex, enhances cognitive function and emotion regulation, and thus improves Stress perception15. Studies have found that physical exercise can effectively improve individual mental toughness, and improve the physical health and mental health of college students, and participation in physical exercise is not only conducive to the healthy development of the body, but also releases negative emotions within, and enhances the ability to withstand psychological stress perception, and regular participation in physical exercise has a positive contribution to the improvement of students’ mental toughness16. Research has shown that physical exercise can also significantly enhance Stress perception by enhancing an individual’s self-efficacy, emotional regulation, and coping ability (Fletcher & Sarkar, 2013)17. Dingdong Liu (2022) stated that college students’ participation in physical exercise can positively affect their Stress perception18. In addition, participation in physical exercise can also have a positive impact on individuals’ subjective well-being, and when their Stress perception is higher, the subjective well-being index will also be higher19. There is a significant positive correlation between college students‘ Stress perception and subjective well-being, and college students’ mental toughness can significantly and positively predict subjective well-being20. Based on this, the research hypothesis H2: mental toughness may mediate the relationship between physical exercise and college students’ subjective well-being is proposed.

Mental toughness refers to an individual’s assessment of the threatening nature of a stressor and his or her ability to cope with it21. Physical exercise has been found to reduce an individual’s mental toughness in a number of ways. Regular participation in physical exercise leads to increased adaptation of the body’s stress response system and reduces an individual’s physiological and psychological responses in other stressful situations, which helps to reduce an individual’s assessment of the threat of a stressor22. Physical exercise can have a buffering effect on perceived stress, which is mainly manifested by the fact that university students who are actively involved in sports can de-stress during exercise, and their well-being indices usually increase when individuals perceive lower levels of stress23. Hezomi and Nadrian (2008), in their study of Iranian female adolescents, found that perceived mental toughness was a significant negative predictor, and this result also indicates the important role of mental toughness perception in determining mental health and well-being in female adolescents24. Physical exercise can indirectly enhance an individual’s subjective well-being by reducing the level of mental toughness perception (Cohen & Wills, 1985). Based on this, research hypothesis H3 is proposed: mental toughness perception may mediate the relationship between physical exercise and the subjective well-being of college students.

Mental Stress perception and stress perception play an important role in college student’s mental health, and both can significantly affect subjective well-being. It has been found that mental resilience is negatively correlated with work stress25. Friborg (2006) and others have shown that mental stress perception, as a dynamic psychological trait, can help individuals to effectively alleviate psychological pain and stress distress in the face of stress and dilemmas, and thus maintain a higher level of mental health26. Based on this, research hypothesis H4: Mental toughness and Stress perception may act as chain mediators between physical exercise and college students’ subjective well-being is proposed.

In summary, the present study intends to explore the psychological mechanisms by which physical exercise affects college students‘ subjective well-being, i.e., the chain mediating role of mental toughness and Stress perception, so as to provide empirical support for the improvement of college students’ subjective well-being and the alleviation of college student’s mental health. Based on the above research hypotheses, this study drew the following three paths with physical exercise as the independent variable, mental toughness, and stress perception as the mediator variables, and subjective well-being as the dependent variable, as follows: Path 1: Physical exercise→Mental toughness→Subjective well-being; Path 2: Physical exercise→Stress perception→Subjective well-being; Path 3 Physical exercise→Mental toughness→Stress perception→Subjective well-being. The constructed diagram of the chain mediator model is shown in Fig. 1.

Fig. 1
figure 1

Diagram of the hypothesized model of physical activity affecting subjective well-being.

Full size image

Method

Objects of the study

In this study, 600 college students (age: 18–25 years old; full-time undergraduates; no physical illness or psychiatric history) who met the criteria in six universities in Liaoning Province, China, were surveyed using convenience sampling, and 600 questionnaires were finally recovered. During the questionnaire screening, one of the following problems was regarded as invalid questionnaires and deleted: (1) short answer time (answering in less than 120 s), (2) regular answers, and (3) inconsistent answers to reverse scoring questions. Finally, 569 valid questionnaires were obtained, and the validity rate of the questionnaires was 94.83%. All the survey respondents in this study had given informed consent and signed the informed consent form. The basic information of the survey respondents is shown in Table 1. In this study, 600 college students (age: 18–25 years old; full-time undergraduates; no physical illness or psychiatric history) who met the criteria in six universities in Liaoning Province, China, were surveyed using convenience sampling, and 600 questionnaires were finally recovered. During the questionnaire screening, one of the following problems was regarded as invalid questionnaires and deleted: (1) short answer time (answering in less than 120 s); (2) regular answers; and (3) inconsistent answers to reverse scoring questions. Finally, 569 valid questionnaires were obtained, and the validity rate of the questionnaires was 94.83%, all the survey respondents in this study had given informed consent and signed the informed consent form. The basic information of the survey respondents is shown in Table 1.

