Measuring Angle and Distance with your Thumb

(Now part of A View from the Back of the Envelope.)

The idea: By holding out your thumb to measure angles, you can tell your distance to things (people, cars, buildings, planes, clouds, etc).

This is a Body Ruler page.

Quick examples

I hold out my arm, look at my thumb, and see a distant car half as high. Cars are about 5 feet (1.5 meters) high. So my thumb appears 10 feet (3 meters) wide. And since I know (see below) my thumb is x30 times as far as it seems tall... I know the car is something like 300 feet (90 meters) away!


Hold your arm straight out in front of you. Make a fist. Point it at a window. The window will appear a couple of fists high. The further away the window, the fewer the fists. Windows in nearby buildings won't even be a fist tall, they will perhaps be a couple of thumb-widths high. Or less. Stick your thumb out sideways. Point your arm at a nearby building. Count how many thumbs high its windows are.

Ok, but how do you tell how far away it is? You need to know two things:
very roughly how big windows are (I don't know, say something like 5 feet),
and that your thumb covers things 30 times bigger.

So, a 5 foot window, which seems 2 thumbs high, makes your thumb look 3 feet wide (5 feet / 2 thumbs), and thus something like 90 feet (3 x 30) away.

Thumbs and Fists and ROUGH Distance

In general, people's thumbs and fists are about:
size distance is (angle)
fist x 6 10°
thumb x 30
½ thumbx 60
¼ thumbx 120½°
Or you can just remember that your thumb is x30, and each time you halve your thumb, its twice as big.



How "roughly, approximately, something like, about" is this?
You will often be within a factor of 2 or 3, and by using greater care, can get it under 20%.

Sources of error:

Calibrating Yourself

The idea is to see how big various things are (fingers, different parts of fingers, combinations of fingers, fist, and perhaps some things you generally have with you, like keys). Then you can find some specific part of your body (like the middle of your thumb nail, or the end of one of your fingers), which is just under 2 degrees. This can then be your angle measurer.

For instance, I personally use the outermost joint of my pointer finger. Not my thumb, which is slightly too big.

There are lots of ways to set up for calibration.

The easiest is to just put things against a rule that has already been calibrated, like this chart or these cards.

Another approach is to draw some degree lines on a wall, and then step back the right distance. The key is that one stand back ~57 times the degree-line separation. Here are some example(s):

Things up in the air

When you have measured the distance to something up in the air, like an airplane, it can be nice to separate its altitude from its ground distance.

Here is one simplification, admittedly not very simple.
We should work out one with just 3 or 4 numbers to remember, as this one's 5% error is excessively precise for most stuff.
anglealtitude factor
ground distance
0° (its on the ground)01
10° (1 fist up)1/61
20° (2 fists up)1/31
30° (3 fists up)1/25/6
40° (4 fists up)2/32/3
50° (5 fists up)2/32/3
60° (3 fists down)5/61/2
70° (2 fists down)11/3
80° (1 fist down)11/6
90° (up)10
which hovers around 5% error.

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Details, details

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Blinking your eyes instead

A reader writes
   When I was about 13 years old (1947) I remember reading somewhere
   (maybe a Boy Scout handbook) that you could estimate distance by
   holding your thumb out in front of you and sight an object with one
   eye closed, then without moving open that eye and sight the object
   with the other eye closed; then estimate how far your thumb
   appeared to move and multiply that number by eight.
Which seems about right. Instead of defining an angle using one eye and two thumb edges, it uses two eyes and one thumb edge. The angle is a bit wider. The distance between one's eyes is about 4 thumbs wide, so 8x sounds reasonable (30x/4).

I wonder if people vary less in their eye "widths", then in their thumb widths. If so, then this approach would have less need for personal calibration.


At Arm's Length a NOVA Teacher's Guide.
Up, Up, and How Far Away?

I welcome questions, comments, and thoughts. -
[Top] [Musings] [Body Ruler]
  This page hasn't drawn much comment over the years,
    and thus hasn't been pursued.

  Try describing from an similar triangles / LvH ratio perspecive.

  2003-Jul-16  Added a reader's note on blinking.  Thanks!
  2003-Feb-04  Fixed 1 link, flagged 4.  Moved WeatherNet ahead of broken services.
  2001-Aug-14  Ripped out `hold rule at arms length' approach to here.
  2001-Aug-09  Added `hold rule approach' (thanks to a reader's question
               about measuring distance for archery).
  1998.Dec.01  Added links to NOVA Balloon science pages.  (Thanks go to a reader.)
  1997.May.05  Added link to A View from the Back of the Envelope.
  1997.Mar.25  Draft fleshed out.
               I will work it further if people are interested.
  1997.Mar.24  Draft begun.
  1997.Mar.23  Idea.