Como Convertir Angles

Converting entre angle unidades es esencial in mathematics, navigation, engineering, y programming. This guia cubre el/la la mayoria comun conversiones with clear formulas y practico ejemplos tu puede apply immediately.

Converting Degrees un/una Radians

El/La la mayoria comun angle conversion in mathematics y programming.

Formula

radians = degrees × (π ÷ 180)

Step-by-Step Process

1. Take el/la angle in degrees
2. Multiplica por π (aproximadamente 3.14159)
3. Divide por 180
4. Simplify si possible

Ejemplos

• 45°: 45 × π/180 = π/4 ≈ 0.785 rad
• 90°: 90 × π/180 = π/2 ≈ 1.571 rad
• 60°: 60 × π/180 = π/3 ≈ 1.047 rad
• 30°: 30 × π/180 = π/6 ≈ 0.524 rad

Converting Radians un/una Degrees

Formula

degrees = radians × (180 ÷ π)

Step-by-Step Process

1. Take el/la angle in radians
2. Multiplica por 180
3. Divide por π
4. Round as needed

Ejemplos

• π/4 rad: (π/4) × 180/π = 45°
• π/6 rad: (π/6) × 180/π = 30°
• 2 rad: 2 × 180/π ≈ 114.59°
• 1 rad: 1 × 180/π ≈ 57.30°

Converting Degrees un/una Gradians

Gradians (tambien called gons) son usado in algunos European surveying.

Formula

gradians = degrees × (10 ÷ 9)

Or: gradians = degrees × 1.1111...

Ejemplos

• 90°: 90 × 10/9 = 100 grad
• 45°: 45 × 10/9 = 50 grad
• 180°: 180 × 10/9 = 200 grad
• 360°: 360 × 10/9 = 400 grad

Converting Gradians un/una Degrees

Formula

degrees = gradians × (9 ÷ 10)

Or: degrees = gradians × 0.9

Ejemplos

• 100 grad: 100 × 0.9 = 90°
• 50 grad: 50 × 0.9 = 45°
• 200 grad: 200 × 0.9 = 180°
• 400 grad: 400 × 0.9 = 360°

Converting DMS un/una Decimal Degrees

DMS (degrees, minutos, segundos) es comun in navigation y surveying.

Formula

decimal degrees = degrees + (minutos ÷ 60) + (segundos ÷ 3600)

Step-by-Step Process

1. Keep el/la degrees as-es
2. Divide minutos by 60
3. Divide segundos by 3600
4. Suma todo three valores

Ejemplo: Convertir 45°30'15" un/una decimal

• Degrees: 45
• Minutes: 30 ÷ 60 = 0.5
• Seconds: 15 ÷ 3600 = 0.00417
• Total: 45 + 0.5 + 0.00417 = 45.50417°

Converting Decimal Degrees un/una DMS

Step-by-Step Process

1. El/La whole numero es el/la degrees
2. Multiply el/la decimal by 60—el/la whole numero es minutos
3. Multiply remaining decimal by 60—esto es segundos

Ejemplo: Convertir 45.50417° un/una DMS

• Degrees: 45
• Decimal: 0.50417 × 60 = 30.25 → Minutes: 30
• Decimal: 0.25 × 60 = 15 → Seconds: 15
• Result: 45°30'15"

Common Angulo Reference Table

Programming Angulo Conversions

JavaScript

const toRadians = degrees => degrees * (Math.PI / 180);

const toDegrees = radians => radians * (180 / Math.PI);

Python

import math

radians = math.radians(degrees)

degrees = math.degrees(radians)

Importante Nota

Most programming language math libraries (sin, cos, tan) expect radians. Always convertir degrees un/una radians before usando estos functions.

Conclusion

Angulo conversion follows straightforward formulas once tu remember el/la key relationships: π radians = 180 degrees, y 90 degrees = 100 gradians. For DMS conversiones, remember eso alli son 60 minutos per degree y 60 segundos per minuto. Practice with comun angles like 30°, 45°, 60°, y 90° un/una build intuition.

Articulos relacionados

• Degrees vs Radians: When un/una Use Each Angulo Unidad
• Angulo Units Worldwide: Degrees, Radians, Gradians, y More