Sun and Seasons | Sun Path Model | Sun Angles


Measuring Sun Angles

How high is the Sun above the horizon? Does it change from season to season?

To measure the angle of the sun above the horizon, you just measure the length of the shadow of an object. Here's how:

  1. Pick a vertical object that is easy for you to measure and that is relatively permanent, like a sign post or fence post.
  2. Measure it's height. Write it down.
  3. Right at noon on a bright sunny day, measure the length of it's shadow on the ground.
  4. Take the vertical measurement and divide it by the shadow measurement. ('b' divided by 'a'). The result is the TANGENT of the angle
  5. Use a scientific calculator or look up the TANGENT in the chart below to find the angle.
  6. You've just done basic Trigonometry!

measuring the angle of the sun in summer measuring the angle of the sun in winter

Above Diagram: 'b' divided by 'a' = Tangent

If you want to compare the sun's height for different seasons, here's how:

  1. Make a measurement on a sunny day near the Summer Solstice (the longest day of the year in the Northern Hemisphere) or the Winter Solstice (the shortest day of the year in the Northern Hemisphere).
  2. You can also make shadow measurements on the Equinoxes, the times in Spring and Fall when the length of the days and nights is equal. This is great if you're making a Sun Path model, and you want to do your own measurements instead of looking them up in a book.
  3. Write down your measurements and put them in a place that you won't forget.
  4. Then wait for the seasons to change until you can make another measurement. Enjoy life!
  5. When you have at least a Winter shadow measurement and a Summer shadow measurement, you're ready to do the math and discover how the height of the sun changes in the sky.


Angles and their Tangents
If the tangent is,  then the angle is:   If the tangent is,   then the angle is:   If the tangent is,   then the angle is:
.088    .700  35   2.14 65 
.176 10   .840  40   2.75  70 
.268 15   1.00 45    3.73 75 
.364  20    1.19 50   5.67  80 
.466 25    1.43  55    11.43 85
.577 30    1.73 60     

Measuring a tall object using the Sun
You can use sun angles to measure very tall things, like buildings, trees and cliffs using just a ruler! You don't even have to climb up anything, or use trigonometry.

Here's how: On a sunny day, first measure something that you can reach that is standing upright, such as a pole or stick. Then measure how long it's shadow is.

Then measure the shadow of the tall thing who's height you're trying to discover. To make it easier, you can use a longer measuring tool, such as a yardstick, meterstick or tape measure. You have to make your measurements without wasting too much time, because the sun is moving!

Now you have all the information you need!

measuring a tall building using sun angles


The height of the building or tree or cliff is PROPORTIONAL to the length of it's shadow, exactly as much as the shorter pole or stick is to it's shadow. Can you do the math?

a is to b = A is to B

Here's an example:
Say the post height of 'a' is 2 meters, and the shadow 'b' is 3 meters. That's 2 over 3, or 2/3. You measure the shadow 'B' as 18 meters. Then the height 'A' must be 12 meters, because two-thirds of 18 is 12.

2 is to 3 = 12 is to 18


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