Blast Radius Calculator - UN IATG 01.80 Stand-off Model

A blast radius calculator is a physics tool that estimates the stand-off distance from a detonating explosive beyond which the expected fragment density is at most one fragment per unit area. The calculation is built on the Hopkinson-Cranz cube-root scaling law, which says identical explosives at different scales produce self-similar blast waves. Doubling the charge mass does not double the stand-off distance - it grows with the cube root of the mass for bare charges and the sixth root for fragmenting munitions.

• • Range safety and ammunition storage planning: Estimate the inhabited-building distance required when storing bulk explosives, with the UN IATG 01.80 formula providing the same constants used in safety regulations.
• • Comparing munition configurations: Switch between bare, fragmenting, and cased models to see how a metal casing changes the fragmentation pattern and forces a much larger stand-off distance per kilogram of explosive.
• • Teaching cube-root scaling in physics classes: Demonstrate the Hopkinson-Cranz cube-root scaling law by asking students to predict how the stand-off distance grows when the charge weight is multiplied by eight.
• • Converting yield estimates to a usable safety distance: When an energy figure is given in joules or in tons of TNT equivalent, convert it into kilograms and use the calculator to translate it into a practical stand-off distance in meters and feet.

The same problem shows up under several names - blast radius, explosion radius, fragment distance, and stand-off distance. The link below connects that backbone to the underlying F=ma and momentum ideas.

If you would like a quick reminder of the F=ma and momentum ideas behind a moving fragment, our forces and Newton's laws calculator covers the same physics from a different angle.

The blast radius calculator picks one of three UN IATG 01.80 formulas based on the type of munition, applies the cube root or sixth root of the TNT-equivalent mass, and multiplies by the matching proportionality constant to return the stand-off distance in meters. The same distance is also rendered in feet, and the scaled distance Z (or Z') is shown so you can verify the arithmetic by hand.

• W (mass): TNT-equivalent mass of the explosive in kilograms. Convert C4, ANFO, or other explosives via their TNT equivalency factor before entering.
• Munition type: Bare exposed uses the cube-root model with K = 130. Fragmenting and cased rounds use the sixth-root model with K = 634 or 444.
• Scaled distance Z: Hopkinson-Cranz scaled distance Z = W^(1/3). The calculator prints this number so you can confirm the cube root used in the formula.
• Proportionality constant K: Empirical constant from UN IATG 01.80 that absorbs units, geometry, and the chosen threat threshold.

To follow the same calculation by hand you only need a cube-root or sixth-root table. The calculator prints the scaled distance Z (cube root) and Z' (sixth root) so you can verify each step, and the constant K is shown next to the formula box. The energy side of the same scaling idea is covered separately.

According to United Nations IATG 01.80, the stand-off distance for a bare-exposed charge is D = 130 W^(1/3), a fragmenting munition in a public-access scenario uses D = 634 W^(1/6), and a public-access-denied scenario uses D = 444 W^(1/6).

According to Omni Calculator Blast Radius, The Omni blast radius calculator reproduces the same UN IATG 01.80 formulas and confirms the worked example: 0.5 kg of bare-exposed explosive yields D = 130 * (0.5)^(1/3) = 103.2 m.

If you want to see how a related energy figure grows with mass, the work energy power calculator covers the energy side of the same Hopkinson-Cranz scaling idea.

Four small ideas explain everything the blast radius calculator shows.

These four ideas are the vocabulary of the formula box. The same scaling laws show up in textbook derivations of general wave physics.

They are the same scaling laws you see in any Hopkinson-Cranz derivation, including the textbook derivations reproduced by the harmonic wave equation calculator for general wave physics.

Five short steps are enough to get a trustworthy stand-off distance.

1. 1 Convert your charge to kilograms of TNT equivalent: If your explosive is C4, ANFO, composition B, or another energetic material, convert the actual mass into kilograms of TNT equivalent using the published equivalency factor.
2. 2 Enter the TNT-equivalent mass: Type the converted mass into the first input. The default of 1 kg reproduces the reference case immediately.
3. 3 Pick the type of munition: Choose Bare exposed for an unconfined charge, Fragmenting for a casing that breaks into pieces, or Public access denied for a heavily cased round.
4. 4 Read the stand-off distance: The result panel shows meters, feet, and the scaled distance Z and Z' so you can verify the arithmetic.
5. 5 Apply the safety reminder: Read the safety reminder in the result panel. The stand-off distance is informational; the surrounding area remains unsafe even outside the computed radius.

Entering 0.5 kg with the bare exposed munition returns 103.2 m (338.6 ft) - the same number Omni publishes and UN IATG 01.80 predicts. Switching to Fragmenting jumps the same 0.5 kg charge to 564.8 m (1853 ft), which is why range safety officers treat cased and fragmenting rounds so differently even when the explosive mass is identical.

A purpose-built blast radius calculator removes the manual cube-root arithmetic and the constant-switching that come from comparing munition types by hand.

• • Three munition models in one tool: Bare exposed, fragmenting, and cased munitions all use the same calculator, so you can compare stand-off distances for the same explosive mass without re-deriving the formulas.
• • Shows the scaled distance Z: The intermediate Z = W^(1/3) (or Z' = W^(1/6)) is printed alongside the answer, which makes it easy to verify the arithmetic in a lab notebook.
• • Both metric and imperial outputs: Meters and feet appear side by side, so range safety officers, engineers, and hobby physics learners can all use the number without converting it themselves.
• • Built on a published standard: Every constant comes from the UN IATG 01.80 formula for ammunition management, matching the formulas used in safety regulations.
• • Reinforces the cube-root scaling idea: Watching the stand-off distance grow with W^(1/3) - 1 kg gives 130 m, 8 kg gives 260 m - is one of the clearest ways to teach the Hopkinson-Cranz scaling law.

When the calculation needs to feed into a fragment trajectory rather than a single stand-off radius, two related calculators finish the job - one traces the trajectory of a piece of casing and the other reports how long that fragment spends in the air.

When the calculation needs to feed into a fragment trajectory rather than a single stand-off radius, our projectile motion calculator handles the trajectory of a piece of casing once you know its initial velocity, and the time of flight projectile motion calculator shows how long that fragment spends in the air.

Three variables decide what the stand-off distance looks like, and three limitations tell you when to double-check the answer.

• • The result is a stand-off distance for an idealized surface burst on flat ground. Real detonations vary with height of burst, terrain, casing thickness, soil coupling, and weather.
• • The calculator returns an informational number only. The area around any real detonation is unsafe even outside the computed radius.
• • The model assumes the explosive mass is converted to a single TNT-equivalent value. Mixed-charge scenarios need each component converted separately and the worst-case distance used.

Two physics calculators cover the underlying motion equations and the connection between a fragment's acceleration and the energy released in the blast.

When the same charge is expressed in joules instead of kilograms of TNT, convert joules to TNT equivalent before entering (1 ton of TNT = 4.184 * 10^9 J).

These limitations are also why UN IATG 01.80 publishes the constants as guidance rather than as hard safety limits.

According to NIST Guide for the Use of the SI (Appendix B.8), one meter is exactly 3.28084 feet, which is the conversion factor used to render the stand-off distance in feet.

If you would like to compare the stand-off distance with the kinematics of a thrown fragment, our kinematics motion calculator covers the underlying motion equations, and the forces and Newton's laws calculator connects the fragment's acceleration back to the energy released in the blast.