Return Period Calculator (100-Year Flood and Earthquake Risk)
The chance of at least one flood, storm or earthquake of a given return period during the years you care about, and the return period a design needs to keep the risk acceptably low.
Results
The dashed line marks the value you entered.
What this tool does
A '100-year flood' does not come once every hundred years: it has a 1 % chance of happening in any single year, with no memory, and over a 30-year mortgage the chance of at least one is about 26 %. Over 100 years it is only 63 %, not 100. Building codes turn this around: a 10 % chance of being exceeded in a 50-year building life corresponds to a return period of about 475 years, the usual design level for earthquake loads in many codes.
Formula
p = 1 ÷ T · P(at least one in n years) = 1 − (1 − 1 ÷ T)ⁿ · T needed = 1 ÷ [1 − (1 − R)^(1/n)]
Variables
| Symbol | Meaning | Unit |
|---|---|---|
tr | Return period (the event happens once every ... years on average) | yr |
n | Number of years you care about | yr |
rk | Risk you are willing to accept over those years | % |
P | Chance of at least one in those years | % |
PA | Chance in any single year | % |
PN | Chance of none in those years | % |
HF | Years until the chance of at least one reaches 50 % | yr |
RQ | Return period needed to keep the risk that low | yr |
EC | Expected number of events | — |
Worked example
- Return period (the event happens once every ... years on average)100 yr
- Number of years you care about30 yr
- Risk you are willing to accept over those years10 %
- Chance of at least one in those years26.03 %
- Chance in any single year1.000 %
- Chance of none in those years73.97 %
- Years until the chance of at least one reaches 50 %69.0 yr
- Return period needed to keep the risk that low285 yr
- Expected number of events0.30
Limitations
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.