Blast Radius Calculator
Enter the explosive type and charge mass to instantly see five concentric damage zones - from the fireball out to the outdoor injury threshold - all computed from the Hopkinson-Cranz scaling law with UFC 3-340-02 coefficients. Switch between metric and imperial, pick from 20 explosive types with pre-loaded TNT-equivalence factors, and use the optional standoff distance field to get the peak overpressure at any point of interest.
Formula
Worked example
A 100 kg TNT charge (RE = 1.00, so W_TNT = 100 kg): cube-root = 4.642 kg^(1/3). Fireball: 0.5 x 4.642 = 2.3 m. Severe collapse: 1.8 x 4.642 = 8.4 m. Moderate damage: 3.5 x 4.642 = 16.2 m. Light damage: 6.3 x 4.642 = 29.2 m. Injury threshold: 11.0 x 4.642 = 51.1 m. At 50 m standoff, Z = 50 / 4.642 = 10.77, so Ps = 1772/10.77^3 - 114/10.77^2 + 108/10.77 = 1.42 - 0.98 + 10.03 = 10.5 kPa (1.52 psi).
How the blast radius calculation works
The calculator applies the Hopkinson-Cranz scaling law, the empirical cornerstone of explosion damage estimation since the 1910s. The law states that chemically similar explosives produce geometrically similar blast waves when their linear dimensions scale as the cube-root of charge mass. In practice this means damage radius R equals a zone-specific coefficient k multiplied by the cube-root of TNT-equivalent mass: R = k times W_TNT^(1/3). The five coefficients used here (k = 0.5, 1.8, 3.5, 6.3, and 11.0) come from UFC 3-340-02, the U.S. Department of Defense standard for protective structures. Each charge mass is first converted to TNT-equivalent by multiplying by the explosive's Relative Effectiveness (RE) factor, also called the TNT equivalent, sourced from the same standard.
Five damage zones explained
Zone 1, the fireball (k = 0.5, roughly 2000 kPa peak overpressure): complete vaporisation and incineration of everything at this distance. Zone 2, severe structural collapse (k = 1.8, about 83 kPa or 12 psi): nearly all unreinforced buildings collapse, reinforced concrete suffers major damage. Zone 3, moderate structural damage (k = 3.5, about 35 kPa or 5 psi): walls blow in, roof structures fail, most residential construction becomes uninhabitable. Zone 4, light damage and glass breakage (k = 6.3, about 7 kPa or 1 psi): windows shatter, doors blow off their frames, minor injuries from flying glass. Zone 5, outdoor injury threshold (k = 11.0, about 2 kPa or 0.3 psi): the pressure at which eardrum rupture becomes possible and lung damage risk begins for unprotected individuals in the open.
TNT equivalence and RE factors
Not all explosives release the same energy per kilogram. TNT is the international reference: 1 kg of TNT releases approximately 4.184 megajoules of chemical energy on detonation. The Relative Effectiveness (RE) factor expresses how much TNT would produce the same peak overpressure as a given explosive. C-4, for example, has an RE of 1.37, meaning 1 kg of C-4 produces blast effects equivalent to 1.37 kg of TNT. CL-20, one of the most energetic practical explosives, reaches RE = 1.87, while black powder only reaches 0.25 because much of its energy is released too slowly to contribute to the shock wave. This calculator includes RE factors for 20 common explosives from military and industrial contexts.
Overpressure at a specific standoff distance
The optional standoff field lets you enter a specific distance and get the peak overpressure using the Kingery-Bulmash polynomial model, a widely used simplification of empirical data for surface-burst charges. The model expresses overpressure Ps in kPa as a function of scaled distance Z = R / W_TNT^(1/3), where the formula Ps = 1772/Z^3 - 114/Z^2 + 108/Z is valid for scaled distances between roughly 0.5 and 40 m/kg^(1/3). Results outside that range are not shown. This is useful for checking whether a proposed safety perimeter meets a target overpressure limit, such as the 7 kPa (1 psi) threshold commonly used as a minimum public safety distance.
Assumptions and limitations
This calculator models an ideal surface hemispherical detonation in free field conditions at sea level, with no confinement, no terrain shielding, no casing or fragmentation, and standard atmospheric pressure (101.3 kPa). Real-world factors that significantly alter results include: confined or partially confined detonations (greatly amplified pressure), buried or elevated charges, reflected blast from walls or the ground, fragmentation from a cased munition, altitude (lower air density reduces overpressure), and urban canyon effects. Always use this tool for educational estimates only. Safety-critical standoff planning must be performed by a qualified explosives engineer using detailed site-specific analysis.
