Blast Radius Calculator

Estimate the blast radius of an explosive charge using the cube-root scaling law, from TNT-equivalent mass to a distance in meters and feet for a chosen damage level.

Quick Facts

Formula
Cube-root (Hopkinson-Cranz) scaling law: R = Z x W^(1/3)
W is TNT-equivalent mass in kg, Z is the scaled distance in m/kg^(1/3) for the chosen damage level.
Cube-root growth
8x the mass is needed to double the radius
Because radius grows with W^(1/3), not W.

Your Results

Calculated
Blast radius (m)
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Distance for the selected damage level
Blast radius (ft)
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Same radius in feet
TNT-equivalent mass
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Charge mass x equivalency factor
Scaled distance Z used
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m/kg^(1/3) for this damage level

Ready

Enter a charge mass, explosive type, and damage level, then press Calculate.

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.

Frequently Asked Questions

What formula does this blast radius calculator use?
It uses the Hopkinson-Cranz cube-root scaling law, R = Z x W^(1/3), where W is the TNT-equivalent charge mass in kilograms, Z is the scaled distance in m/kg^(1/3) for a chosen damage level, and R is the resulting blast radius in meters. This cube-root relationship is the standard method for scaling blast effects across different charge sizes.
Why doesn't doubling the explosive mass double the blast radius?
Because blast radius scales with the cube root of mass, not mass itself. Doubling W multiplies the radius by 2^(1/3), about 1.26, so a 26% increase in radius. To double the blast radius you need roughly 8 times the explosive mass (2^3).
What is TNT-equivalent mass?
TNT equivalent converts the energy released by a given explosive into the mass of TNT that would release the same energy, so different explosives can be compared on one scale. This calculator multiplies your entered charge mass by the equivalency factor for the selected explosive type to get the TNT-equivalent mass used in the formula.
How accurate is this blast radius estimate?
It is a planning-level estimate assuming a hemispherical surface burst in open air at sea-level atmospheric conditions. Actual blast effects also depend on charge shape and confinement, burst height, terrain, and weather, so treat the result as an order-of-magnitude figure rather than an exact boundary.