Arctangent Calculator

This arctangent calculator returns the arctangent, the angle whose tangent equals the value you enter. The result is given in degrees as the headline and in radians beside it. Arctangent is the inverse of the tangent function, so it answers the question, what angle has this tangent. Any real number is valid, because tangent takes every value. The calculator computes the principal value, which is the standard single answer in the usual range for this inverse function. Use it for trigonometry and geometry, working back from a ratio to an angle, physics, surveying and navigation. The definition, the domain, a worked example and the assumptions are set out below.

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Value (any real number)

Angle (radians)

Input value

The formula

Arctangent is the inverse of tangent: if tan(theta) = x then arctan(x) = theta. The principal value lies between -90 and 90 degrees (-pi/2 and pi/2 radians). Any real input is allowed.

Worked example

Arctangent of 1 is 45 degrees, because tan 45 = 1. Enter 1 to confirm.

Frequently asked questions

What does arctangent give me?

The angle whose tangent is the number you enter. It is the inverse of tangent.

What is the valid input range?

Any real number is valid, because tangent takes every value.

In what range is the angle returned?

Arctangent returns an angle between -90 and 90 degrees.

Who this calculator is for

This calculator is for students, engineers and surveyors who need to find an angle from its tangent.

What this calculator assumes

You enter a value any real number.
The principal value is returned.
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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