## 1 Introduction  
Gas boilers [1] remain integral components of modern heating systems, delivering reliable and efficient heat and domestic hot water in residential and commercial applications [2]. By converting a significant proportion of fuel into usable thermal energy, these systems help reduce energy costs and limit greenhouse gas emissions [3]. The ability to maintain a stable and comfortable indoor climate is not only essential for physical well-being but also linked to cognitive performance and emotional stability. Even minor temperature variations can impact productivity and comfort, underscoring the continued importance of efficient heating solutions.  
In recent years, condensing boiler technologies have advanced substantially increasing efficiency of gas boilers significantly [4, 5], particularly in heating systems powered by natural gas. Additional advancements include high-performance heat exchangers, smart control systems with remote access, and hydrogen-ready models capable of operating on natural gas-hydrogen blends [6]. Such innovations improve energy efficiency, enhance user convenience, and contribute to environmental sustainability.  
The heating landscape is evolving in response to climate change. Rising global temperatures are projected to reduce heating demand in many regions, potentially lowering overall energy consumption. Nevertheless, the need for high-efficiency boilers remains critical. Extreme weather events still demand reliable heating, and improved efficiency supports household energy savings while advancing the European Union's climate and energy goals [7, 8].  
As the building sector transitions toward low-carbon heating technologies [9, 10], efficient natural gas boilers are expected to play a key transitional role. Their performance under realistic seasonal conditions is increasingly important for informed policy decisions and energy planning. Among the most relevant performance metrics is seasonal efficiency, which directly determines a boiler's energy efficiency class and regulatory compliance.  
This study examines the seasonal efficiency of household gas boilers through the lens of the algorithmic framework used in European energy labeling schemes. By applying a standardized algorithm for calculating seasonal efficiency, the research systematically evaluates boiler performance and cost effectiveness. Key factors influencing energy use and savings are analyzed, with a focus on how efficiency algorithms shape regulatory classifications. A comparative assessment of selected boiler models available on the Serbian market is included [11, 12], offering insights relevant to both national and broader European contexts. By combining computational modeling with market data, the study contributes to the theoretical and practical understanding of gas boiler optimization within the ongoing energy transition.  
The correctness of energy efficiency calculations for domestic gas boilers is verified through standardized European procedures [13]. Boilers are tested under controlled conditions following harmonized standards, measuring performance at different loads. Seasonal efficiency is calculated using a defined formula incorporating these test results. Accredited labs perform the tests, and regulatory bodies oversee compliance, ensuring results are reliable, comparable, and transparent across the market.