<p>When we say there was 1 mm (or 0.001 m) of rain, it is assumed that it is on a 1 square meter area, so it is equivalent to a volume of water of 0.001 <span class="math-container">$\small\mathsf{m^3}$</span> (or one liter). So first you have to divide your data by 1000.</p>

<p>Then you have time, which is easy: there are 3600 seconds in one hour. So to convert L/h in m<span class="math-container">$\small\mathsf{^3}$</span>/s, you have to divide your data by 3,600,000:
<strong>1 L/h = 2.7778 x 10<span class="math-container">$\small\mathsf{^{-7}}$</span> m<span class="math-container">$\small\mathsf{^3}$</span>/s.</strong></p>

<p>You can ask this sort of things in <a href="https://www.wolframalpha.com/input/?i=1%20l%2Fh%20in%20m3%2Fs" rel="nofollow noreferrer">WolframAlpha</a>; the trick here is to "convert" mm/h, assumed by the engine to be a speed, in L/h, the volume flow rate hidden by the mm/h unit.</p>

CC BY-SA 4.0
2019-10-31T09:30:45.760Z
2020-01-05T19:04:50.153Z
2020-01-05T19:04:50.153Z
Jean-Marie Prival
<p>There is no such simple relationship between rainfall and runoff (I wish there was!).
How much of the rainfall ends up as runoff depends upon at least the following variables:</p>

<p>temperature,
humidity,
wind-run,
hours per day of bright sunshine, 
latitude,
altitude,
type and density of vegetation cover,
soil type, thickness and consistency,
antecedent conditions,
soil moisture content,
land slope and orientation with respect to the sun,
underlying geology (lithology, structure, connectivity with surface soils, degree of weathering),
degree of urbanization,
heat island effect,
human intervention,
seasonality.</p>

<p>That is why all catchment models used to estimate the overall rainfall-runoff have to be carefully calibrated using rainfall AND runoff time-series of data. You can't do it by remote sensing. For all the fancy gimmicks and new equipment there is no substitute for boots on the ground.</p>

<p>Golden Rule Nr 1: you can't manage what you don't understand</p>

<p>GRNr2: You can't understand it unless you measure it.</p>

<p>GRNr3: You can't measure it by sitting in an office. </p>

CC BY-SA 4.0
2019-11-03T07:05:22.910Z
2019-11-03T07:05:22.910Z
Gordon Stanger
<p>I have precipitation data in mm/h but to use them for my model I need them in m³/s. Is there a formula to convert them? </p>

<meteorology><hydrology><mathematics>
formula to convert precipitation in mm/h to runoff in m³/s
DGIS
# formula to convert precipitation in mm/h to runoff in m³/s

(Asked by: username_0 on 2019-10-31)

I have precipitation data in mm/h but to use them for my model I need them in m³/s. Is there a formula to convert them?

**Tags:** meteorology, hydrology, mathematics


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## 2 answers

### Answer by username_1 on 2019-10-31. Score: 1 | Accepted answer

When we say there was 1 mm (or 0.001 m) of rain, it is assumed that it is on a 1 square meter area, so it is equivalent to a volume of water of 0.001 $\small\mathsf{m^3}$ (or one liter). So first you have to divide your data by 1000.

Then you have time, which is easy: there are 3600 seconds in one hour. So to convert L/h in m$\small\mathsf{^3}$/s, you have to divide your data by 3,600,000:
**1 L/h = 2.7778 x 10$\small\mathsf{^{-7}}$ m$\small\mathsf{^3}$/s.**

You can ask this sort of things in [WolframAlpha](https://www.wolframalpha.com/input/?i=1%20l%2Fh%20in%20m3%2Fs); the trick here is to "convert" mm/h, assumed by the engine to be a speed, in L/h, the volume flow rate hidden by the mm/h unit.


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### Answer by username_2 on 2019-11-03. Score: 1

There is no such simple relationship between rainfall and runoff (I wish there was!).
How much of the rainfall ends up as runoff depends upon at least the following variables:

temperature,
humidity,
wind-run,
hours per day of bright sunshine,
latitude,
altitude,
type and density of vegetation cover,
soil type, thickness and consistency,
antecedent conditions,
soil moisture content,
land slope and orientation with respect to the sun,
underlying geology (lithology, structure, connectivity with surface soils, degree of weathering),
degree of urbanization,
heat island effect,
human intervention,
seasonality.

That is why all catchment models used to estimate the overall rainfall-runoff have to be carefully calibrated using rainfall AND runoff time-series of data. You can't do it by remote sensing. For all the fancy gimmicks and new equipment there is no substitute for boots on the ground.

Golden Rule Nr 1: you can't manage what you don't understand

GRNr2: You can't understand it unless you measure it.

GRNr3: You can't measure it by sitting in an office.


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