# How To Calculate A Recurrence Interval

Recurrence Intervals help to estimate the likelihood of some event taking place. For example, if you were to say something occurs once every 10,000 years, the likelihood of it happening tomorrow is not probable. However, if you were to say something occurs every couple of minutes, then it is probable to occur. Recurrence intervals come in two flavors: simple recurrence intervals and those that take into account the magnitude of the event.

## Simple Recurrence Intervals

### Step 1

Find the required data, which will be the number of occurrences and the number of years observed. As an example, five floods recorded in 100 years.

### Step 2

Use the formula: Recurrence Interval equals the number of years on record divided by the number of events.

### Step 3

Plug in your data and calculate the recurrence interval. In the example, 100 years divided by five occurrences produces a recurrence interval of 20 years.

## Recurrence Intervals with Orders of Magnitude

### Step 1

Order your data data by severity of the event, numbered from most severe to least severe, such that the most severe is numbered one. This gives you the magnitude rank on a descending scale, i.e. the higher the rank, the less severe the event. Count the total number of years on record.

### Step 2

Use the formula: Recurrence Interval equals the number of years, plus one, divided by the magnitude rank for which you wish to calculate the recurrence interval.

Recurrence Interval = (Years + 1) / Rank

### Step 3

Plug in your data to calculate the recurrence interval. Say you wanted the recurrence interval for the fourth-worst flood in 100 years. Then 100 plus 1 equals 101. Divide that by 4, i.e., because the fourth-worst flood would have a magnitude rank of 4, and you get a recurrence interval of 25.25 years. This tells you that on average, a flood of that severity or more occurs every 25.25 years.

### References

### Cite This Article

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Taylor, C.. "How To Calculate A Recurrence Interval" *sciencing.com*, https://www.sciencing.com/calculate-recurrence-interval-7491065/. 13 March 2018.

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Taylor, C.. How To Calculate A Recurrence Interval last modified March 24, 2022. https://www.sciencing.com/calculate-recurrence-interval-7491065/