Cotangent Calculator

What the Cotangent Calculator Does

Many students meet cotangent as the flip side of tangent, and this page makes that idea concrete. Type your angle into the Angle field, press Calculate, and the tool returns cot(x), the reciprocal of the tangent at that angle, as a clean decimal.

It suits homework checks, engineering slope work, surveying adjustments, and AC circuit phase calculations. Anywhere tangent appears, its reciprocal usually follows close behind, and graphing y = cot(x) one point at a time is exactly where this saves the most effort.

How Cotangent Is Defined

Cotangent is 1 divided by tangent, which also equals cosine divided by sine, written as cot(x) = cos(x) / sin(x). The function is undefined wherever sine is zero, at 0, 180, and 360 degrees, and it crosses zero wherever cosine does, at 90 and 270 degrees.

A quick worked check: at 45 degrees, sine and cosine both equal about 0.7071, so the ratio is exactly 1, which also matches cot 45 = 1. At 30 degrees, tangent is about 0.5774, and dividing 1 by it gives a cotangent of about 1.7321, the square root of 3.

Using the Calculator Well

Enter the angle in the Angle box, set degrees or radians to match your problem, and click Calculate. Decimals work too, so 15.5 degrees computes as smoothly as 15. If you instead hold a cotangent value and want the angle behind it, that reverse trip belongs to an arccot calculator.

Watch the sign pattern: cotangent is positive in the first and third quadrants and negative in the second and fourth. Near 0 or 180 degrees the tangent collapses toward zero, so cotangent shoots toward huge values, and results there are sensitive to tiny input changes.