Table 1 Basic information on survey respondents (N = 569).
Full size table

Survey instruments

Physical exercise rating scale (PERS)

The Chinese version of the Physical Exercise Rating Scale (PERS), revised by D.C. Liang27 (1994), was used to assess the amount of physical exercise an individual had done in the past month. The scale included 3 dimensions of physical exercise intensity, frequency, and duration of each exercise (e.g., how intense was each exercise?). The scale is scored on a 5-point Likert scale. Total score = intensity × frequency×(duration of each exercise − 1). The Cronbach’s alpha coefficient for the scale calculated in this study was 0.723, indicating the high reliability of the scale.

Psychological resilience scale (CD-RISC)

The scale was developed by Connor and Davidson, translated and revised by Zhang, Jianxin, and Xiaonan Yu28, et al. (2007), and subsequently has been widely used to assess Stress perception in college students and adults both at home and abroad, with the dimensions categorized as strength (e.g., I am proud of myself.), resilience (e.g., I will not be easily defeated.) and optimism (e.g., When faced with a problem, I try to look at the humorous side of things.). Three dimensions. The scale is scored on a Likert 5 scale with 25 entries, and a higher total score indicates a better Stress perception of the subject. The Cronbach’s alpha coefficient for the scale calculated in this study was 0.956, indicating the high reliability of the scale.

Pressure perception questionnaire (PSS)

Individuals’ level of mental toughness in the past month was assessed using the revised Stress Perception Scale by Tingzhong Yang29 (2003) and others. The scale consists of 14 entries and contains feelings of loss of control (e.g., feeling confident about having the ability to deal with one’s own private problems) and Sense of Stress (e.g., feeling upset that something unanticipated is happening). The 2 dimensions were scored on a Likert5 scale with a total score of 14–70, with higher scores indicating higher levels of mental toughness perceived by the individual. The Cronbach’s alpha coefficient of the scale calculated in this study was 0.793, indicating the high reliability of the scale.

Subjective well-being scale (GWB)

The General Well-Being Scale, revised by Duan30 (1996), was used to measure the subjects’ level of well-being. The scale consists of 18 entries containing worries about health (e.g., Are you bothered by illness, physical discomfort, pain, or fear of illness?), energy (e.g., How do you feel in general?), Life Satisfaction (e.g., Are you happy, contented, or enjoying your life?), pleasant state of mind (e.g., are you in a state of doubt that anything is worth doing because of sadness, loss of confidence, disappointment, or having a lot of trouble?), Behavioral control (e.g., Are you always firmly in control of your behavior, thinking, feelings, or sensations?), relaxation, and nervousness (e.g., Are you bothered by your nervousness?) 6 dimensions. Higher scores indicate higher levels of subjective well-being among survey respondents. The Cronbach’s alpha coefficient for the scale calculated in this study was 0.810, indicating the high reliability of the scale.

Statistical analysis

IBM SPSS 25.0 statistical software was used for data analysis. First, the common method bias test was conducted, second, the descriptive statistics results were calculated and Pearson correlation analysis between variables was performed, and again, according to the procedure and approach of the mediation effect test introduced by Wen Zhonglin et al.31, model 6 of Process 4.1 plug-in was used to conduct the moderated mediation model test, and the paths of the relationship between physical activity and subjective well-being were analyzed. The independent mediating effects of mental toughness, and stress perception, and the chained mediating effects of both were further verified by the bootstrap method. All regression coefficients were tested by the bias-corrected nonparametric percentile bootstrap method with 5000 random samples, and 95% confidence intervals were calculated, which indicated a significant effect if the confidence intervals did not contain zero.

Results

Common method bias test

The collected data were tested for common method bias using the Harman one-factor test32. The results showed that the total number of factors with eigenroots greater than 1 was 10, and the explained variance of the first factor was 30.16%, which was less than the critical criterion of 40% (Fuller et al., 2016)33, indicating that there was no serious common method bias in this study.

