Cotangent Calculator

This cotangent calculator works out the cotangent of any angle you enter, whether you prefer to work in degrees or radians. Cotangent is one of the six trigonometric functions, the reciprocal of tangent, calculated as cos(x) divided by sin(x) or one divided by tan(x). It turns up in right-triangle trigonometry, physics, engineering, surveying and navigation, giving you an exact ratio for a given angle without reaching for a scientific calculator. You enter a single angle, then choose whether that figure is in degrees or radians from the dropdown. The calculator converts internally to radians, since that is what the underlying maths requires, and returns the cotangent as the main result. Alongside it, you get the same angle shown in both radians and degrees, so you can confirm you entered what you meant and use whichever unit suits your next step. Because cotangent is undefined wherever sine equals zero, such as at 0 or 180 degrees, the calculator shows "undefined" at those points rather than a misleading number. Cotangent also repeats every 180 degrees rather than the 360 degrees you might expect from sine and cosine, so do not be surprised to see the same value reappear at regular intervals. Use this tool for homework, exam checks or quick lookups when working through trigonometry, geometry or applied maths problems and you need a fast, accurate answer.

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Angle

Angle unit

Angle (radians)

Angle (degrees)

The formula

Cotangent is the reciprocal of tangent, cot(x) = cos(x) / sin(x) = 1 / tan(x). It is undefined wherever sine is zero.

Worked example

Cotangent of 45 degrees is cos 45 / sin 45 = 1. Enter 45 degrees to confirm.

Frequently asked questions

How do I find the cotangent of an angle?

Enter the angle and pick degrees or radians. The calculator converts to radians and evaluates the cotangent.

Degrees or radians?

Either. Choose the unit in the dropdown. The angle is shown in both units beside the result so you can check.

Why is the result the same every 180 degrees?

Cotangent is periodic with a period of 180 degrees (pi radians), so cot(x) = cot(x + 180 degrees). Although sine and cosine repeat every 360 degrees, the sign changes cancel in cos/sin, giving cotangent a 180-degree period.

Who this calculator is for

This calculator is for students, engineers, surveyors and anyone who needs the cotangent of an angle.

What this calculator assumes

You enter a single angle in the chosen unit.
The angle is converted to radians for the calculation.
Results are rounded for display.

Formula and sources

Related calculators

Trig Calculator: all six trig functions at once.
Degrees to Radians Calculator: convert angle units.
Right Angle Triangle Calculator: solve a right triangle.

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