---
title: "Average precipitation by isohyetal method"
subject: "Engineering Hydrology"
chapter: 2
key: "semester_5/engineering_hydrology:isohyetal-average-depth"
source: https://www.bctengineer.com/q/semester_5/engineering_hydrology/isohyetal-average-depth
site: BCT Engineering
---

# Average precipitation by isohyetal method

Engineering Hydrology · Chapter 2: Precipitation

- Asked in: 2068 Chaitra, 4 marks; 2067 Shrawan (old course), 4 marks (asked 2 times)
- Video: [Isohyetal Method to Calculate Mean Precipitation | Engineering Hydrology](https://www.youtube.com/watch?v=EIltfmAtvsE) — APSEd
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/engineering_hydrology/isohyetal-average-depth
- Whole chapter: https://www.bctengineer.com/md/semester_5/engineering_hydrology/chapter-2

## Question

Estimate the average depth of precipitation over the drainage basin with the following data.

| Isohyetals (intervals, cm) | 15-12 | 12-9 | 9-6 | 6-3 | 3-1 |
|---|---|---|---|---|---|
| Inter-isohyetal area (km$^2$) | 92 | 128 | 120 | 175 | 85 |

## Short answer

Using the isohyetal method, each interval's mean depth is averaged and weighted by area. Summing area–weighted depths (4443.5 cm·km²) and dividing by total area (600 km²) yields an average precipitation depth of 7.41 cm.

## Answer

In the isohyetal method the mean depth between two isohyets is taken as the average of their values, and the weighted average is found with the inter-isohyetal areas.

$$
\bar P = \frac{\sum A_i \bar P_i}{\sum A_i}
$$

For the last band (3-1 cm) the mean is $(3+1)/2 = 2$ cm.

| Isohyetal range (cm) | Mean depth $P_i$ (cm) | Area $A_i$ (km²) | $A_iP_i$ |
|---|---|---|---|
| 15-12 | 13.5 | 92 | 1242 |
| 12-9 | 10.5 | 128 | 1344 |
| 9-6 | 7.5 | 120 | 900 |
| 6-3 | 4.5 | 175 | 787.5 |
| 3-1 | 2.0 | 85 | 170 |
| **Total** |  | **600** | **4443.5** |

$$
\bar P = \frac{4443.5}{600} = 7.41\ \text{cm}
$$

**Answer: Average depth of precipitation = 7.41 cm (about 74 mm).**

## Check yourself

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

1. Mean depth between isohyets 15 and 12 cm:
   A. 13.5 cm
   B. 15 cm
   C. 12 cm
   D. 3 cm
   Answer: A. Average of the two. (Key point: Mean depth)

2. Mean for the 3-1 cm band:
   A. 3 cm
   B. 2 cm
   C. 1 cm
   D. 4 cm
   Answer: B. (3+1)/2. (Key point: Last band)

3. Average depth is:
   A. 600 / 4443.5
   B. ΣP / 5
   C. ΣAP / ΣA = 4443.5 / 600 = 7.41 cm
   D. 4443.5 cm
   Answer: C. Area-weighted. (Key point: Average)

4. Total area:
   A. 500 km^2
   B. 640 km^2
   C. 1000 km^2
   D. 600 km^2
   Answer: D. 92+128+120+175+85. (Key point: Total area)

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