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How to Use the ATAN Function in Excel

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Perhaps you are a photography enthusiast! Knowing the angle of view between two objects, one of which is straight ahead or perpendicular to you, and the other at right angles, i.e. along the horizon line of the first object, might be pretty nice or essential to know in answering a field of view query. You will learn to use the ATAN function in Excel to calculate the degrees of an angle whose tangent is known to you, or obtain the radians thereof. That is, if you know the x horizontal and the y vertical, or the x straight ahead and the y left or right in terms of distance, then you know the tangent, y/x. When we say "the angle whose tangent is alpha, a", that means we have performed the division of y/x is all, and fed it into the ATAN() formula properly. For every trigonometry function, there is an inverse function that works in reverse. These inverse functions have the same name but with 'arc' in front. (On some calculators the arctan button may be labelled atan, or sometimes tan-1.) So the inverse of tan is arctan etc. When we see "arctan a", we understand it as "the angle whose tangent is a". This function could well be on your scientific or math calculator as well as in Excel. In art composition theory, we learn that a vertical line along the horizon is much more dramatic than a horizontal line of exactly the same length and width; we identify with its struggle to overcome gravity. And is a diagonal line being supported, or dropping parts of itself, or clashing with cross-diagonals in a struggle? Every picture or painting tells a compositional story, and ATAN() can help you figure out the basics along the horizon line first. The Golder Ratio is also useful compositionally.


  1. 1
    Recall that the tangent = y/x or sin a / cos a, where sin a = y/r and cos a = x/r for radius r, which is eliminated between the numerator and denominator, and also equals the hypotenuse.
  2. 2
    Open a new Excel workbook.
  3. 3
    Enter to cell A1 the label x;
  4. 4
    Enter to cell B1 the label y;
  5. 5
    Enter to cell C1 the label y/x = tan a where a is the angle alpha;
  6. 6
    Enter to cell D1 the label Arctan a;
  7. 7
    Enter to cell E1 the label DEGREES;
  8. 8
    Enter to cell F1 the label Radians;
  9. 9
    Enter to cell A2, 15 and Format Cells Fill canary yellow (for Input);
  10. 10
    Enter to cell B2, 15 and Format Cells Fill canary yellow (for Input);
  11. 11
    Enter to cell C2 the formula, =B2/A2
  12. 12
    Enter to cell D2 the formula, =ATAN(C2)*180/PI()
  13. 13
    Enter to cell E2 the formula, =DEGREES(ATAN(C2))
  14. 14
    Enter to cell F2 the formula, =ATAN(C2)
  15. 15
    Edit Copy cell range A2:F2 and Edit Paste it to cell range A3:A11;
  16. 16
    Change the values in cell range A3:B11 and see what results but be aware that ATAN() calculates from +90º to -90º and, in terms of Radians, from π/2 to -π/2. It is based, to my knowledge, always upon a right angled triangle as well.
  17. 17
    Be aware that both column D and column E results are in degrees, and you may format them so by using the Option (or Alt) + Zero keys on a Mac and doing Format Cells Number Custom #.00"º".
  18. 18
    You're finished and have arrived at a very useful function, ATAN(), when you want to know the angle and you already know y and x and can assemble from them the tangent, y/x, for input into the ATAN() function. Herewith is a picture of the file and a chart.
  19. 19
    And here is an example of a Perspective Image which may have benefited from mathematical applications such as ATAN().

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Categories: Microsoft Excel | Mathematics


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