Tan 18°


Welcome to tan 18°, our post about the tangent of 18 degrees. For the tangent of 18 degrees we use the abbreviation tan for the trigonometric function together with the degree symbol °, and write it as tan 18°. If you have been looking for what is tan 18°, or if you have been wondering about tan 18 degrees in radians, then you are right here, too. In this post you can find the tan 18° value, along with identities. Read on to learn all about the tan of 18°.

Tan 18 Degrees

If you want to know what is tan 18 degrees in terms of trigonometry, then navigate straight to the explanations in the next paragraph; what’s ahead in this section is the value of tan 18°:


tan18° = 0.32492
tan 18° = 0.32492
tan 18 degrees = 0.32492

The tan of 18 degrees is 0.32492, the same as tan of 18 degrees in radians. To obtain 18 degrees in radian multiply 18° by $\pi$ / 180° = 1/10 $\pi$. Tan 18degrees = tan (1/10 × $\pi)$.

Our results of tan18° have been rounded to five decimal places. If you want tangent 18° with higher accuracy, then use the calculator below; our tool displays ten decimal places.

To calculate tan 18 degrees insert the angle 18 in the field labelled °, but if you want to calculate tan 18 in radians, then you have to press the swap unit button first.

Calculate tan [degrees]

        ° :
value :


Besides tan18°, similar trigonometric calculations on our site include, but are not limited, to:

The identities of tangent 18° are as follows:

tan18°
= cot (90°-18°) = cot 72°

-tan18°
= tan (-18°) = -tan 18°
= cot (90°+18°) = cot 108°
= tan (180°-18°) = tan 162°

Note that tan18° is periodic: tan (18° + n × 180°) = tan 18 degrees, n$\hspace{5px} \varepsilon \hspace{5px} \mathbb{Z}$.

There are more formulas for the double angle (2 × 18°), half angle ((18/2)°) as well as the sum, difference and products of two angles such as 18° and β.

You can locate all of them in the respective article found in the header menu. To find everything about tan -18° click the link. And here is all about cot 18°, including, for instance, a converter.

In terms of the other five trigonometric functions, tan of 18° =

  • $\pm\frac{\sin 18^\circ}{\sqrt{1 – \sin^{2} 18^\circ}}$
  • $\pm\frac{\sqrt{1 – \cos^{2} 18^\circ}}{\cos 18^\circ}$
  • $\pm \sqrt{\sec^{2} 18^\circ -1}$
  • $\pm\frac{1}{\sqrt{\csc^2 18^\circ – 1}}$
  • $\frac{1}{\cot 18^\circ}$

As the cotangent function is the reciprocal of the tangent function, 1 / cot 18° = tan18°.

In the next part of this article we discuss the trigonometric significance of tan18°, and there you can also learn what the search calculations form in the sidebar is used for.

What is tan 18°

In a triangle which has one angle of 90 degrees, the tangent of the angle of 18° is the ratio of the length of the opposite side o to the length of the adjacent side a: tan 18° = o/a.

In a circle with the radius r, the horizontal axis x, and the vertical axis y, 18 degrees is the angle formed by the two sides x and r; r moving counterclockwise is the positive angle.

Applying the unit-circle definition found on our homepage, assumed r = 1, in the intersection of the point (x,y) and the circle, y = sin 18°, x = cos 18° and tan 18° = sin 18°/cos 18°.

Bringing together the triangle definition and the unit circle definition of tangent 18 degrees, a = x, o = y and h = r = 1. It follows that $y/x\hspace{5px} =\hspace{5px}\frac{opposite}{adjacent}\hspace{5px}=\hspace{5px}\tan 18^\circ$.

Note that you can locate many terms including the tangent18° value using the search form. On mobile devices you can find it by scrolling down. Enter, for instance, value of tan18°.

Along the same lines, using the aforementioned form, can you look up terms such as tan 18° value, tan 18, tan18° value and what is the tan of 18 degrees, just to name a few.

Given the periodicity of tangent of 18°, to determine the tangent of an angle > 180°, e.g. 738°, calculate tan 738° as tan (738 Mod 180)° = tangent of 18°, or look it up with our form.

The frequently asked questions in the context include what is tan 18 degrees and what is the tan of 18 degrees for example; reading our content they are no-brainers.

But, if there is something else about tangent 18° you would like to know, fill in the form on the bottom of this post, or send us an email with a subject line such as tangent 18 degrees.

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