---
title: "Define return period, frequency and risk"
subject: "Engineering Hydrology"
chapter: 6
key: "semester_5/engineering_hydrology:define-return-period-frequency-risk"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/define-return-period-frequency-risk
site: BCT Engineering
---

# Define return period, frequency and risk

Engineering Hydrology · Chapter 6: Flood Hydrology

- Asked in: 2082 Bhadra, 1+1+2 marks
- Video: [Return Period | Engineering Hydrology](https://www.youtube.com/watch?v=kbALGtJYSxk) — APSEd
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/define-return-period-frequency-risk
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-6

## Question

Define the terms return period, frequency and risk.

## Short answer

Return period T is the average interval between events, frequency is the annual exceedance probability P=1/T, and risk is the probability of at least one occurrence in n years: R=1-(1-1/T)^n.

## Answer

#### Return period
The **return period (recurrence interval)** $T$ is the average number of years within which an event of a given magnitude is equalled or exceeded once. It is the reciprocal of the exceedance probability, $T=1/P$. A 100-year flood has a 1% chance of being equalled or exceeded in any year; it does not mean it occurs exactly once in 100 years.

#### Frequency
The **frequency** of an event is the number of times it occurs (or the probability that it occurs) in a given period. In flood analysis it is expressed as the annual exceedance probability $P=1/T$ (e.g. P = 0.02 for a 50-year flood), or as the number of occurrences per unit time.

#### Risk
The **hydrologic risk** $\bar R$ is the probability that an event of return period $T$ will occur at least once during the n-year life of a structure:

$$
\bar R=1-\left(1-\frac1T\right)^{n}
$$

For example, a 100-year flood has a risk of $1-(0.99)^{50}=0.395$ (39.5%) in a 50-year project life. The **reliability** is $1-\bar R$.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. What does a 100-year flood mean?
   A. It cannot occur twice in 10 years
   B. It occurs exactly once every 100 years
   C. It happens only after 100 years
   D. 1% chance of being equalled or exceeded in any year
   Answer: D. T = 1/P is an average interval; occurrences are random. (Key point: Return period)

2. How is frequency expressed in flood analysis?
   A. Annual exceedance probability P = 1/T
   B. Peak discharge
   C. Sum of floods
   D. P = T
   Answer: A. For example P = 0.02 for a 50-year flood. (Key point: Frequency)

3. What is hydrologic risk?
   A. Probability of at least one event of return period T during n years: 1 - (1 - 1/T)^n
   B. n/T
   C. (1 - 1/T)^n
   D. 1/T
   Answer: A. Risk is the chance of at least one occurrence in the structure's life; (1 - 1/T)^n is the chance of none. (Key point: Risk)

4. Risk of a 100-year flood in a 50-year life?
   A. 39.5%
   B. 1%
   C. 50%
   D. 63%
   Answer: A. 1 - 0.99^50 = 0.395. It is not simply 50/100. (Key point: Risk value)

## Related in Engineering Hydrology

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- [Return period of 350 m3/s design flood by Gumbel](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-return-period-350-25yr) — Engineering Hydrology, chapter 6, asked 2×
- [Gumbel flood for 500-year return period](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-100-50-500) — Engineering Hydrology, chapter 6
- [24-hr maximum rainfall for 50-year return period](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Agumbel-24hr-max-50yr-semilog) — Engineering Hydrology, chapter 6
- [Continuous vs discrete variables, return period formulae](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Acontinuous-discrete-variables-return-period) — Engineering Hydrology, chapter 6

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