Tan Inverse Calculator — Angle from Opposite & Adjacent
Enter the opposite and adjacent side lengths of a right triangle to find the angle using tan⁻¹ — get degrees, radians, sin, cos, hypotenuse, and the complement angle.
tan⁻¹(opposite ÷ adjacent) — the angle between the adjacent side and the hypotenuse
- 1
Tangent ratio
3 ÷ 4 = 0.75 - 2
Hypotenuse
√(3² + 4²) = √25 = 5 - 3
Angle θ = tan⁻¹(opp ÷ adj)
atan2(3, 4) × (180 ÷ π) = 36.8699Converts the arctangent result from radians to degrees.
How does this calculator work?
θ = tan⁻¹(opposite ÷ adjacent). For a 3-4-5 triangle, θ = tan⁻¹(3/4) ≈ 36.87°. From θ the calculator also gives radians, sin, cos, hypotenuse = √(opp² + adj²), and the complement angle (90° − θ). This is the standard method for finding a right-triangle angle from two known legs.
Formula
How this is calculated
In a right triangle, the tangent of an angle θ equals the ratio of the side opposite that angle to the side adjacent to it: tan(θ) = opposite/adjacent. Reversing this — taking the inverse tangent — gives the angle itself: θ = tan⁻¹(opposite ÷ adjacent). This is the most common real-world use of the inverse tangent: finding an angle when you know two sides of a right triangle.
Once the angle θ is known, all other triangle quantities follow from it. The hypotenuse is √(opp² + adj²) (Pythagoras). The sine and cosine are derived as opposite/hypotenuse and adjacent/hypotenuse. The complement angle is 90° − θ — the other acute angle in the right triangle — because the three angles of a triangle always sum to 180°, and one angle is already 90°.
This calculator uses Math.atan2(opposite, adjacent), which correctly handles the case where either side is negative (e.g. a vector pointing in a negative direction), returning angles in all four quadrants. For the standard right-triangle geometry where both sides are positive, the result is always in the first quadrant (0° to 90°). If the adjacent side is zero the angle would be exactly 90° and tan is undefined; enter a small non-zero value instead.
Frequently asked questions
If you know opposite and adjacent, use tan⁻¹(opposite/adjacent). If you know opposite and hypotenuse, use sin⁻¹(opposite/hypotenuse). If you know adjacent and hypotenuse, use cos⁻¹(adjacent/hypotenuse). This calculator handles the tan⁻¹ case.
If you have the hypotenuse and the opposite side, use a sin⁻¹ calculator. If you have the hypotenuse and the adjacent side, use a cos⁻¹ calculator. Once any angle is known, Pythagoras gives the third side, so this calculator can then be used with the derived adjacent and opposite.
Math.atan(y/x) works for positive x but gives the wrong sign when x is negative (pointing left). Math.atan2(y, x) checks the signs of both values independently, returning the correct quadrant angle in all cases — useful for compass bearings, vector directions and other applications where sides can be negative.
Also known as
TG we-Calculate Editorial Team. (2026). Tan Inverse Calculator — Angle from Opposite & Adjacent [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/tan-inverse-calculator
TG we-Calculate Editorial Team. "Tan Inverse Calculator — Angle from Opposite & Adjacent." TG we-Calculate. 2026. https://we-calculate.com/calculator/tan-inverse-calculator.
TG we-Calculate Editorial Team, "Tan Inverse Calculator — Angle from Opposite & Adjacent," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/tan-inverse-calculator
@misc{wecalculate_tan_inverse_calculator, title = {Tan Inverse Calculator — Angle from Opposite & Adjacent}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/tan-inverse-calculator}}, year = {2026}, note = {TG we-Calculate} }
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