Floods can occur at any time. If you’re designing something that could be affected by flooding, it’s important to consider the cumulative probability of flooding: that is, how likely that flooding is to occur *at some point* over its expected lifespan (aka “design life”). Often people are surprised at how likely such an event is!

The probability that an event of a certain size or larger will occur at least once over a given time period is

1 - (1 - \mathrm{AEP})^n

where AEP is the annual exceedance probability and n is the number of years. If you have an ARI (average recurrence interval) number instead, convert it to AEP first.

For example, imagine that a 24-hour AEP of 1% equated to 100 mm rainfall. Over a 50 year design life, the probability of one or more rainfall events occurring that have 100 mm **or more** in 24 hours is 1 - (1 - \mathrm{1\%})^{50} = 39.5%.

This formula represents “1 minus the probability that the event *does not* occur over n years”. In the above example, the probability of a 1% AEP not occurring in 1 year is 99%, and the probability of it not occurring in 50 years is 99%^50. Therefore the probability of it occurring *at some point* is 1 – 99%^50.

### More examples

The cumulative probability of a 100 year ARI event occurring at some point within a 10 year period is 9.5%.

The cumulative probability of a 100 year ARI event occurring at some point within a 100 year period is 63.2%.