Helical coils are integral to numerous engineering and domestic applications, from room heaters and vehicle suspensions to nuclear reactors, owing to their high surface area-to-volume ratio that facilitates efficient heat transfer. This study investigates the natural convection heat transfer characteristics of tapered helical coils under radiative heat loss, focusing on both straight and inverted configurations, within an unconfined air medium. The numerical simulations were validated against experimental results with a maximum deviation of 5 % before proceeding to establish the numerical findings. The analysis considers geometric parameters such as non-dimensional pitch (p*), cone angle (θ), and emissivity (ε), along with Rayleigh number (Ra), to elucidate their impact on average Nusselt number (Nu), mass flow rate of air through the coil core, and heat transfer mechanisms. Results reveal distinct behaviors for straight and inverted coils, with varying Ra and θ influencing heat transfer dynamics and airflow patterns. Notably, inverted coils exhibit enhanced heat transfer characteristics compared to straight coils. For straight coils, Nu initially decreases with increasing θ at lower Ra but rises beyond a critical θ at higher Ra due to independent heat dissipation by the coil turns. When θ changes from 0° to 50° at p* = 6, the change in average Nu is approximately 3 % and 10 % for Ra = 108 and 104 respectively. In contrast, for inverted coils, Nu increases with θ across all Ra, owing to the wider top opening facilitating airflow. Furthermore, empirical correlations are developed to predict Nu based on key parameters, achieving high accuracy with deviations of ± 6 % and ± 4 % for straight and inverted coils, respectively. These correlations provide robust tools for optimizing thermal management in diverse applications. Overall, this study contributes significant insights into tapered coil performance, essential for advancing heat transfer technology and design optimization.