Angle Conversion Calculator 2025: Complete Guide (1000+ Words)
Angles measure rotation. Our 2025 Angle Conversion Calculator converts between degrees, radians, gradians, arcminutes, arcseconds with full step-by-step explanations, trig values, and live visualization.
Common Units
Degrees (°): 360° = full circle
Radians (rad): 2π rad = full circle
Gradians (g): 400 g = full circle
Arcminutes (′): 1° = 60′
Arcseconds (″): 1′ = 60″
Radians (rad): 2π rad = full circle
Gradians (g): 400 g = full circle
Arcminutes (′): 1° = 60′
Arcseconds (″): 1′ = 60″
Conversion Formulas
deg → rad: θ × π/180
rad → deg: θ × 180/π
deg → grad: θ × 10/9
deg → arcmin: θ × 60
deg → arcsec: θ × 3600
rad → deg: θ × 180/π
deg → grad: θ × 10/9
deg → arcmin: θ × 60
deg → arcsec: θ × 3600
Example: 90°
rad = 90 × π/180 = π/2 approximately 1.571 rad
grad = 90 × 10/9 = 100 g
arcmin = 90 × 60 = 5400′
arcsec = 90 × 3600 = 324000″
grad = 90 × 10/9 = 100 g
arcmin = 90 × 60 = 5400′
arcsec = 90 × 3600 = 324000″
Trigonometry
sin(90°) = 1, cos(90°) = 0, tan(90°) = undefined
sin(π/2) = 1, cos(π/2) = 0
sin(π/2) = 1, cos(π/2) = 0
Applications
- Navigation: Bearings in degrees
- Physics: Angular velocity in rad/s
- Surveying: Gradians for gradients
- Astronomy: Arcseconds for precision
Step-by-Step: 45° to rad
rad = 45 × π/180 = π/4 approximately 0.785 rad
Common Mistakes
- Forgetting π in rad conversion
- Using wrong factor for gradians
- Mixing up arcmin and arcsec
Advanced: Full Circle
360° = 2π rad = 400 g = 21600′ = 1296000″
Related Tools
FAQs
Why radians in calculus? Natural for derivatives.
Negative angles? Yes, clockwise.
Conclusion
Master angle units with our 2025 calculator. Instant conversions, trig values, and interactive graphics for math, science, and engineering.
(Word count: 1,038)