Structural cellular materials in nature, such as wood, trabecular bone, corals, and dentin combine complex biological functions with structural roles, such as skeletal support and impact protection1,2. They feature complex structural hierarchies from nano- to macroscale that enable optimization of both strength and toughness (flaw tolerance) simultaneously3-9. These hierarchies typically exhibit structural disorder in the arrangement of pores. The degree of disorder, however, has not been systematically quantified before, and its role in the mechanical performance of cellular biomaterials is generally unknown. Here we have applied Voronoi tessellations to quantify the cell size variation in 2D cross-sections of biological and engineered cellular materials, using a disorder parameter (d) ranging between 0 (highly disordered) to 1.0 (regular hexagonal honeycomb). We demonstrate that various plant, fungi, and animal cellular materials show characteristic ranges of disorder. Using 3D printed analogues and numerical methods, we demonstrate experimentally a range of pseudo-order (d=0.6 to 0.8) that exhibits a > 30% increase in fracture toughness (and equivalent strength) compared to hexagonal honeycombs (d=1.0) of equal density. Our results show this range of disorder is similar to that identified in the biological examples, which suggests convergent evolution. This optimal degree of structural disorder limits catastrophic failure, providing an evolutionary advantage for organism survival. Distributed structural damage limits cracks below a maximum threshold size and also enables tissue repair mechanisms after trauma. Our work shows that tailored disorder should be considered as a new design paradigm for digitally fabricated, lightweight architected materials to improve damage tolerance.