Eng Unit Converter

Angles measure rotation or the opening between two lines meeting at a point. The SI unit is the radian (rad), defined as the angle subtended by an arc equal in length to the radius. Degrees (°) remain dominant in everyday engineering practice. Key conversions: π rad = 180°, 1 rad = 57.2958°, 1° = 0.017453 rad, 1° = 60 arcminutes = 3,600 arcseconds, 360° = 400 grad (gradians). Common values: 30° = π/6, 45° = π/4, 90° = π/2. Angle conversion is critical in surveying (bearings and azimuths), CNC machining (angular positioning), robotics (joint angles), navigation (compass headings), and structural analysis (slope and deflection calculations). The most common pitfall is mode confusion: all standard programming languages and most scientific calculators can operate in both degree and radian modes. sin(90) = 1 in degree mode but sin(90) ≈ 0.894 in radian mode. The small-angle approximation (sinθ ≈ θ) is valid only in radians and only for θ < ~0.25 rad (15°). Accidentally using gradians (where 100 grad = 90°) produces subtly wrong results that can be hard to detect.