How to Estimate Distance Using Just Your Thumb | Hacker News Reader

How to Estimate Distance Using Just Your Thumb

lifehacker.com

177 pointsm-watson45 comments

The orignal linked piece is a clearer read/explanation with fewer seo/ads: https://www.mathsisfun.com/measure/estimate-distance.html

Bonus: Metric.

The original page is so bogged down with ads I had to force close chrome on my phone to escape it.

Some other basic units of measure I learnt in the military that are generally useful. Your index finger held up arm outstretched covers 10 meters at 1km. Two fingers together (index + middle) is 20-30 meters, Your closed fist edge to edge is about 50m, and your open hand from tip of thumb to tip of little finger is about 150 meters.

The method in the link only gives you one measure, your thumb, where as having a few different scales means you can do a bit of math for closer or further away objects. And it's handy to be able to know the distance between two places if you know the distance to one object.

Index fingers vary wildly in the length though, so how do you account for that?

Even taking some idea of an "average" hand is going to assume a lot when you start considering the differences between the sexes.

It's not a perfect system, it's a estimate system. Generally it'll work generally well. Having a set of optics with a mils reticle really too, because then you can take the human element out of it.

Women's fingers tend to be appreciably thinner, yes, given that this is infantry lore it's safe to say that it's calibrated to men in fighting trim (which implies no extra fat on the fingers).

There's still some variation but (the only reason I'm commenting) larger hands tend to be on longer arms, so this normalizes well enough for a rule of thumb.

Last point is that with a rangefinder one can calibrate this to one's own body, which is, after all, what gets used as a metric.

I think he's referring to finger thickness, not length. Index and middle fingers together supports this view, as well as the closed fist.

Yes, I am. Sorry I didn't describe that well. It's usually something you demonstrate in person.

Oh also, being able to tell how things visually change over distance is useful too. I use these less and less, but generally looking at a person at 100 meters you can make out a face. At 200 you can't see a face but see a head, shoulders and arms. at 300 you start to not be able to make out arms so well, and at 400 a head blends into the shape of the body. There's like a stack of different things you can use to create you're own references as well. Cities are great because generally if you can look down a long street you can see lots of things and people and start picking the differences in what you can characterize over a set of blocks.

So for the other 95% of the world, had someone for the metric version?

Edit. Got it https://www.mathsisfun.com/measure/estimate-distance.html

This seems like a fun thing to practice while I'm out, thanks.

All the relevant numbers are in ratios between distances, meaning you don't need to change anything about the procedure if you're using the standard units of measurement.

True. It still thew me off having to estimate metric units from the imperial units and doing that estimation while reading an article about estimation.

The point is you didn't have to do that at all! It works for any unit of length. Bring your own units!

Miliradians aren’t metric. That’s hard for a lot of people to figure out.

1 banana at 1000 bananas away

I just tried it with a cup using cm and it works just fine. Whatever your estimate of length is is the same unit as your estimate for distance.

Similarly you can estimate the time before sunset using your body.

Hold out your arm and see how many fingers fit between the bottom of the sun and the horizon.

Each finger is about 15 minutes.

A bit longer if you're within a polar circle.

I doubt the method does give a good approximation even at about 60° north in July, although I did not verify by how much. I live near 49° north and recently travelled to Scandinavia. While my intuition at home is pretty accurate, my idea of how long it takes for the sun to set so far north in the evening was completely off the mark at first. To calibrate it, I changed my mental model of the sunset to a double-flat angle and estimated how long it might take the sun to (virtually) cover the longer resulting distance.

I was taught 1 fist == 1 hour. Then you'd stack fist over fist to determine how many hours left of sunlight. I just tried using fingers and that also seems pretty easy, and likely to result in a similar estimate.

As long as you have four fingers on each hand, a fist is about the same height as four fingers, so I think the math checks out.

...how do you do this without looking at the sun?

