Blast radius calculator

This blast radius calculator estimates the distance at which a condensed-phase explosion still produces a chosen peak side-on overpressure. Enter the explosive mass in kilograms, a TNT equivalence factor, and a target overpressure in kilopascals. The engine converts the charge to TNT-equivalent mass, inverts the Kinney–Graham scaled-distance overpressure curve with a fixed bisection, and returns the Hopkinson–Cranz radius in metres. Typical screening thresholds include about seven kilopascals for window breakage and about thirty-five kilopascals for severe building damage. The model is a free-field air-blast idealization: it omits reflections, confinement, terrain, and injury.

What scaled distance and peak overpressure mean

Hopkinson–Cranz cube-root scaling is the standard first-order way to compare air blasts from different charge masses. Two explosions that are geometrically similar produce the same peak overpressure at the same scaled distance Z, defined as the physical radius R divided by the cube root of TNT-equivalent mass W. That is why eight kilograms of TNT, at the same overpressure, reach twice as far as one kilogram: the cube root of eight is two.

TNT equivalence converts a real explosive into an equivalent mass of TNT using a published relative-effectiveness factor, so a charge of C-4, ANFO, or black powder can be screened with the same overpressure curve after multiplication. This calculator then inverts the Kinney–Graham 1985 side-on overpressure formula, which gives the ratio of peak overpressure to standard atmospheric pressure as a smooth decreasing function of Z.

The ratio uses the closed product of three square-root denominators that Kinney and Graham fitted to free-field air-blast data, with P-zero equal to one hundred one point three two five kilopascals. Solving for Z at your target overpressure, then multiplying by the cube root of W, yields the radius in metres. Peak side-on overpressure is the sudden pressure jump above ambient on a surface parallel to the blast wave; it is not reflected pressure on a facing wall, not impulse, and not a fragment radius.

Common planning checkpoints include roughly seven kilopascals near one pound per square inch for window breakage and roughly thirty-five kilopascals near five pounds per square inch for heavy structural damage. Those checkpoints are screening numbers, not injury criteria. The engine is a point-source free-field model: it has no ground reflection, no street canyon, no bunker, and no Monte Carlo weather.

Where a blast-radius estimate belongs — and where it does not

Process-safety engineers use a scaled-distance blast radius as a first contour when screening storage of energetic materials, accident consequence sketches, or standoff around a process unit before anyone opens a full Kingery–Bulmash workbook or a computational fluid-dynamics run. Teachers and students meet the same cube-root identity in explosion-physics and civil-protection courses: given mass, TNT equivalence, and a textbook overpressure, what is R, and does eight times the mass really double the distance.

Prefer it when you already have a charge mass, a published TNT factor, and a free-field overpressure threshold in kilopascals; convert pounds and pounds per square inch first if your source document is imperial. Keep requests inside the documented limits, pin the rounded radius in tests, and remember that ground, buildings, and confinement can move the true contour by a large factor. Pair the calculator with other free deterministic physics helpers when you are assembling a small lab of screening tools rather than a full consequence model.