Descriptive statistics and correlation analysis of physical activity, mental toughness, stress perception, and subjective well-being

Table 2 Correlation analysis between variables.
Full size table

Correlation analysis was used to analyze the relationship between the variables (Table 2), and the results showed that there were correlations between college students’ gender, grade, physical activity, mental toughness, stress perception, and subjective well-being, while there was a significant correlation between physical activity and gender (r=−0.456, p < 0.01) and grade (r = 0.294, p < 0.01), and there was a significant positive correlation between physical activity and subjective well-being (r = 0.229,p < 0.01), a significant positive correlation with mental toughness (r = 0.225,p < 0.01), and a significant negative correlation with perceived stress (r=−0.270,p < 0.01). Mental toughness was significantly negatively correlated with perceived stress (r=−0.540, p < 0.01), and significantly positively correlated with subjective well-being (r = 0.605, p < 0.01). Perceived stress and subjective well-being were both significantly negatively correlated (r=−0.579, p < 001). The results of this analysis provided a strong basis for the subsequent mediation effect test.

Chain mediation effect test of mental toughness, stress perception between physical exercise and college students’ subjective well-being

In this study, structural equation modeling tests were analyzed using AMOS software, and the results showed that χ2/df = 2.71, RMSEA = 0.078, CFI = 0.94, TLI = 0.91, and GFI = 0.93, and that all the fitted indices were within a reasonable range, details are shown in Table 3.

Since there were significant correlations between physical exercise, mental toughness, stress perception, and subjective well-being, the statistical requirements for direct and indirect effect tests between physical exercise and college students’ subjective well-being were Met. The data were normalized, and the data in this study conformed to a normal distribution, using model 6 in the SPSS process macro, the non-parametric percentile bootstrap Met.od (Davison & Hinkley, 1997)34 for mediated effects testing, with 5,000 replicated samples. The independent variable was physical exercise, the dependent variable was subjective well-being, and the mediator variables were mental toughness and stress perception, gender and grade level were used as control variables to test the chained mediation effect of mental toughness and stress perception between physical exercise and college students’ subjective well-being at the 95% confidence interval.

Table 3 Model fit indices for the mediating role of mental toughness and stress perception.
Full size table
Table 4 Regression analysis of variable relationships.
Full size table

Regression analysis showed (Table 4; Fig. 2) that physical activity had a significant direct positive predictive effect on college students’ subjective well-being (β = 0.298, p < 0.001) before the inclusion of the mediating variable. After including mental toughness and stress perception in the regression equation, physical activity still had a significant positive predictive effect on college students’ subjective well-being (β = 0.077, p < 0.05). Meanwhile, physical exercise had a significant positive predictive effect on mental toughness (β = 0.298, p < 0.001) and a significant negative predictive effect on stress perception (β= −0.170, p < 0.001). In addition, mental toughness had a significant negative predictive effect on stress perception (β= −0.502, p < 0.001) and a significant positive predictive effect on college students’ subjective well-being (β = 0.402, p < 0.001). Stress perception had a significant negative predictive effect on college students’ subjective well-being (β= −0.346, p < 0.001).

Table 5 Bootstrap mediation effects and confidence intervals.
Full size table

The mediation effect analysis showed (Table 5) that there was a chain mediation between mental toughness and stress perception between physical activity and college students’ subjective well-being. The total effect value was 0.187 and its 95% confidence interval was [0.131, 0.244]. The direct effect value was 0.047 and its 95% confidence interval was [0.002, 0.092]. The total indirect effect value was 0.140 and its 95% confidence interval was [0.104, 0.181]. Since none of the above three effects were included in the 95% confidence interval, it indicates that the mediating effect was significant. The mediating effect included three indirect paths: (1) physical activity → mental toughness → subjective well-being, whose path had an indirect effect value of 0.073, with a 95% confidence interval that did not contain 0, indicating that the indirect effect of the mediating variable of mental toughness was significant and accounted for 39.03% of the total effect; (2) physical activity → stress perception → subjective well-being, whose path had an indirect effect value of 0.036, with a 95% confidence interval does not contain 0, indicating that the indirect effect of the mediating variable of stress perception is significant, accounting for 19.25% of the total effect; (3) physical exercise → mental toughness → stress perception → subjective well-being, the indirect effect value of its path is 0.032, and the 95% confidence interval does not contain 0, indicating that the chained mediating effect of both mental toughness and stress perception is significant, accounting for 17.11% of the total effect. Further comparison of the indirect effects of the 3 paths showed that the indirect effect of mental toughness was significantly higher than the indirect effect of stress perception. The chain-mediated effect between both mental toughness and stress perception was significantly lower than the indirect effect of mental toughness and not significantly different from the indirect effect of stress perception.

Fig. 2
figure 2

Chain mediation effect model diagram.

