<p>Assessing the validity of tensile strength determination in the Brazilian test is a classical problem in fracture mechanics. According to reports, the Brazilian splitting strength is generally lower than the direct tensile strength in most cases, while in a minority of cases it is higher. Based on the analytical solution of the stress field in an uncracked disc under parabolic loading and Griffith's fracture criterion, this paper proposes a novel modified formula for calculating tensile strength <i>σ</i>_t that accounts for the influence of the load contact angle. Additionally, according to the principles of error analysis, an error transfer function is derived to evaluate the effect of measurement error on contact angle. Finally, the modified formula presented in this paper is applied to calculate the tensile strength of sandstone under both flat-platen and curved-jaw loading conditions. The results are then compared with those obtained using a classical formula. The theoretical analysis shows that the classical formula underestimates the tensile strength of materials at small contact angles, whereas it overestimates the tensile strength at large contact angles. Additionally, measurement errors in the contact angle have a certain influence on the determination of <i>σ</i>_t. For the case of contact semi-angle <i>γ</i> ≥ 10° with measurement error Δ<i>γ</i> ≤ 1°, the tensile strength determination error remains below 5%. The experimental results show that the classical formula yields lower tensile strength values for sandstone under flat-platen loading compared to curved-jaw loading, whereas the proposed modified formula demonstrates excellent consistency between both loading configurations. The modified formula accounts for the dual-aspect influence of contact angle on tensile strength determination: (i) qualitative—governing the fracture initiation position of the disc, and (ii) quantitative—modulating the magnitude distribution of internal stress components.</p>