# Methods of approximation?

August 12, 2014 9:34 AM Subscribe

I've never been very good at either math or at eyeballing things like weight or dimension, but was thinking recently about how to more or less accurately weigh things without using a scale. What good methods are out there to approximate other kinds of measurements?

For weight, I figured the easiest way is to start with a known weight that can be easily divided (say a bag of sand), and that's heavier than what you're weighing. Compare it with what you want to measure. If it feels too heavy, divide it in half, set one half aside, and compare that. If it's too light, split the other half, set part aside, add that to your reference weight, and so on.

I realize this is super basic stuff that was figured out a long time ago and is in some sense just using your hands as a scale, but it seems interesting how precise you could be as long as you were it accurately and knew how heavy the reference was to start. Also, the fractions you end up with at the end are easy to add up since they all have powers of two at the bottom. Is there a name for this kind of thing (continually splitting in half and adding back the fractional parts to get closer to what you want)? And is there a more generalized technique here that applies easily to estimating other kinds of things?

For weight, I figured the easiest way is to start with a known weight that can be easily divided (say a bag of sand), and that's heavier than what you're weighing. Compare it with what you want to measure. If it feels too heavy, divide it in half, set one half aside, and compare that. If it's too light, split the other half, set part aside, add that to your reference weight, and so on.

I realize this is super basic stuff that was figured out a long time ago and is in some sense just using your hands as a scale, but it seems interesting how precise you could be as long as you were it accurately and knew how heavy the reference was to start. Also, the fractions you end up with at the end are easy to add up since they all have powers of two at the bottom. Is there a name for this kind of thing (continually splitting in half and adding back the fractional parts to get closer to what you want)? And is there a more generalized technique here that applies easily to estimating other kinds of things?

I've gotten pretty good at eyeballing volumes and weights just by repeatedly experiencing real-world things.

I know how much volume a teaspoon or tablespoon of something takes up in my hand.

A gallon of milk weighs about 8 and a half pounds.

A pint glass is 16 ounces and holds two 8 ounce cups (unless you are someplace silly like the UK). You can pour 8 of those from a gallon of milk.

A jug for a water cooler weighs a shade under 70 pounds.

I know how tall I am.

After spending a bunch of time looking at this I've become reasonably good at estimating height/weight of guys. (Women have wildly variant fat distribution types and are much more difficult for me to guess.)

And so on. So it's less take a known volume and divide it in half and physically try it out and more approximate from this mental rolodex of known things.

It's one of those things you really just have to get a feel for over time. If you want to intentionally cultivate the skill, when you're cooking or when you're picking something up, find out its actual weight and volume and just feel it out. See what it looks like in your hand, think about how long it takes to pour, move it around and see what kind of heft and inertia it has, that kind of thing. You'll start to have a learned experience of measurement before you know it.

posted by phunniemee at 9:56 AM on August 12, 2014

I know how much volume a teaspoon or tablespoon of something takes up in my hand.

A gallon of milk weighs about 8 and a half pounds.

A pint glass is 16 ounces and holds two 8 ounce cups (unless you are someplace silly like the UK). You can pour 8 of those from a gallon of milk.

A jug for a water cooler weighs a shade under 70 pounds.

I know how tall I am.

After spending a bunch of time looking at this I've become reasonably good at estimating height/weight of guys. (Women have wildly variant fat distribution types and are much more difficult for me to guess.)

And so on. So it's less take a known volume and divide it in half and physically try it out and more approximate from this mental rolodex of known things.

It's one of those things you really just have to get a feel for over time. If you want to intentionally cultivate the skill, when you're cooking or when you're picking something up, find out its actual weight and volume and just feel it out. See what it looks like in your hand, think about how long it takes to pour, move it around and see what kind of heft and inertia it has, that kind of thing. You'll start to have a learned experience of measurement before you know it.

posted by phunniemee at 9:56 AM on August 12, 2014

The halving thing will work fine so long as you have a balance that is fairly precise or can make one. Your hands are iffy in terms of this. I'm not sure if you are looking for other ways of estimating. US pennies (current ones, I don't know about the older ones)and nickels both have very precise weights of 2.5 and 5.0 grams for example.