Full size image

Discussion

The relationship between physical exercise and college students’ subjective well-being

The results of this study indicated that physical exercise significantly and positively predicted college students‘ subjective well-being, which suggests that engaging in physical exercise is an effective way to enhance college students’ subjective well-being35,36,37,38, validating research hypothesis H1. This finding is consistent with previous research (Smith et al., 2023; Mammen & Faulkner, 2013), further supporting the idea of physical exercise as an effective way to enhance well-being39,40. College students are in a critical period of their lives, and more and more of them are dissatisfied with their lives under the influence of various pressures such as study pressure, employment pressure, and economic pressure41. Physical exercise, as a positive way of coping, and regular participation in physical exercise can reduce and alleviate the psychological stress response, improve the individual’s coping ability, and enhance subjective well-being42. However, in contrast to Claus’s (2017) study, the present study found that physical exercise not only reduces anxiety through progressive relaxation but also indirectly enhances well-being through multipath mechanisms (e.g., mental toughness and Stress perception)43. Appropriate physical exercise can make individuals more enjoyable, and the ‘smooth’ (cool, intoxicated, peak) experience that participants get during exercise can make people forget about things that undermine their sense of well-being, thus contributing to an increase in the baseline of well-being; physical exercise can bring people closer to each other, and lead to an increase in social skills and more social support. Sports participation can bring people closer together, enhance their social skills, and increase their social support, which will undoubtedly raise the ‘set point’ of happiness8. From a physiological point of view, physical exercise can promote the secretion of endorphins and cortisol, endorphins have a strong analgesic effect, which can bring a strong sense of ‘pleasure’ and ‘euphoria’44. Cortisol is associated with the regulation of stress, oxytocin affects subjective well-being by directly mediating empathy45, and 5-hydroxytryptophan affects subjective well-being by regulating feelings of contentment, happiness, and optimism46. The above studies are consistent with the findings of the present study that physical exercise can significantly and positively predict subjective well-being in college students.

The mediating role of mental toughness between physical exercise and college students’ subjective well-being

The results of this study indicate that mental toughness mediates the relationship between physical exercise and college students‘ subjective well-being and that college students engaging in physical exercise positively predicts their level of mental toughness, and individuals with higher mental toughness may experience higher well-being, which is consistent with other scholars’ studies18,19 and verifies the research hypothesis H2. However, in contrast to Zhang et al.‘s (2022) study, the mediating effect of Stress perception was found to be more significant in the Chinese college student population, which may be related to the differences in stressors in the cultural context47. As an important part of college students’ lives, long-term physical exercise has the effect of significantly enhancing self-confidence and frustration for individuals48. This process not only promotes the overall development of physical and mental health but also enhances an individual’s resilience and self-confidence in the face of challenges49. Physical exercise has a certain effect on mental Stress perception, which can predict mental Stress perception to a certain extent, there is a positive correlation between physical exercise and mental Stress perception, and the more frequent the physical exercise, the better the mental Stress perception36. Stress perception can effectively alleviate negative emotions such as loneliness and depression and improve mental health, as well as bring more positive emotions and courage in the face of setbacks, while positive emotions and confidence in the future are protective factors for well-being50. Mental toughness has a mediating role between physical exercise and college students‘ subjective well-being, and there is a strong relationship between mental toughness and college students’ subjective well-being, the higher the level of mental toughness of college students, the stronger their subjective well-being51. College students overcome the difficulties encountered in physical exercise through internal mindset adjustment, self-effort, and help from others, which will cultivate a more Stress perception, maintain a positive attitude towards life and optimistic emotions, and thus enhance subjective well-being.

The mediating role of stress perception between physical exercise and college students’ subjective happiness

The results of this study show that stress perception mediates the relationship between physical exercise and college students‘ subjective well-being, and physical exercise can negatively predict stress perception, and when the perceived stress is lower the experience of well-being is higher, which is consistent with the results of other scholars’ studies22,23, and verifies the research hypothesis H3. Zhou Hao et al. believe that appropriate physical exercise can accumulate mental energy and improve the ability to resist and adapt to stress52. Regular physical exercise is more effective in relieving stress, and appropriate physical exercise will make people feel happy and relaxed, and release stress53. Physical exercise can negatively predict mental toughness perception, and performing an appropriate physical exercise can reduce emotional experience thus reducing the effects of stress, anxiety, and other adverse emotions54. Compared with students who did not participate in school physical exercise, students who consistently participated in school physical exercise during school had lower mental toughness and higher mental health55. People who are under long-term stress are prone to depression, anxiety, and other problems, which also seriously affect their subjective well-being56. According to this study, it is known that college students’ mental toughness and subjective well-being are significantly negatively correlated, and the greater the individual’s stress, the lower their subjective well-being will be. College students‘ subjective well-being has a close relationship with life events, the more negative life events an individual experiences, the more stress will increase, and stress not only affects students’ mental health but also affects their subjective well-being. This is because at the university stage, not only do they have to face the pressure of coursework, parental expectations, interpersonal interactions, and other problems, but also involves many choices such as employment and further education, and these life events will bring them great pressure, which in turn affects their subjective well-being57. Selye’s theory of stress also points out that an individual has the optimal level of stress, and that once the level of stress is too high or persists too long, the individual’s resources to cope with the pressure and psychological energy are reduced, which leads to lower levels of well-being58.

