Angle Conversion: Degrees to Radians
This interactive visualization demonstrates the conversion between different angle units (degrees, arcminutes, arcseconds) and radians. Adjust the angle to see how the conversions change in real-time.
Degrees to Radians
1° = π/180 rad ≈ 0.01745 rad
Calculation: 360° = 2π rad ⇒ 1° = 2π/360 = π/180 rad
Arcminutes to Radians
1' = 2.908 × 10⁻⁴ rad
Calculation: 1° = 60' = π/180 rad ⇒ 1' = π/(180×60) rad
Arcseconds to Radians
1" = 4.848 × 10⁻⁶ rad
Calculation: 1' = 60" = 2.908×10⁻⁴ rad ⇒ 1" = 2.908×10⁻⁴/60 rad
Example 2.1 Results
(a) 1° = π/180 rad = 1.745 × 10⁻² rad
(b) 1' = 2.908 × 10⁻⁴ rad ≈ 2.91 × 10⁻⁴ rad
(c) 1" = 4.847 × 10⁻⁶ rad ≈ 4.85 × 10⁻⁶ rad
These conversions are essential in astronomy, physics, and engineering where precise angular measurements are required. The radian is the standard unit of angular measure in mathematics, providing a direct relationship between angle and arc length.
