What is the Tangent Angle Calculator?
This tool finds the angle θ of a right triangle when you know the lengths of the side opposite the angle and the side adjacent to it. It is based on the fundamental trigonometric relationship that the tangent of an angle equals the ratio of the opposite side to the adjacent side. By taking the inverse tangent (arctangent), the calculator returns θ in both degrees and radians.
How to use it
Enter the length of the opposite side (the leg across from the angle) and the adjacent side (the leg next to the angle, not the hypotenuse). Click calculate and you'll get the angle along with the raw tangent ratio. Any consistent units work — only the ratio matters, so meters, feet, or pixels all give the same angle.
The formula explained
In a right triangle, \(\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}\). To solve for the angle itself you apply the arctangent function: $$\theta = \arctan\!\left(\frac{\text{Opposite}}{\text{Adjacent}}\right)$$ This calculator uses a two-argument arctangent (atan2) internally so it handles edge cases like a zero adjacent side gracefully, returning 90° rather than dividing by zero.
Worked example
Suppose the opposite side is 1 and the adjacent side is 1. Then \(\tan(\theta) = \frac{1}{1} = 1\), and \(\theta = \arctan(1) = 45°\). If the opposite side were \(\sqrt{3}\) and the adjacent side 1, \(\tan(\theta) = 1.732\), giving \(\theta = 60°\).
FAQ
Which side is opposite and which is adjacent? The opposite side faces the angle θ; the adjacent side touches θ and the right angle. The hypotenuse is never used in this calculation.
Why is my answer in degrees and radians? Degrees are common in everyday geometry, while radians are standard in calculus and physics — both describe the same angle.
What if the adjacent side is 0? The angle is 90° (a vertical line), which the calculator reports without error.
