Arctangent Calculator

This arctangent calculator works out the angle whose tangent equals a value you give it, which is the everyday task of turning a ratio, a slope or a rise-over-run figure back into an angle. Arctangent, sometimes written as tan to the power of minus one or atan, is the inverse of the tangent function: instead of starting with an angle and finding its tangent, you start with the tangent and recover the angle. You enter any real number, positive, negative, zero, whole or decimal, because tangent can produce every possible value, so there is no invalid input to worry about. The calculator returns the angle as its headline result in degrees, with the same angle shown again in radians beside it and your original input value repeated for reference. It always returns the principal value, the single standard answer between minus 90 and 90 degrees, which is the convention used across mathematics, engineering and navigation software. This makes it useful for trigonometry and geometry homework, for working out a gradient or pitch from a rise and run in construction and surveying, for physics problems involving vectors and forces, and for programming or spreadsheet work where you need to check an atan formula by hand. Simply type your value into the field and the angle updates instantly in both units, with a worked example below showing that an input of 1 gives exactly 45 degrees.

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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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