Cotangent Calculator – Calculate cot(x)

Find the cotangent of an angle using the cot calculator below. Start by entering the angle in degrees or radians.



How to Find the Cotangent of an Angle

In a right triangle, the cotangent of angle α, or cot(α), is the ratio between the angle’s adjacent side and its opposite side.

illustration of a triangle showing the formula for cotangent being equal to adjacent side b divided by opposite side a

Cotangent is a trigonometric function abbreviated cot. Use the formula below to calculate the cotangent of an angle.

Cotangent Formula

The cotangent formula is:

cot(α) = adjacent bopposite a

Thus, the cotangent of angle α in a right triangle is equal to the length of the adjacent side b divided by the opposite side a.

To solve cot, simply enter the length of the adjacent and opposite sides, then solve.

This formula might look very similar to the formula to calculate tangent. That’s because cotangent is the reciprocal of tangent.

Cotangent should not be confused with arctan, which is the inverse of the tangent function. The difference being that cotangent is equal to 1tan(x), while arctan is the inverse of the tangent function.

cot(x) = 1tan(x) = tan(x)-1
arctan(y) x where y = tan(x)

For example, let’s calculate the cotangent of angle α in a triangle with the length of the adjacent side equal to 8 and the opposite side equal to 4.

cot(α) = 84
cot(α) = 21

Cotangent Graph

If you graph the cotangent function for every possible angle, it forms a series of repeating curves.

graph of the repeating curves representing possible cotangent values

One important property to note in the graph above is that the cotangent of an angle is never equal to 0 or an even multiple of π radians, or 180°

Cotangent Table

The table below shows common angles and the cot value for each of them.

-√3

Table showing common angles and cot values for each.
Angle (degrees) Angle (radians) Cotangent
0 undefined
15° π12 2 + √3
30° π6 √3
45° π4 1
60° π3 1√3 = √33
75° 12 2 – √3
90° π2 0
105° 12 -2 + √3
120° 3 1√3 = –√33
135° 4 -1
150° 6 -√3
165° 11π12 -2 – √3
180° π undefined
195° 13π12 2 + √3
210° 6 √3
225° 4 1
240° 3 1√3 = √33
255° 17π12 2 – √3
270° 2 0
285° 19π12 -2 + √3
300° 3 1√3 = –√33
315° 4 -1
330° 11π6
345° 23π12 -2 – √3
360° undefined

You might also be interested in our secant and cosecant calculators.