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Cube-Root Blast-Scaling Radius — result sheet
Scale a reference blast-effect radius to a different TNT-equivalent yield with the cube-root scaling relationship.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: R₂ = R₁ × (W₂/W₁)^(1/3), holding the chosen blast-effect criterion and environment constant.
Blast-effect distances are often compared with a cube-root scaling law: if the TNT-equivalent yield changes while the selected effect threshold stays the same, the corresponding distance scales with the cube root of yield. This calculator does not predict damage, casualties, safe distances, pressure, fragments, thermal effects, or legal limits; it only rescales a supplied reference radius.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- New TNT-equivalent yield — kg TNT; minimum 1.0E-6; maximum 1.0E+15
- Reference TNT-equivalent yield — kg TNT; minimum 1.0E-6; maximum 1.0E+15
- Reference radius for the same effect — m; minimum 1.0E-6; maximum 1000000000
Worked example
| Input | Value |
|---|---|
| New TNT-equivalent yield | 8000 |
| Reference TNT-equivalent yield | 1000 |
| Reference radius for the same effect | 100 |
The scaled radius is 200 m because an eightfold yield gives a twofold distance under cube-root scaling.
Assumptions and limits
- The reference radius and new radius represent the same measured effect threshold and comparable charge geometry and environment.
- Yield is expressed as TNT equivalent, and cube-root scaling is treated as a first-order comparison rather than a complete blast model.
- The result must not be used for safety decisions, explosive design, emergency response, or clearance distances without qualified site-specific analysis.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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