A lot of this, unsurprisingly, will depend on what you want to measure. Many specialized organizations have ways of doing this within their profession to get back of envelope sorts of numbers

horses: weight (kg)=(heartgirth

round faceted stones: weight = average diameter * average diameter * total depth * specific gravity * .0018

standing hardwood trees: diameter x height x species adjustment (refer to chart)

posted by jessamyn at 9:58 AM on August 12, 2014

A lot of this, unsurprisingly, will depend on what you want to measure. Many specialized organizations have ways of doing this within their profession to get back of envelope sorts of numbers

horses: weight (kg)=(heartgirth

^{2}x body length) / (11,880 cm^{3})round faceted stones: weight = average diameter * average diameter * total depth * specific gravity * .0018

standing hardwood trees: diameter x height x species adjustment (refer to chart)

posted by jessamyn at 9:58 AM on August 12, 2014

Carpentry fun!

Figure out where on your thumb an inch is, it will likely b at about the first knuckle. Your elbow to your middle finger should be about 1'-6" or a cubit, give or take a few knuckles. Know your own height/wingspan and measure things based on whether or not they are taller or shorter than you.

posted by edbles at 10:09 AM on August 12, 2014

Figure out where on your thumb an inch is, it will likely b at about the first knuckle. Your elbow to your middle finger should be about 1'-6" or a cubit, give or take a few knuckles. Know your own height/wingspan and measure things based on whether or not they are taller or shorter than you.

posted by edbles at 10:09 AM on August 12, 2014

Oh, another one you can bust out to impress your friends: a pound of (USD) change comes out to about $11.20.

posted by phunniemee at 10:23 AM on August 12, 2014 [1 favorite]

posted by phunniemee at 10:23 AM on August 12, 2014 [1 favorite]

You can make rough measurements of ground distance if you know your pace.

posted by mbrubeck at 10:56 AM on August 12, 2014

posted by mbrubeck at 10:56 AM on August 12, 2014

You have all sorts of measuring devices at hand (sorry)! My favorite trick is the dollar bill trick, where you use the known length of a dollar bill, 6.25 inches, and fold it appropriately to measure other things. Then there are your body parts, your finger lengths and widths, your hand, your elbow, your foot, plus everyday objects we all have around.

posted by Lynsey at 11:10 AM on August 12, 2014

posted by Lynsey at 11:10 AM on August 12, 2014

*A jug for a water cooler weighs a shade under 70 pounds.*

In terms of approximation, a gallon of water weighs 8 pounds. (Something like 8.34 exactly.)

A jug for a water cooler is five gallons, and so weighs ~40 pounds.

posted by OmieWise at 12:07 PM on August 12, 2014

The only way I've improved at estimation is by measuring things frequently. I used to be a really crappy estimator of time/duration. I could never accurately estimate how long it would take to go to the market, drive to the bank, park the car...and therefore, my earliness/tardiness was super variable.

I started keeping a notebook in my car and writing down estimated time and actual time. (Estimate: it takes 5 minutes to drive to the office. Actual: 20 minutes door to door including parking.) Measuring increases the number of known data points. I know it takes 10 minutes to get from my house to the highway because I measured it a bunch of times. That makes every drive duration estimate a bit more accurate.

Same with volume. I can accurate estimate portion size because I've measured it a lot. I can accurately estimate calories because I know the general calories of a portion of fruit/meat/shiny veggie/unshiny veggie. By increasing the knowns, I'm better at estimating the unknown.

posted by 26.2 at 12:47 PM on August 12, 2014

I started keeping a notebook in my car and writing down estimated time and actual time. (Estimate: it takes 5 minutes to drive to the office. Actual: 20 minutes door to door including parking.) Measuring increases the number of known data points. I know it takes 10 minutes to get from my house to the highway because I measured it a bunch of times. That makes every drive duration estimate a bit more accurate.

Same with volume. I can accurate estimate portion size because I've measured it a lot. I can accurately estimate calories because I know the general calories of a portion of fruit/meat/shiny veggie/unshiny veggie. By increasing the knowns, I'm better at estimating the unknown.

posted by 26.2 at 12:47 PM on August 12, 2014

A healthy, adoptable kitten weighs about 2 pounds. This fact has been surprisingly useful for buying anything by weight.

posted by blnkfrnk at 2:00 PM on August 12, 2014 [1 favorite]

posted by blnkfrnk at 2:00 PM on August 12, 2014 [1 favorite]

Consider getting comfortable with the metric system. It's perfect for approximating and scaling.

posted by Iteki at 11:53 PM on August 12, 2014

posted by Iteki at 11:53 PM on August 12, 2014

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half, but if you haven't already you might like to read about Fermi Estimation. Wiki, XKCD.posted by ftm at 9:42 AM on August 12, 2014