# How to Calculate a Blast Radius

••• gumpy/iStock/GettyImages
Print

An explosion unleashes a sphere of pressure over normal air pressure that damages whatever is in its radius. The pressure in excess of normal atmospheric pressure generated by an explosion is called overpressure. In the case of a nuclear bomb at 2-psi overpressure, approximately 45 percent of the population is injured, 5 percent of the population is dead, smaller buildings are destroyed and larger buildings are damaged. Overpressure is useful in calculating a blast radius, especially for nuclear bombs, since certain levels of overpressure consistently produce certain levels of destruction.

Scale the height of the burst for a 1-kiloton explosion. Divide the height at which the bomb was exploded by the cube root of the yield. For instance, with a 43-kiloton explosion at 500 feet, the value will be 142.9 feet. This is the height at which a 1-kiloton bomb must be exploded, in order to have the same overpressure as the original bomb.

Read the graph of the overpressure of a 1-kiloton explosion to obtain the 2-psi distance using the value scaled. A 1-kiloton bomb exploded at 142.9 feet has a 2-psi overpressure extending to 2,700 feet.

Convert the 1-kiloton values back to the values for the actual yield. Multiply the value read in the graph by the cube root of the yield. At 2,700 feet with a 43-kiloton bomb, the distance for a 2-psi overpressure is 9,450 feet.

Convert to miles. Divide the converted value by 5,280, the number of feet in one mile; 9,450 feet would be 1.79 miles.

Calculate the blast radius. Square the distance of the blast and multiply it by pi (3.14). With a 1.79 mile distance, the blast radius of a 2-psi overpressure would be 10.1 square miles.

#### Things You'll Need

• Yield of the bomb
• Height at which the bomb was exploded
• Graph of the overpressure of a 1-kiloton explosion

#### Tips

• To calculate a blast radius for a smaller explosion, obtain an overpressure graph of a smaller explosion.