## 1 Introduction  
In educational settings, inadequate indoor air quality (IAQ) has been widely recognized as a key factor affecting students' health, cognitive performance, and overall academic outcomes [1, 2, 3]. Various standards establish threshold values for carbon dioxide (CO\({}_{2}\))--a gas primarily produced by occupants' respiration--as an indicator of ventilation adequacy. Exceeding concentrations of 1000 parts per million (ppm) suggests potential air quality issues. Prolonged exposure to elevated CO\({}_{2}\) levels can contribute to stagnant indoor environments, triggering symptoms associated with Sick Building Syndrome (SBS), such as headaches [4; 5], fatigue [6], eye irritation [4], reduced concentration [7], impaired cognitive performance [8], decision-making difficulties [9], and respiratory tract symptoms [10], while also increasing susceptibility to airborne infections.  
The COVID-19 pandemic further highlighted the importance of managing IAQ in educational buildings [11; 12]. However, numerous studies conducted before and after the pandemic have shown that indoor CO\({}_{2}\) concentrations in classrooms often exceed outdoor levels--ranging from 350 to 2500 ppm [13; 14; 15; 16]--and may surpass 4000-4500 ppm in some cases [17; 18]. For example, [PERSON] et al. [19] reported that indoor CO\({}_{2}\) levels exceeded recommended thresholds during 70% of school hours in winter across eight Chilean schools. [PERSON] et al. [20] found that CO\({}_{2}\) concentrations in 32 Spanish classrooms averaged 1194 ppm during winter, with about half of the teaching time exceeding national limits. Similarly, [PERSON] et al. [21] found that nearly two-thirds of one hundred Swiss classrooms failed to meet IAQ standards, while [PERSON] et al. [22] observed that both mechanically and naturally ventilated classrooms in China frequently exceeded CO\({}_{2}\) limits.  
These findings emphasize the critical need for effective IAQ management in educational settings, both during the design phase and in ongoing operation [9; 23]. In this context, the present study proposes a simplified Classroom Indoor Air Quality (CIAQ) Risk Index as a practical tool for assessing the potential of a classroom--designed for specific occupancy and activity patterns--to maintain CO\({}_{2}\) levels within acceptable limits.  
The CIAQ Risk Index serves as a decision-support tool that integrates key parameters such as occupancy, activity level, ventilation capacity, and spatial characteristics to estimate the risk of exceeding CO\({}_{2}\) thresholds. It enables early identification of high-risk classrooms and supports proactive planning by school administrators, designers, and facility managers. When applied during the design phase, the index allows users to explore various \"levers\" such as occupancy limits, ventilation strategies, activity types, and room dimensions, helping to identify optimal configurations before construction or refurbishment begins. In existing buildings, it informs targeted interventions--such as ventilation upgrades, schedule modifications, or occupancy adjustments--aimed at improving air quality outcomes.  
The index is built on three core components: (1) the likelihood of CO\({}_{2}\) levels exceeding predefined thresholds (hazard); (2) the number and sensitivity of individuals potentially exposed to those conditions (exposure); and (3) the classroom's ability to mitigate or withstand the impact of those conditions (vulnerability).  
By quantifying these components, the CIAQ Risk Index contributes to ongoing efforts to improve IAQ in schools. Beyond identifying high-risk situations, it also supports broader risk management strategies--including estimating the scale of necessary investments for retrofitting, adjusting student-to-volume ratios, or upgrading ventilation systems. Ultimately, understanding and addressing IAQ-related risks can reduce the likelihood of health problems, enhance well-being, and improve academic performance and quality of life across the educational community.