Explosive TNT-equivalence reference (RE factors)
| Explosive | RE Factor | Det. Velocity (m/s) | Density (g/cm³) | Common Use |
|---|---|---|---|---|
| TNT | 1.00 | 6900 | 1.63 | Baseline reference |
| C-4 | 1.37 | 8050 | 1.60 | Military demolition |
| RDX | 1.60 | 8750 | 1.82 | Military/industrial |
| PETN | 1.66 | 8400 | 1.77 | Blasting caps, det cord |
| HMX | 1.70 | 9110 | 1.89 | Rocket propellant |
| Semtex | 1.28 | 7700 | 1.55 | Demolition |
| ANFO | 0.82 | 4500 | 0.85 | Mining & quarrying |
| Ammonium Nitrate | 0.42 | 2700 | 0.83 | Fertiliser / industrial |
| Dynamite | 1.20 | 5500 | 1.48 | Mining, construction |
| Comp B | 1.35 | 7920 | 1.67 | Artillery shells |
| Pentolite | 1.42 | 7470 | 1.65 | Boosters |
| Tritonal | 1.07 | 6700 | 1.77 | Aerial bombs |
| Tetryl | 1.25 | 7570 | 1.73 | Booster charges |
| Black Powder | 0.25 | 450 | 1.00 | Fireworks, historic |
| Nitroglycerin | 1.54 | 7700 | 1.59 | Medical, explosives |
| CL-20 | 1.87 | 9400 | 2.04 | Advanced military |
| TATB | 0.90 | 7350 | 1.94 | Insensitive nuclear devices |
| Picric Acid | 0.90 | 7350 | 1.77 | Munitions (historic) |
| Amatol | 0.81 | 5060 | 1.55 | WWII shells |
| Torpex | 1.30 | 7900 | 1.80 | Underwater warheads |
RE factors from UFC 3-340-02 and TM 5-1300. Detonation velocity and density are approximate mid-range values.
Frequently asked questions
What is the Hopkinson-Cranz scaling law?
Also called the cube-root scaling law, it states that for geometrically similar charges of the same explosive, blast wave parameters (peak overpressure, duration, impulse) at a given scaled distance Z = R / W^(1/3) are the same regardless of absolute charge size. This means doubling the blast radius of a given pressure requires an eightfold increase in charge mass, because (2R)^3 = 8R^3. It was established independently by Bertram Hopkinson (1915) and Carl Cranz (1926) and underpins essentially all modern explosion-effects engineering.
What does TNT-equivalent mean?
TNT-equivalent is the mass of TNT that would produce the same peak overpressure as the charge under study. It is obtained by multiplying the actual mass by the Relative Effectiveness (RE) factor of the explosive. RE factors are determined experimentally by comparing pressure histories from different explosives and are tabulated in standards such as UFC 3-340-02. TNT (RE = 1.00) is the baseline because it has been studied more extensively than any other explosive.
Why does doubling the mass not double the blast radius?
Because the shock wave expands in three dimensions. Blast energy spreads over the surface area of an ever-growing sphere, which grows as the cube of radius. Doubling the mass only increases the radius by 2^(1/3), about 26 percent. To double the radius you need eight times the mass, not twice. This cube-root relationship is the fundamental reason large bombs are only moderately more destructive at a given distance than medium ones.
Is this calculator suitable for safety planning or legal purposes?
No. This tool is intended for educational and illustrative purposes only. It uses simplified empirical models that assume ideal free-field conditions. Real safety standoff distances for magazines, storage sites, and public events must be determined by a licensed explosives engineer using site-specific analysis and applicable regulations such as UFC 3-340-02, ATFEX tables, or local national standards. Never rely on this calculator for decisions involving human safety.
What is scaled distance and why does it matter?
Scaled distance Z = R / W^(1/3) collapses the blast wave behaviour of all charge sizes onto a single curve. At a given Z, the peak overpressure is the same regardless of whether you have 1 kg or 1000 kg of TNT. This makes tabulation and comparison straightforward: instead of a separate table for every charge size, a single curve of Ps versus Z describes everything. The Kingery-Bulmash model used here expresses Ps directly as a polynomial in Z.
What is the 1 psi (7 kPa) rule of thumb?
A peak overpressure of around 1 psi (6.9 kPa) is widely cited as the approximate threshold at which residential windows begin to shatter and minor, largely indirect injuries (flying glass) become likely for people inside buildings. It is often used as a minimum public safety separation distance in initial screening calculations. Structural damage to ordinary wood-frame buildings begins to be significant at around 5 psi (35 kPa), which corresponds to the moderate-damage zone in this calculator.
How accurate is the Kingery-Bulmash overpressure model?
The Kingery-Bulmash polynomial is a widely used engineering approximation fit to experimental hemispherical surface-burst data and is incorporated in U.S. Army manuals and many commercial blast-effects codes. For free-field conditions within the valid Z range (0.5 to 40 m/kg^(1/3)) it typically matches measured peak overpressures within about 10 to 20 percent. Accuracy degrades for near-field scaled distances below 0.5, for highly asymmetric charges, and whenever structural reflections are present.