I would think that a single quick glance in the general direction of the sun won't do much harm

You don't, but it won't work until the answer is three fists or less, and glancing at the sun in the evening isn't going to hurt you for the time it takes to put your fist/fingers next to it.

cover the sun with your left hand and position it so the bottom of that hand is just covering the bottom of the sun. then start measuring with your other hand, from the sun to the horizon

Is there a measure of when the sun is behind the “horizon” (tall mountains) so it’s not directly visible but is still producing a lot of daylight? Maybe length of dusk or something

"The distance from your eyes to your thumb is *about 10 times* the distance between your eyes."

Which means you could calibrate this formula using your own body. Let's find the exact value for my eye/arm ratio!

EDIT For me it's about 12.5 ratio. I'm 187cm tall.

12.5 sounds to me more like measurement error than natural variation. Did you measure the eye distance between the centres of your pupils?

You don't think the original claim of an even ten sounds a lot like rounding?

If you have trouble measuring your pupils distance (which is hard), you can also just calibrate using a set of known object sizes and distances.

That is exactly what I did.

I placed a ruler of 40cm on a closet at eye level. I did the thumb trick and found the exact distance I had to stand so my thumb jumped from left to right of the 40cm ruler. Then I measure the distance I was standing from the ruler. distance / 40cm = your body ratio.

So there is no reason to measure length of arm or distance between eyes. We are only interested in their ratio here. You basically run the "thumb trick" in reverse. From the distance and object size => you get the ratio.

This is awesome. It's a cool way to teach your kids both math and science.

Math because of the triangle similarity proof of the "recipe", and science because of the method of calibration.

Thank you.

Did you keep your shoulders facing the object, or did you rotate one shoulder towards the object?

It's also basically the way how distances are measured in space. Parsec comes from paralax second, which is around 3.26 lightyears.

For relatively nearby objects. The parallax used is the apparent angular shift of an object as the earth orbits the sun. The angle gets very small the further an object is and observing it will depend on the resolution of your telescope. In practice we can only use this method for objects within our galaxy or in very nearby galaxies/star clusters.

These measurements are used to calibrate the cosmic distance ladder[0] which lets us get distance estimates for further objects using other methods. The calibration between different methods is still a very active area of research because of the discrepancy between measurements of the Hubble constant based on this ladder compared with the cosmic microwave background radiation.

[0] https://en.wikipedia.org/wiki/Cosmic_distance_ladder

This is essentially how drawing with comparative measurement works. Along with sight-size and grids, intentionally practicing this technique helps with learning to see the true proportions of shapes, and therefore to also make more accurate marks, whether drawing from life or imagination. It's one of the key training methods for visual art and a major missing link for many self-taught artists.

If you grind out studies of the Bargue plates - or really, any pictures with some detail and complexity, though Bargue's system is designed to gradually increase in difficulty - you will become very good at estimating distances and angles. It doesn't solve all drawing problems, but it makes them much easier.

Sounds like a great rule of thumb.

That was the most useful thing I have ever read on LifeHacker. Even more useful than their current top article, “8 Zoo Animals That Might Escape One Day (and How to Protect Yourself).”

https://en.wikipedia.org/wiki/Parallax

That works for the car in:

> https://www.mathsisfun.com/measure/estimate-distance.html

But how about the tree?

Also, let's say you are walking towards a city and you see its skyline. You don't know anything about the buildings (how tall or wide they are). How far away is the city?

It's a clever use of maths that makes it simple to take information you have and work out related information. It's not magic that can always give an answer even when you don't have enough information to start with.

Yes, it only works for objects that you can estimate the size of. The tree is pretty easy (trees don't have that much variation in width, especially given that you can determine the type of tree from other clues). A far away city is a bit more difficult but you can still get a rough estimate by guessing, say, how big some building is (or better yet how wide the road you're walking down towards the city is!).

I thought it would ivolve estimating an arc-tan by memory. Thankfully it’s just a geometric feature that the distance to the thumb is ~10 times the distance between the eyes.

If your thumb hurts, the distance between the nail and the hammer's head was off by a few mm.

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