About

Miscalculating blast standoff distances kills people. The Hopkinson-Cranz scaling law relates explosive yield to damage radius through cube-root proportionality: R = k ⋅ W^1/3, where W is TNT-equivalent charge mass in kg and k is an empirically derived damage-zone coefficient. This calculator applies RE (Relative Effectiveness) factors from UFC 3-340-02 to convert common explosives to TNT equivalence before computing five concentric damage zones: fireball, severe structural collapse, moderate structural damage, light damage (glass breakage), and the outdoor injury threshold. Results assume hemispherical surface detonation with ideal atmospheric conditions at sea level. Real-world blast propagation is affected by terrain, structures, confinement, and casing fragmentation. This tool approximates free-field conditions only.

Formulas

The Hopkinson-Cranz (cube-root) scaling law is the standard method for predicting blast damage radii from a known explosive charge mass. It assumes geometric similarity of blast waves across different charge sizes.

R = k ⋅ W_TNT^1/3

where R = damage radius in m, k = zone-specific empirical coefficient, W_TNT = TNT-equivalent charge mass in kg.

TNT equivalence conversion:

W_TNT = W_actual × RE

where RE = Relative Effectiveness factor (dimensionless ratio of the explosive's blast energy to TNT's blast energy).

Scaled distance (Hopkinson-Cranz parameter):

Z = RW_TNT^1/3

where Z = scaled distance in m/kg^1/3. At a given Z, the peak overpressure P_s is constant regardless of charge size. Approximate peak overpressure from the Kingery-Bulmash simplified model for hemispherical surface burst:

P_s ≈ 1772Z³ − 114Z² + 108Z kPa

Damage zone coefficients (k) used in this calculator: Fireball k = 0.5, Severe structural k = 1.8, Moderate structural k = 3.5, Light damage (glass) k = 6.3, Outdoor injury k = 11.0. These correspond approximately to overpressures of 2000, 83, 35, 7, and 2 kPa respectively (UFC 3-340-02 / TM 5-1300 guidelines).

Reference Data

Explosive	RE Factor (TNT = 1.00)	Detonation Velocity m/s	Density g/cm³	Common Use
TNT	1.00	6900	1.65	Military standard reference
C-4 (Composition C-4)	1.34	8040	1.59	Military demolition
RDX (Cyclonite)	1.60	8750	1.82	Detonators, military munitions
PETN (Pentrite)	1.66	8400	1.77	Detonating cord, boosters
Semtex	1.35	7900	1.40	Commercial demolition
HMX (Octogen)	1.70	9100	1.91	Shaped charges, rocket propellant
Dynamite (commercial)	0.60	5000	1.30	Mining, quarrying
ANFO	0.82	4500	0.84	Mining, bulk blasting
Nitroglycerin	1.50	7700	1.59	Dynamite component, medicine
Amatol (80/20)	0.97	6100	1.50	Military shells, bombs
Torpex	1.30	7200	1.81	Naval torpedoes, depth charges
Tetryl	1.25	7850	1.73	Booster charges, detonators
TATB	1.17	7760	1.94	Insensitive munitions (IHE)
Picric Acid	1.17	7350	1.77	Historical artillery shells
Black Powder	0.55	400	1.70	Pyrotechnics, historical
Ammonium Nitrate (pure)	0.42	2700	1.72	Fertilizer (accidental detonation)
CL-20	1.87	9380	2.04	Experimental high-performance
Comp B (60/40 RDX/TNT)	1.33	7900	1.72	Bomb fills, shaped charges
Pentolite (50/50)	1.38	7530	1.66	Grenades, boosters
Tritonal (80/20 TNT/Al)	1.07	6700	1.72	Air-dropped bombs

Frequently Asked Questions

The RE factor converts any explosive's actual mass into its TNT-equivalent mass before cube-root scaling is applied. For example, 10 kg of C-4 with RE = 1.34 yields 13.4 kg TNT equivalent. Since radius scales as the cube root, a 34% increase in equivalent mass produces only about a 10% increase in blast radius. This nonlinear relationship means explosive type matters less than charge mass for radius estimation.

A charge detonated on a reflecting surface (ground) produces a hemispherical shock wave that effectively doubles the energy directed outward compared to a free-air burst. UFC 3-340-02 specifies a ground reflection factor of approximately 1.8 (often rounded to 2.0). The k-coefficients in this calculator already account for this surface enhancement. For elevated or buried charges, actual radii will differ significantly.

Standard annealed glass fractures at peak overpressures as low as 3 - 7 kPa (0.4 - 1.0 psi). Because overpressure decays roughly as the inverse cube of distance, the radius at which this low threshold is met extends far beyond the structural damage zone. Glass fragments propelled at velocities exceeding 15 m/s are a primary source of blast injuries, which is why building codes (GSA, ISC) establish minimum standoff distances based on this zone.

The polynomial fit used here is valid for scaled distances Z between approximately 0.5 and 40 m/kg^1/3. Below Z = 0.5, detonation product gases dominate and the blast wave model breaks down. Above Z = 40, overpressures drop below 1 kPa and atmospheric absorption, wind, and temperature gradients become dominant factors not captured by the scaling law.

Significantly. A cased charge (e.g., pipe bomb, artillery shell) converts a portion of explosive energy into fragment kinetic energy, reducing the blast wave energy by 20 - 50%. Conversely, detonation inside a confined space (room, tunnel) can amplify peak overpressure by factors of 2 - 8 due to multiple shock reflections. This calculator models unconfined, uncased charges only. For confined scenarios, multiply overpressure estimates by the confinement enhancement factor from TM 5-1300 Table 2-7.

No. Vapor cloud explosions produce significantly lower overpressures than condensed-phase detonations at equivalent energy. The TNT equivalency method overestimates VCE damage at close range and underestimates it at far range. For VCE, use the Baker-Strehlow-Tang method. Nuclear detonations follow different scaling laws due to thermal radiation (which dominates casualties beyond 2 km) and nuclear-specific phenomena like EMP and fallout that are entirely outside this model's scope.