Inverse Tangent CalculatorFree online math calculator — instant results, no sign-up
Calculate the principal inverse tangent in degrees.
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About the Inverse Tangent Calculator
The Inverse Tangent Calculator converts a tangent value into its principal angle in degrees. It uses the arctangent function to return an angle strictly between −90° and 90°. With the default tangent value of 1, the result is 45°.
- Tangent value
- The dimensionless tangent ratio whose principal angle you want to find; in a right triangle, it is the opposite side length divided by the adjacent side length.
Formula and method
θ = arctan(t) × 180/π; for t = 1, θ = (π/4) × 180/π = 45°.
- tThe input tangent value, a dimensionless real number.
- θThe principal inverse tangent angle expressed in degrees.
- arctan(t)The principal angle in radians whose tangent equals t.
- πThe mathematical constant pi; 180/π converts radians to degrees.
The calculator evaluates the principal arctangent of the entered tangent value, then multiplies the angle in radians by 180/π to express it in degrees. For the default input of 1, arctan(1) is π/4 radians, so the calculated result is 45°.
Worked example
These are the calculator's starting values and the results it actually produces for them.
Inputs
- Tangent value1
Results
- Result45
How to use the Inverse Tangent Calculator
- 1Enter the ratio in the Tangent value field, or keep the default value of 1.
- 2Check that the input is a dimensionless tangent value rather than an angle in degrees.
- 3Run the calculation to evaluate the principal inverse tangent and convert it to degrees.
- 4Read the Result row: with the default input of 1, Result = 45, meaning 45°.
Reading your result
The Result row shows the principal angle in degrees whose tangent matches your input. Result = 45 means the angle is 45°, because tan(45°) = 1. Positive tangent values produce positive principal angles, negative values produce negative principal angles, and a zero tangent value produces a zero angle.
Limitations
The calculator accepts finite real tangent values and returns only the principal angle, strictly between −90° and 90°; the endpoints are never reached for a finite input. Tangent repeats every 180°, so this result does not identify every angle with the same tangent or determine an original angle's quadrant. It is not a two-coordinate atan2 calculation. Displayed values may be rounded, and extremely large inputs can be affected by numerical precision.
Common questions
Why does the default tangent value of 1 give a result of 45?+
The tangent of 45° equals 1, so the principal inverse tangent of 1 is 45°. The calculator reports this angle in degrees.
Is inverse tangent the same as the reciprocal of tangent?+
No. Inverse tangent, written arctan or tan⁻¹ in this context, finds an angle from a tangent value. The reciprocal of tangent is cotangent, not arctangent.
Why does this calculator return only one angle when tangent repeats?+
It uses the principal arctangent branch, which selects one angle strictly between −90° and 90°. All other angles with the same tangent are obtained by adding an integer multiple of 180° to the result.
Can a tangent value alone tell me the original angle's quadrant?+
No. A tangent value alone cannot distinguish angles separated by 180°. If you have signed horizontal and vertical coordinates and need quadrant information, use an atan2 calculation instead.
Does the calculator save my information?+
Calculations run in your browser. While signed in, inputs and results are automatically recorded in account history; saving a result creates a separate saved record.
Further reading
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Results are estimates for informational purposes and are not financial, medical or legal advice.