Arctan Calculator
Enter a tangent value x to compute arctan(x), the angle whose tangent equals that value.
3/4), and pi notation (e.g., pi, 2pi/3).What does “arctan” mean on a calculator?
arctan (also written as tan-1 or atan) is the inverse of tangent. If tangent turns an angle into a ratio, arctan does the opposite: it takes a ratio and returns an angle.
In practical terms, if you know that
tan(θ) = x, then
θ = arctan(x).
This is used everywhere from trigonometry homework to physics, engineering, graphics, and navigation.
How to use arctan on a scientific calculator
Step-by-step
- Set the calculator to the angle mode you need: DEG (degrees) or RAD (radians).
- Find the inverse tangent key. On many devices, it is tan-1 or atan.
- Enter your tangent value (for example,
1). - Press equals (or close parenthesis on graphing calculators).
Example: in degree mode, arctan(1) = 45°.
In radian mode, arctan(1) ≈ 0.785398....
Degrees vs radians: why results may look different
The same angle can be expressed in different units. If your answer seems “wrong,” the most common reason is angle mode mismatch.
- Degrees: full circle = 360
- Radians: full circle = 2π
So 45° and π/4 represent the same direction.
Before using arctan in exams, labs, or programming, verify your required unit.
Important property: principal value range
A calculator’s arctan function returns the principal value, which is always in this interval:
(-π/2, π/2) or (-90°, 90°).
That means if you’re solving geometry or vector problems where the angle could be in another quadrant,
plain arctan may be insufficient. In those cases, use the two-argument function atan2(y, x) when available.
Quick examples
1) arctan(0)
arctan(0) = 0. Tangent of 0 is 0.
2) arctan(√3)
In degrees: 60°.
In radians: π/3.
3) arctan(-1)
In degrees: -45°.
In radians: -π/4.
Common mistakes when using arctan
- Confusing
tan^-1(inverse tangent) with1/tan(cotangent-like reciprocal operation). - Forgetting to set degree/radian mode before calculation.
- Using arctan for quadrant-sensitive vector angles instead of
atan2. - Rounding too early, which can create noticeable final-answer error.
When arctan is useful in real life
Arctan appears whenever slope or rise/run is known and an angle is needed:
- Roof pitch and construction measurements
- Camera tilt and field geometry
- Game development and object orientation
- Robotics and trajectory control
- Signal processing and phase analysis
Final takeaway
If you remember one thing, remember this: arctan converts a tangent ratio into an angle.
Always verify angle mode, and for coordinate-based direction use atan2 when needed.
Use the calculator above to check homework, build intuition, and avoid unit mistakes.