Blast Radius Calculator — Nuclear Yield Scaling

Formula

How this is calculated

Blast damage from a nuclear detonation is governed by the Hopkinson-Cranz scaling law: at a given scaled distance Z = R / W^(1/3), blast overpressure and impulse are the same regardless of absolute yield — so all destructive radii scale with the cube root of yield. This is the same principle used for conventional explosives.

The coefficients here are parameterised from Glasstone & Dolan, 'The Effects of Nuclear Weapons' (US Dept. of Defense, 1977), a declassified reference still widely used in civil-defence and academic work. The 20 psi zone produces heavy structural damage and near-total fatalities among unprotected people; 5 psi causes severe to moderate building damage and high casualties; 1 psi can shatter windows and cause injuries from glass. The fireball radius uses exponent Y^0.4 because fireball size scales with total thermal energy release rather than with pure blast mechanics.

An airburst at optimum altitude allows the blast wave and its ground reflection to merge (Mach stem effect), maximising the area covered at each overpressure level. A surface burst detonates at ground level: blast radii are approximately 0.68 × the airburst values, but there is greater ground cratering and radioactive fallout. These are order-of-magnitude estimates — real effects depend on burst altitude, terrain, atmospheric density and building construction.