300 million gallons and other dam(n) measurement units

In a recent BBC news article about the Toddbrook Reservoir in Derbyshire, it was reported that, following storm damage, the dam was in danger of collapse with the potential of releasing 300 million gallons of water onto the nearby town of Whaley Bridge.


In 2019, readers could be forgiven for having no idea what 300 million gallons of water looks like.

To visualise large volumes it is often useful to calculate the length of a side of a cube with an equivalent volume.

Using imperial units, this is something that has always been difficult to do, due to the fact that liquid volumes are traditionally measured in units that don’t relate easily to length units. For example, in this instance we would want to know how many cubic feet, or cubic yards, there are in 300 million gallons. Without knowing the conversion factor for gallons to cubic feet, this would require the use of a search engine and calculator. We would also need to make an assumption as to which gallon is being used. Is it the imperial gallon which hasn’t been used for trade for at least 30 years, or is it the US gallon, which is sometimes reported in parentheses for American readers.

If we are given the value in metric units (litres or cubic metres), the exercise is straight forward, and requires practically no arithmetic. Converting litres (cubic decimetres) to cubic metres is simply a matter of dividing by 1000. A cubic metre is quite easy to visualise and is the standard unit used on all water utility bills.

The volume of water is approximately 1.3 million cubic metres. For visualisation purposes, we can approximate this to a cube of 1 million cubic metres. Such a cube has a side of length 100 metres, or one hectometre. Therefore, with little effort, it is possible to visualise the enormous volume of water reported as being slightly more than one cubic hectometre, or a cube with a side as long as a 100 metre running track.

The report continues, and mixes units when it quotes the metric units being used by the emergency services: The fire services are quoted as “pumping out 7,000 litres of water a minute”, in a bid to bring down the water level, and the police were quoted as having plans for scenarios including the dam collapsing “which holds back 1.3 million tonnes of water”.

At the time of writing, the emergency services are still in a race against time to prevent further deterioration of the dam from more heavy rain. We wish everyone involved well.

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6 Responses to 300 million gallons and other dam(n) measurement units

  1. Martin Vlietstra says:

    One tonne of water has volume of a cubic metre, so knowing that the the dam holds 1.3 million tonnes of water also tells us that itโ€™s capacity is 1.3 million cubic metres.

  2. BrianAC says:

    Probably just as disappointing is that today, Monday 5th, they are still converting rainfall in inches, and decimal inches at that!

  3. Daniel Jackson says:

    In the US, many towns were built along a 6 mile x 6 mile grid called a township, which easily approximates to 10 km x 10 km (100 km^2) or 10 000 m x 10 000 m (100 000 000 m^2). 1 300 000 m^3 (0.0013 km^3) of water divided into 100 000 000 m^2 would 13/1000 or 13 mm of water depth. The city I live in is about 10 km x 10 km in area. This is how I would imagine this water volume to be. It would cover my town in 13 mm of water, assuming of course, the entire town were perfectly flat, which it isn't.

    It isn't very deep once it settles, but the major damage would come from the inrush as 0.013 km^3 of water comes gushing out all at once.

  4. Cliff says:

    The BBCs use of outmoded metrology seems to contradict the first two edicts of its royal charter to 'inform, educate and entertain'. Very few people accurately understand measures in decimal inches or decimal miles but the BBC keeps on trotting them out. How many tape measures are graduated in tenths and how many people know how many metres, feet or yards there are in three tenths of a mile without using a calculator? It's not informative OR educational to offer the public something obscure when a simpler and more precise form exists.
    I doubt that more than 5% of the population know what an acre is, other than a way estate agents and the media describe land, but hectares, which have been taught at schools for fifty years, and are the legal units of measure, are still passed over by the BBC in preference to the more obscure unit.
    If I remember correctly, gallons were replaced at the petrol pump in the UK in the late eighties and I can't think of anything else other than fuel that people would still buy or sell in gallons in the twenty first century. It's a little like the BBC using shillings and pence to describe financial transactions. At least they don't do that.
    Sadly, and as perverse as it seems, I think the main reason the BBC dumbs down with customary measurements is to try to compete with the popular media which seems to think that anything not emanating from the USA is elitist and 'uncool'.
    The BBC should not drop its principles to appease that sort of wooly-minded thinking but it will continue to do so until it's challenged. Unfortunately I can't see any politicians or influential members of the public doing anything as enlightened as that right now.

  5. BrianAC says:

    As we can probably guess, all these conversions are done automatically with some form of auto-inkorrecting software. It would seem that high volumes of water are converted to gallons. This was so on BBC (300 mgall) and ITV (286 mgall) TV news, I think all the others did similar.
    This is probably the same auto-inkorrecting software that changes degrees Celsius to F's without knowing the context, not to mention the 'First Letter Capitalisation' responsible for changing kg to Kg, and removing the second capital in other units which is even more annoying.
    I think we have our eyes on the wrong targets with this issue.

    Maybe rather dubiously I can claim to be one of the 5% of people in the whole world that 'understands' acres, miles, yerds, chains, furlongs, cwt, stones and even Lsd, now is that not a wonderful feeling (not)?

  6. Ezra Steinberg says:

    Just saw a BBC news report on the impeachment of Trump and the connections to Ukraine. Sadly, all the distances were given in "miles" (not even "kilometers" added).

    Sad commentary both on the BBC and on the failure of the government to convert road signs back in the sixties when it had the chance. ๐Ÿ™


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