Abstract: Accurate prediction of penetration depth for earth‑penetrating projectiles in geomaterials is essential for protective‑engineering design. Widely used empirical formulas, including Young’s formula and the modified Berezan formula, apply to rock, concrete and soil. However, their practical use is limited by narrow valid ranges for projectile mass, caliber and impact velocity. Traditional solid‑penetration theoretical models offer clear physical explanations for penetration behavior, but their engineering application is constrained by idealized assumptions and boundary effects from finite‑size targets. To address these limitations, a unified prediction formula for penetration depth in rock, concrete and soil was developed based on the internal‑friction pseudo‑fluid penetration theory. Variations in penetration resistance from the pseudo‑fluid penetration model were analyzed in detail. Considering calculation safety and practical engineering requirements, a simplified analytical solution for penetration depth was derived. Key dimensionless parameters including the jet coefficient, generalized Mach number and internal‑friction correction coefficient were examined to characterize the influences of impact velocity, projectile geometry and dynamic target properties on penetration resistance. Coefficient f, which describes projectile-target coupling effects, was fitted by the least-squares method over the Mach-number range relevant to practical engineering and subsequently converted to coefficient λ. The conversion coefficient α relating the characteristic velocity c* to the target longitudinal-wave velocity cp was determined from the dynamic failure behaviour of geomaterials subjected to intense dynamic loading, and recommended α values for different media were summarized. Furthermore, an equivalent calculation scheme coupling wave impedance and coefficient α was formulated for penetration prediction in multi-layered targets. Calculation outputs of the unified formula were validated against full‑scale test data and compared with predictions from the modified Berezan formula and Young’s formula. For concrete, the unified formula yields more conservative penetration‑depth estimates, while the two empirical formulas produce unsafe predictions. For rock, the unified formula and modified Berezan formula provide higher safety margins than Young’s formula, which underestimates penetration depth. For soil, predictions from the unified formula fall between results of the two empirical formulas. Serving as an upper‑bound solution for penetration‑depth assessment, this formula quantifies safety margins and feasible application ranges of existing empirical formulas and offers technical references for anti‑penetration design and specification revisions.