Free Blast Radius Calculator

Understanding Blast Radius in Explosive Safety

When an explosive detonates, it releases a concentrated burst of energy that generates a shock wave capable of causing severe injuries and structural damage. The blast radius—often called the detonation radius—represents the distance beyond which the explosion’s effects (fragments, pressure wave) are greatly reduced. This free, online blast radius calculator (an explosion safety distance calculator) applies the Hopkinson‑Cranz scaling law to quickly estimate that safe stand‑off distance.

Important: The computed blast radius is only an indicative safety number. In a real‑world scenario, being anywhere near this limit is still unsafe. Always consult official safety guidelines and use the calculated distance as a conservative reference.

The Nature of Blast Waves

When a high explosive detonates, a shock wave forms and travels outward, compressing the air and producing an abrupt pressure rise. The pressure at a given point jumps almost instantly to a peak value $p_s$ and then decays exponentially with time. This time‑history of overpressure is described by the modified Friedlander equation:

$$p(t) = p_s \left(1 - \frac{t - t_a}{t_d}\right) e^{-\frac{t - t_a}{\theta}}, \quad \text{for } t_a \le t \le t_a + t_d$$

Where:

• $p_s$ — peak incident overpressure
• $p_a$ — ambient atmospheric pressure
• $t_a$ — arrival time
• $t_d$ — duration of the positive phase
• $\theta$ — exponential decay constant

The Friedlander equation is essential for evaluating pressure loads on structures and personnel. The blast radius is effectively the distance at which the pressure and fragment kinetic energy fall below dangerous thresholds.

Hopkinson‑Cranz Scaling Law (Cube‑Root Law)

The Hopkinson‑Cranz scaling law, also known as the cube‑root law, enables engineers to predict blast characteristics for large explosions using data from smaller tests. It states that two explosive charges of the same geometry yield self‑similar blast waves when their scaled distances are equal. The scaled distance is:

$$Z = \frac{R}{W^{1/3}}$$

where $R$ is the stand‑off distance (in meters) and $W$ is the TNT‑equivalent mass (in kg). Rearranged, the stand‑off distance becomes:

$$R = Z \cdot W^{1/3}$$

In practice, the blast radius is written in a simpler form:

$$R = C \cdot W^{1/3}$$

The constant $C$ (in m/kg$^{1/3}$) depends on the type of explosive, the munition design, and the accessibility of the area.

Blast Radius Formulas for Different Scenarios

The calculator implements several well‑known blast‑radius formulas based on the Hopkinson‑Cranz law:

• Bare exposed explosive (e.g., a loose TNT charge): $R = 130 \cdot W^{1/3}$ (meters). This is the standard equation for unconfined open‑air detonations.
• Fragmenting munition with public access possible: A larger constant is applied (typically $C = 180$) to account for additional debris and projectile hazards.
• Ranges where public access is denied: An even larger constant is used (often $C = 300$), reflecting the higher risk tolerance in controlled or remote zones.

These formulas are widely adopted in range‑safety manuals and help planners establish conservative exclusion zones.

How to Use the Blast Radius Calculator

Using the tool is straightforward:

1. Enter the explosive mass $W$ (in kg) of the TNT‑equivalent charge.
2. Select the munition type – choose between “bare exposed”, “fragmenting (public access)”, or “restricted range” to apply the appropriate constant.
3. The calculator instantly displays the blast radius $R$ in meters.

For example, for a bare exposed TNT charge of 0.5 kg:

$$R = 130 \times 0.5^{1/3} \approx 130 \times 0.7937 \approx 103.2\ \text{m}$$

The same steps work for any explosive expressed in TNT equivalent—simply enter the correct equivalent mass and the calculator returns the corresponding safety distance.