Chain mediation between mental toughness and stress perception

The results of this study show that mental toughness and stress perception play a chain mediating role between physical exercise and college students’ subjective well-being, and individuals with higher levels of mental toughness tend to form a lower degree of subjective perception of stress, and mental toughness can significantly negatively predict the level of stress perception, and there is a negative correlation between the two, which is consistent with the results of the previous study59, and it verifies the research hypothesis H4. Study, people with high mental toughness can better buffer the negative impact of stress and reduce the level of stress perception, they will not be immediately overwhelmed by negative emotions in the face of stressful events, but rather view and cope with a more positive and optimistic mindset, so that they feel relatively less stress60, mental toughness to a certain extent can negatively predict individual Stress perception. Meanwhile, individuals with higher Stress perception tend to be better at coping with adversity, trauma, and major stress in their lives. They can view difficulties in a positive light and see stress as a challenge rather than a threat, thus reducing their subjective perception of stress. There is a significant negative correlation between mental Stress perception and employment stress in the college student population, and college students with higher mental Stress perception tend to cope better with employment stress61. In summary, the chain mediating role of mental toughness and Stress perception between physical exercise and college students’ subjective well-being is feasible.

Conclusion

Conclusions of the study

Physical exercise can directly and positively predict college students‘ subjective well-being, and it can also indirectly predict college students’ subjective well-being through the independent mediating role of mental toughness and Stress perception and the chain mediating role between them. Therefore, in the process of college students‘ cultivation, colleges and universities should pay attention to the effects of physical exercise on college students’ subjective well-being, as well as the mediating roles of mental toughness and Stress perception between physical exercise and students’ subjective well-being.

Outlook and limitations

This study explored the relationship between physical exercise and college students‘ subjective well-being, and the constructed chain mediation model revealed the mechanism of physical exercise’s influence on college students’ subjective well-being, which provided an important theoretical foundation and practical guidance for improving college students’ subjective well-being. However, the study has limitations and needs to be improved.

At the variable level, this study only explored the mediating role of mental toughness and Stress perception in the relationship between physical exercise and subjective well-being of college students. There are many other variables such as social support, parenting style, self-control, and social anxiety that may also influence this relationship. There may also be interactions between variables, such as whether happier college students are more inclined to engage in physical exercise. The possibility of unforeseen circumstances (injuries, etc.) during physical exercise can affect subjective well-being, and it remains to be considered whether variables such as social support will reduce the negative effects of unforeseen circumstances. Therefore, subsequent studies will incorporate these variables and investigate the interaction between variables through more dimensions to promote the deepening of research on physical exercise and subjective well-being.

In terms of sample selection, college and university students include specialists, undergraduates, and postgraduates, and there are differences in physical exercise and psychological status among students at different academic stages. The sample of this study was only freshmen to senior undergraduates, which is a single sample, and caution should be taken when generalizing the results to other academic stages. To make the results more general and representative, future studies will expand the sample to cover students from different types of colleges and universities and different academic levels, and may even consider including students from different geographical regions and different professional backgrounds in the study, to adequately take into account the different characteristics of different groups of students, and thus reflect more accurately the true relationship between physical exercise and college students’ subjective well-being.

In terms of research methodology, this study used questionnaires to collect data, which were all from students’ self-assessments and were susceptible to subjective cognitive bias and social expectation effects, resulting in less accurate measurement results. Future research will obtain data from multiple sources such as teachers, peers, and parents to reduce the bias of a single data source and improve the accuracy of the results. Although this study has achieved some results, there are limitations in variable research, sample selection, and research methodology. However, after controlling for demographic variables and further introduction of mental toughness and Stress perception in this study, the explanatory power of the model meets the criterion of medium effect size (Cohen, 1988). Future research needs to focus on these limitations to carry out in-depth exploration and continuously improve the research on the relationship between physical exercise and college students‘ subjective well-being, so as to provide more solid theoretical support for the promotion of college students’ mental health.