Abstract An analytical model which describes the impact of a hazard on the surrounding area has been given previously. The basis of the model is a uniform population density, the inverse square law for the decay of the intensity of the physical effect and the lognormal distribution, or probit equation, for the relation between the causative, or injury, factor and the probability of injury. It was shown that if these assumptions hold, the number of people injured may be approximately estimated by calculating the radius for 50% injury and assuming ,that all persons inside the circle suffer injury while all those outside it escape injury, and that a simple correction factor can be derived to compensate for the error in this method. It is shown in the present paper that the restriction of the inverse square law for the decay of the intensity of the physical effect can be relaxed and that for the more general case where the decay is inversely proportional to some power n of the distance, the correction factor is o= exp (σ2/n2), where σ is the spread parameter of the lognormal distribution. T001 . List of symbols C concentration (kg/m3) dp density population (persons/m2) i normalised intensity of physical effect Ip impulse (N s/m2) kV, kVW, kW constants m index for concentration m* location parameter in lognormal distribution n decay index for the injury factor nV power index for the injury factor nW decay index for the intensity of physical effect Ni total number of people injured po peak overpressure of explosion (N/m2) P probability of injury r radial distance (m) ro radius of physical phenomenon (m) t time (s) υ injury factor (various units) w intensity of physical effects (various units) x normalised injury factor z scaled distance (m/kg 1 3 ) σ spread parameter in lognormal distribution (σ2 = variance) o correction factor for variance and decay index Φ normal distribution function Subscript 50 for probability of injury equal to 0.5