About the Blast Radius Calculator
This tool estimates how far the effects of an explosion reach using the cube-root blast scaling law, sometimes called Hopkinson-Cranz scaling. It is the standard method for relating explosive charge size to blast distance across engineering, explosive-safety, and physics references, because blast waves from geometrically similar charges of different sizes behave the same way when distance is scaled by the cube root of the charge mass.
The formula
The blast radius is calculated as R = Z × W^(1/3), where W is the TNT-equivalent charge mass in kilograms, Z is the scaled distance in m/kg^(1/3) associated with a chosen damage or overpressure level, and R is the resulting blast radius in meters. The scaled distance Z is what makes the law useful: it packages the physics of blast-wave decay into a single constant per damage level, so the same Z applies whether the charge is 1 kg or 1,000 kg.
TNT-equivalent mass
Different explosives release different amounts of energy per unit mass, so charge mass alone is not comparable across explosive types. TNT-equivalent mass fixes this by multiplying the actual charge mass by an equivalency factor referenced to TNT (equivalency 1.00 by definition). This calculator applies the equivalency factor for the selected explosive type before running the scaling law, so the formula always operates on an energy-equivalent TNT mass.
Why radius scales with the cube root
Blast energy spreads outward through a roughly spherical volume, and overpressure falls off quickly with distance as that energy is spread over an ever-larger surface. The practical consequence is that radius grows much more slowly than charge mass: doubling the mass only multiplies the radius by 2^(1/3), about 1.26, so it takes roughly 8 times the explosive mass to double the blast radius. This is why small increases in a bomb-threat or industrial-explosion scenario do not proportionally increase the danger zone.
Assumptions and limits
This calculator assumes a hemispherical surface burst in open air at sea-level atmospheric pressure, with no significant confinement, cratering, or reflecting surfaces nearby. The scaled-distance values offered for each damage level are typical planning-level approximations, not a substitute for a site-specific blast assessment. Actual outcomes also depend on charge geometry, burst height, terrain, structures in the blast path, and weather, so treat results as order-of-magnitude estimates for education and general planning.