Measure for Measure

I still remember my delight in realising – from a throwaway comment by my physics-teacher father – that a Newton, the unit of force, was roughly equivalent to the weight of an apple. I had known its scientific meaning for some time, but all of a sudden I could visualise it in a way I never had before, and an apple… well it just seemed so appropriate!

I’ve been thinking about scientific units and measurements, and illustrations that can help one understand them in terms of daily life. Here are a couple of others that I find pleasing:

* Thanks to plate tectonics, America and Europe are moving apart at about the speed that fingernails grow. (Thanks to Bill Bryson)

* The distance from London to Cambridge is about one degree. (I worked that out before realising it was a nice academic double-entendre!)

* A nanosecond is the time it takes light to travel one foot.

* A microwave oven is about one horsepower. (Not sure if that’s useful, but it’s interesting)

Anyone got any others? Please add them in the comments if so!

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Did you know the area bounded by Offa’s Dyke, the Seven Estuary, and the Irish Sea is about 1 Wales, a common unit of area in British news.

I have to point out that 1N is the approximate weight of an apple on the surface of planet Earth, not the weight of an apple per se.

On the same topic, 1 degree of latitude is (fairly) constant but the length of a degree of longitude varies with latitude. How else would it be possible to travel north 10km, east 10km and then south 10km back to your start point?!

I promise to try to contribute to your list in a subsequent comment rather than criticising it!

I have a taste for sillier units – the furlong/firkin/fortnight system yields the microfortnight, about 1.2 seconds, and 1 furlong per fortnight is about 1cm/min. And, of course, the standard length of a lecture is a microcentury – about 52.5 minutes.

I also like the way one can roughly guesstimate moderate-length road travel times by simply using the distance in miles as the estimate for time in minutes. 60mph isn’t a bad guess for overall average speed on journeys I tend to make on main roads, allowing for moderate congestion. It’s systematically biased to over-estimate the time, which better than being biased the other way.

But for practical use, I love the whole metric system’s simplicity, and the way 1 kg is about 1 litre of water, and 1 g about 1 ml. So you can make simple guesstimates about mass given volume (and vice versa) for things that are largely or mostly water. Including people (although we do float).

For a sense of weight, I use a scale something like this. Warning! Very approximate measures:

1000 kg: very small car e.g. Mini, Fiat Punto
100 kg: me wearing full outside gear and carrying a full suitcase
10 kg: my work bag when overpacked
1 kg: bag of sugar
100 g: piece of fruit (will fix this on apple now I know the 1N thing, ta)
10 g: pencil or pound coin
1-2 g: piece of dried pasta
1 g : many people suggest a paperclip but I haven’t verified it so don’t trust it, and prefer my vaguer pasta measure because I regularly handle pasta but might handle maybe six paperclips in a year
500 mg: paracetamol tablet
25 mg: grain of rice
1 mg: two long, thick human hairs (technically I suppose I should list it as one hair is 0.5mg, or 500 micrograms, but I don’t remember it that way, and this is probably as wildly variable a measure as any)

Richard –

You are, of course, correct, though notice that I did say ‘in terms of daily life’ which, for me, excludes both polar and interplanetary travel 🙂

I should probably have said ‘degree of a great circle’, though… but that’s a bit more than the distance from London to Cambridge.

Actually, after a rough calculation, I think the distance from London to Cambridge is pretty close to the average of one degree of latitude and one degree of longitude at that location!

Doug –

A good list – thanks. I particularly like the microcentury.


@Doug Clow (and prepared to be corrected) I thought 1 litre of water weighs exactly 1kg.

I also like period of 1m pendulum = 2 seconds (ie 1 second for the swing in one direction and 1 sec for the swing back to the starting point, a frequency of 1/2Hz). In fact, as some scoffer will probably point out, you need a pendulum 994m in length, in standard gravity, probably only when there’s an ‘r’ in month, &c, &c… but I still it.

And silly units in common use: the double-decker bus as a measure of… not sure actually – difficulty of motorcycle leap?
Football pitches as a measure of area, even though the official dimensions of a football pitch are variable…

Good point: you did say “daily life”.

Well, here’s my contribution.

Acceleration due to gravity (at the surface of the earth and all that) is roughly 9.8 metres per second per second. That’s about the same as a Bugati Veyron, the world’s “fastest car”, which does 0-60mph in 2.7sec. If my sums are right.

I’m rather fond of the somewhat misleading measures of double decker busses or “times around the world if placed end to end”. Particularly when such a measure is used instead of an actual, meaningful quantity. Did you know that if you placed 4,761,905 double decker busses end to end they would circle the earth.

Of course, on the more frivolous side, I’ve always liked the millihelen, which is the SI unit of feminine beauty required to launch one ship…


For almost all practical purposes, yes, a litre of water weighs one kilogram. But not quite exactly.

Until the mid-60s, 1 litre was defined to be the volume of 1 kg of water at 4 C/760mmHg, so it was exactly the same – but only at 4 degrees C (close to the maximum density for water). These days 1 litre is defined to be 1dm^-3, or 1/1000 of a cubic metre. So 1 litre of water at 4 C weighs something like 0.99997 kg. Which is close enough for most practical work. But water expands as it warms up, so if you measure it out at room temperature – say 20 C – it’s only 0.998 kg, and at body temperature (say 40 C) it’s more like 0.992 kg.

That’s close enough to be equivalent – and way more than good enough for ‘rules of thumb’ like the ones we’re talking about here! But not exactly the same, which is why I hedged.

You’re right to have pulled me up though – using “about” suggests a much looser equivalence than is the case. “Almost exactly” would have been much better.

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