Arccot Calculator
What the Arccot Calculator does
The Arccot Calculator reverses the cotangent function: enter a value and it returns the angle that produces it. Because cot(x) is 1/tan(x), it answers questions such as which angle has a cotangent of 1. Trigonometry students, physics learners, and engineers analyzing linkages all lean on this inverse.
The reciprocal formula with a worked example
Since cot(x) = 1/tan(x), the arccot of y equals the angle whose tangent is 1/y. Check it numerically: cot(45 deg) = 1/tan(45 deg) = 1, so arccot(1) = 45 degrees, or pi/4 radians. Likewise cot(60 deg) = 1/1.732 = 0.577, so arccot(0.577) returns 60 degrees.
Two boundary cases come up often in practice. Inputting 0 returns 90 degrees, because cotangent vanishes exactly there, while a negative input such as minus 1 returns 135 degrees in the 0 to 180 degree convention used by most textbooks. Electronics learners meet the same arithmetic when a reactance ratio sets a phase angle, and surveying problems use it for slope corrections, so checking one hand-solved case against the output is a good calibration habit.
Entering values and reading the result
Type your ratio into the Cotangent field, choose degrees or radians as the output unit, then press Calculate. The domain includes every real number, while the principal range runs from just above 0 to 180 degrees (0 to pi radians). The endpoint of 0 degrees never appears because cotangent is undefined there.
Frequently Asked Questions
What does arccot of 1 equal?
Arccot(1) is 45 degrees because cot(45 deg) = 1/tan(45 deg) = 1. In radians the same result is pi/4, about 0.7854, and it shows up inside every isosceles right triangle.
How does arccot relate to arctan?
Cotangent is the reciprocal of tangent, so arccot(y) returns the same angle as arctan(1/y) for positive y. For example arccot(2) equals arctan(0.5), and both are 26.57 degrees.
Are negative cotangent inputs allowed?
Yes. Negative values return obtuse angles: arccot(-1) = 135 degrees because cot(135 deg) = -1. The principal interval of 0 to 180 degrees absorbs every negative input.
Why can arccot never be 0 degrees?
Cotangent is undefined at 0 degrees because tan(0) = 0 and division by zero is impossible. The output range therefore runs strictly between 0 and 180 degrees, and an input of 0 returns 90 degrees.
What unit options does the output have?
Results appear in degrees or radians: 45 degrees equals pi/4 radians, and 135 degrees equals 3 pi/4. Pick the unit that matches your worksheet or CAD package before pressing Calculate.