Inverse Tangent (Arctan) Calculator
Find the angle whose tangent you know, in degrees and radians, using arctan or atan2.
Angle in degrees
45.000000°
- Angle in radians
- 0.78539816
- Angle in terms of π
- 0.25π
- Angle in gradians
- 50
The angle is 45 degrees.
Calculation breakdown
| Step | Formula | Result |
|---|---|---|
| Angle in radians | arctan(1) | 0.78539816 |
| Angle in degrees | 0.7854 × 180 ÷ π | 45.000000° |
How it works
Choose arctan for one number, or atan2 for a point (x, y).
Worked example
arctan(1):
- The angle with tangent 1 is π/4 radians, or 0.785398
- In degrees: 0.785398 × 180 ÷ π = 45°
- In gradians: 50
Sources
Frequently asked questions
What is the inverse tangent?
The inverse tangent, written arctan or tan⁻¹, gives the angle whose tangent is a given number. Since tan(45°) = 1, arctan(1) = 45°. The answer is always between −90° and 90°.
What is the difference between arctan and atan2?
Arctan takes one number, the ratio y ÷ x, so it cannot tell which quadrant the point is in. Atan2 takes y and x separately and uses their signs, giving an angle from −180° to 180°. The point (−1, 1) has atan2 of 135°, while arctan(−1) is −45°.
How do I convert radians to degrees?
Multiply by 180 and divide by π. One radian is about 57.2958 degrees, and π radians is 180 degrees. The calculator shows both, plus the angle in terms of π.
How do I find an angle from a slope or a right triangle?
Take the arctan of rise over run, or of the opposite side over the adjacent side. A slope of 1.5 has an angle of arctan(1.5) = 56.31°.
Is arctan the same as 1 divided by tan?
No. That is the cotangent. Arctan is the inverse function, which undoes the tangent. Do not confuse tan⁻¹ with 1/tan.