Before getting into the details, let us define ‘Risk’ and ‘Uncertainty’.
"Risk is defined as what we stand to lose or gain, if certain events occur."
"Uncertainty refers to the lack of confidence that we express w.r.t events that we want to observe".
Risk is typically calculated using the formula “Risk = Probability of happening X Impact of the event” – when ‘the event’ happens. i.e. Risk is a function of Probability and Impact.
Expressing mathematically, Risk = f(probability, impact).
Probability has an element of Uncertainty Associated with it. Probability and hence uncertainty, is a factor in arriving at Risk.
This relation can be expressed mathematically as Risk = f[Probability(uncertainty), Impact]
People usually have this in mind when they mix up Uncertainty and Risk. But if we look into the equation above, we will see that it is not only the uncertainty, but also the impact, that determines whether a particular event that will happen in the future, qualifies to be a risk.
So while Risk definitely has an element of Uncertainty Associated with it, all Uncertainty translates into Risk, only based on the impact.
That is why it is not right to use Risk and Uncertainty Interchangebly.
Let me know what you think.