Arctan calculator
The arctangent (arctan, or tan⁻¹) is the inverse of the tangent: this calculator takes the tangent value x and returns the angle whose tangent is x, as the principal value in degrees (°) and radians (rad). Everything runs locally in your browser.
Arctan Calculator
Enter the tangent value x and press Calculate to get arctan(x), the inverse tangent angle in degrees (°) and radians (rad), as the principal value between -90° and 90°.
The angle in degrees, the angle in radians, and the calculation appear here after you press Calculate.
Enter the tangent value x
Type any finite real number — decimals and scientific notation both work (for example 1, -0.5, 0.577350269, or 1e6). Arctan is defined for every real number, so there is no domain to stay inside.
Press Calculate
The angle in degrees and the angle in radians appear on their own lines, together with the calculation written out, e.g. arctan(1) = 45° = 0.785398 rad. Values are shown with up to 6 decimal places.
Reset and try the table values
Reset clears the field, the results, and any error. Try the classic pairs: arctan(0.577350269) = 30° = π/6, arctan(1) = 45° = π/4, and arctan(1.732050808) = 60° = π/3.
Understanding arctangent
- What is arctan (inverse tangent)?
- The arctangent function is the inverse function of y = tan(x): if tan(45°) = 1, then arctan(1) = tan⁻¹(1) = 45°. In general arctan(y) = tan⁻¹(y) = x + kπ for every k = …, −2, −1, 0, 1, 2, …, so this calculator returns the single principal value and the full solution family is obtained by adding multiples of π.
- What range does the result fall in?
- The principal value of arctan(x) always lies between −90° and 90° (−π/2 and π/2 radians), for every real x. Large positive inputs approach 90° and large negative inputs approach −90° without ever reaching exactly ±90° for a finite input, and arctan(−x) = −arctan(x).
- Common arctangent table values
- y = −1.732050808 → −60° = −π/3; y = −1 → −45° = −π/4; y = −0.577350269 → −30° = −π/6; y = 0 → 0° = 0; y = 0.577350269 → 30° = π/6; y = 1 → 45° = π/4; y = 1.732050808 → 60° = π/3. The values 0.577350269 and 1.732050808 are the decimal forms of 1/√3 and √3.
- How do you convert the result between degrees and radians?
- Radians = degrees × π/180, and degrees = radians × 180/π. The calculator shows both lines for you: for x = 2 the principal value is 1.107149 rad, which is 1.107149 × 180/π ≈ 63.434949°.
- How do you get arctan on a physical calculator?
- Press shift + tan to enter the tan⁻¹ function, enter the value, then press = — the same three steps this online calculator replaces with a single Calculate press.
Privacy: every calculation runs in your browser tab — no value you type is sent anywhere. Results are the principal-value arctangent at up to 6-decimal display rounding.