Como to Converter Angles

Converting entre angle unidades é essential in mathematics, navigation, engenharia, e programming. Este guia covers o mais comum conversions com clear formulas e prático examples you can apply immediately.

Converting Degrees to Radians

O mais comum angle conversão in mathematics e programming.

Formula

radians = degrees × (π ÷ 180)

Passo a Passo Process

1. Take o angle in degrees
2. Multiply by π (aproximadamente 3.14159)
3. Divide by 180
4. Simplify if possible

Examples

• 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 to Degrees

Formula

degrees = radians × (180 ÷ π)

Passo a Passo Process

1. Take o angle in radians
2. Multiply by 180
3. Divide by π
4. Round as needed

Examples

• 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 to Gradians

Gradians (também called gons) são usado in alguns European surveying.

Formula

gradians = degrees × (10 ÷ 9)

Or: gradians = degrees × 1.1111...

Examples

• 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 to Degrees

Formula

degrees = gradians × (9 ÷ 10)

Or: degrees = gradians × 0.9

Examples

• 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 to Decimal Degrees

DMS (degrees, minutes, seconds) é comum in navigation e surveying.

Formula

decimal degrees = degrees + (minutes ÷ 60) + (seconds ÷ 3600)

Passo a Passo Process

1. Keep o degrees as-é
2. Divide minutes by 60
3. Divide seconds by 3600
4. Add todos three values

Exemplo: Converter 45°30'15" to decimal

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

Converting Decimal Degrees to DMS

Passo a Passo Process

1. O whole number é o degrees
2. Multiply o decimal by 60—o whole number é minutes
3. Multiply remaining decimal by 60—este é seconds

Exemplo: Converter 45.50417° to DMS

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

Comuns Ângulo Reference Table

Programming Ângulo 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

A maioria programming language math libraries (sin, cos, tan) expect radians. Always converter degrees to radians before usando estes functions.

Conclusão

Ângulo conversão follows straightforward formulas once you remember o key relationships: π radians = 180 degrees, e 90 degrees = 100 gradians. For DMS conversions, remember esse lá são 60 minutes per degree e 60 seconds per minute. Practice com comum angles like 30°, 45°, 60°, e 90° to build intuition.

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• Degrees vs Radians: Quando to Usar Cada Ângulo Unidade
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