Created by Rahul Dhari
Reviewed by Steven Wooding
Based on research by
United Nations IATG 01.80 - Formulae for Ammunition Management - Clause 9.1 (March 2021)
Last updated: Jun 05, 2023

This blast radius calculator helps you determine the distance for detonations, after which there would be no fragments. An explosive, upon detonation, releases a large amount of energy. Interaction with the blast wave can cause severe injuries (see injury severity score calculator) depending on the stand-off distance. The blast radius becomes a critical parameter in such scenarios. This calculator and the accompanying article will explain what explosion radius is and how to calculate blast radius.

CAUTION
The blast radius is merely an indicative number, and it is still UNSAFE to be anywhere close to the blast radius in a real-world scenario. Extreme caution is advised.

## What is blast radius — blast wave

First, let's talk about blast waves. Upon an explosive detonation, a shock wave originates and compresses the air, causing an abrupt increase in pressure. This high-pressure wave, i.e., the blast wave, travels until it interacts with an object and reflects back. The time of interaction is very short. During this interval, the pressure rises abruptly to a peak value and then decays exponentially over time. The shock wave is usually spherical or hemispherical in shape. For a spherical blast wave, the change in pressure is:

$\scriptsize p(t) = (p_\mathrm{s} - p_\mathrm{a}) \left [ 1 - \frac{t - t_\mathrm{a}}{t_\mathrm{d}} \right ] e^{-(t - t_\mathrm{a})/\theta},$

where

• $p_\mathrm{s}$ – Peak pressure;
• $p_\mathrm{a}$ – Ambient pressure;
• $t_\mathrm{a}$ – Arrival time;
• $t_\mathrm{d}$ – Time duration of the positive phase; and
• $\theta$ – Time decay constant.

The above equation is known as the modified Friedlander equation, and it is used to calculate the change in pressure over time. This calculation helps us in finding the pressure loads on objects. A blast wave unleashes a large amount of energy that causes changes in pressure and temperature along its path. Such a wave can be catastrophic depending upon its intensity. The blast radius is the distance up to which the explosion will have an effect. In other words, beyond this distance, one can assume there would be fewer or no fragments flying.

Shock waves
Find out more about shock waves in our oblique shock calculator and Prandtl Meyer expansion calculator

## Hopkinson-Cranz scaling law

The scaling law is a convenient way to estimate the properties of a large explosion using the data from smaller explosions. This law states that two identical explosives produce similar blast waves but have different sizes, given the conditions, geometry, and scaled distances are identical. Such that:

$W \propto R^3$

You can calculate the blast radius or stand-off distance using the Hopkinson-Cranz scaling law. For an explosion of TNT equivalent mass, $W$ and scaled distance, $Z$. The stand-off distance is:

$R = ZW^{1/3}$

## How to calculate blast radius

The Hopkinson-Cranz equation is useful for estimating safety distances for explosives. For a fragmenting munition where public access is possible, the TNT explosion radius, $D$, is:

$D = 634 W ^{1/6}$

This distance is different for the bare explosives. The TNT explosion radius becomes:

$D = 130 W ^{1/3}.$

In case of ranges where the public access is denied, the blast radius becomes:

$D = 444 W ^{1/6}.$

Energy from different sources
You can also compare energy generated from different reactions with respect to the mass of TNT using our energy conversion calculator.

## Using the blast radius calculator

Now that you know how to calculate blast radius, you can use the calculator to estimate safety distances. Let's estimate the safety distance for the detonation of bare exposed $0.5~\mathrm{kg}$ of TNT.

1. Enter the mass of explosive, $W = 0.5~\mathrm{kg}$.
2. Select the type of munition to bare exposed.
$\qquad \footnotesize D = 130 \times (0.5) ^{1/6} = 103.2~\mathrm{m}$

Similarly, you can estimate the blast radius for c4 explosives too.

## FAQ

### What is blast wave?

It is a spherical or hemispherical-shaped wave that originates upon the detonation of explosives. This wave leads to an abrupt increase in pressure. A typical blast wave has a high-pressure jump, which denotes the wavefront. The pressure decays exponentially over time and has positive and negative (suction) phases.

### How do I calculate blast radius?

1. Find the all up weight of the explosive.
2. Find the cube root of the all-up weight.
3. Multiply the cube root by 130 to obtain the blast radius of the bare exposed explosive.

### What is the blast radius for 1 kg bare explosive?

The blast radius for the 1 kg bare explosive detonation is 130 m. This answer is obtained by using the range safety equation, based on Hopkinson-Cranz Law:

R = 130 × W(1/3) = 130 × 1(1/3) = 130 m

The intensity of the blast wave front is inversely proportional to the cube of the distance. Therefore, just by doubling the distance, you'll be shielding yourself from significant exposure.

### What law does blast radius follow?

The blast radius follows Hopkinson-Cranz Law which states that identical explosives with the same geometry but different sizes and distances will produce self-similar blast waves in the same atmosphere. Mathematically, the ratio of the weight of the explosives (W₁ and W₂) is proportional to the ratio of the cube of range (R₁ and R₂), i.e. (W₁/W₂) = (R₁/R₂)³.

Rahul Dhari
All-up weight of base explosives (W)
kg
Type of munition
Fragmented munitions
Public access
Yes
Distance
ft
The distance estimated by this calculator does not guarantee safety. It is the distance outside of which no more than one fragment would be expected. However, the areas outside the distance remains UNSAFE.
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