Arctangent Calculator

How it is calculated

You enter a tangent value v, which is a ratio such as rise ÷ run and has no unit. The tool returns θ = arctan(v), the angle strictly between −90° and +90° whose tangent equals v. The result is found in radians (6 decimal places) and converted with θdeg = θrad × 180 ÷ π (4 decimal places). Any real number is accepted, because a tangent can be any size: v = 0 gives 0°, v = 1 gives 45°, and a negative v gives a negative angle. Very large values approach 90° but never reach it, so 1,000,000 shows 89.9999°. An empty box gives no result. The tool does not know which quadrant you are in, so it cannot return angles beyond ±90°.

Common mistakes

• Entering the slope as a percentage. A 75 % grade means a ratio of 0.75; typing 75 gives about 89.24°, a nearly vertical wall.
• Dividing run by rise instead of rise by run. Tangent is opposite ÷ adjacent, so swapping them returns the complementary angle (53.13° instead of 36.87°).
• Using the result for a direction in the second or third quadrant. Both (−1, −1) and (1, 1) give a ratio of 1 and the same 45°, so you must add 180° yourself or use atan2.
• Expecting a result at exactly 90°. A vertical line has no finite tangent, so there is no value to enter for it.
• Reading degrees and radians as the same quantity. 0.643501 is the radian line, not a smaller angle in degrees.