Define hazard, risk, vulnerability

Hazard

A hazard is a potentially damaging natural or man-made event or phenomenon (such as earthquake, landslide, flood) that may cause loss of life, injury, property damage or environmental harm. It is described by its magnitude, location, frequency and probability.

Vulnerability (danger)

Vulnerability is the degree of loss or damage likely to occur to a given element (people, buildings, roads) when exposed to a hazard of given intensity. It is expressed from 0 (no loss) to 1 (total loss). It depends on construction quality, poverty, preparedness and location.

Risk

Risk is the expected loss (lives, injuries, property, economic activity) caused by a hazard in a given area and time. It combines the probability of the hazard, the elements at risk and their vulnerability.

$$\text{Risk} = \text{Hazard} \times \text{Vulnerability} \times \text{Elements at risk}$$

Example: a landslide on a steep slope is a hazard; the weak houses below are vulnerable; the possible loss of those houses and lives is the risk.