Decimal Degrees to DMS Converter
Convert between decimal degrees and degrees, minutes, seconds format for angular measurements
Angle Conversion Calculator
Enter angle in decimal degrees format (e.g., 30.51°)
Conversion Results
Conversion Formula: Decimal → DMS: Extract degrees, multiply remainder by 60 for minutes, multiply remainder by 60 for seconds
Step-by-Step Conversion
Step 1: Start with decimal degrees = 0°
Step 2: Take the whole number part for degrees = 0°
Step 3: Take decimal part = 0.000000
Step 4: Multiply decimal part by 60 = 0.000000 × 60 = 0.0000
Step 5: Take whole number for minutes = 0'
Step 6: Take decimal part = 0.000000
Step 7: Multiply by 60 for seconds = 0.000000 × 60 = 0.00"
Final result: 0° 0' 0.00"
Example Conversions
Example 1: 30.51° to DMS
Given: 30.51° (decimal degrees)
Step 1: Degrees = 30 (whole number part)
Step 2: Decimal part = 0.51
Step 3: Minutes = 0.51 × 60 = 30.6, so 30 minutes
Step 4: Seconds = 0.6 × 60 = 36 seconds
Result: 30° 30' 36"
Example 2: 45° 15' 30" to Decimal
Given: 45° 15' 30" (DMS format)
Step 1: Degrees = 45
Step 2: Minutes in decimal = 15/60 = 0.25
Step 3: Seconds in decimal = 30/3600 = 0.008333
Step 4: Total = 45 + 0.25 + 0.008333 = 45.258333°
Result: 45.258333°
Conversion Formulas
Decimal to DMS
• Degrees = whole number part
• Minutes = (decimal part × 60) whole number
• Seconds = (minutes decimal part × 60)
DMS to Decimal
D + M/60 + S/3600
• D = degrees
• M = minutes
• S = seconds
Quick Reference
Common Applications
Geographic coordinates (latitude/longitude)
Astronomy and celestial navigation
Surveying and mapping
Navigation systems (GPS)
Engineering and construction
Understanding Degree Formats
Decimal Degrees Format
Decimal degrees express angles as a single decimal number. This format is commonly used in modern GPS systems, computer applications, and scientific calculations because it's easier for mathematical operations.
When to Use Decimal Degrees
- •GPS coordinates and mapping software
- •Mathematical calculations and programming
- •Scientific and engineering applications
- •Digital mapping and GIS systems
DMS Format
Degrees, Minutes, Seconds (DMS) format breaks angles into three components: degrees (°), minutes ('), and seconds ("). This traditional format is intuitive and commonly used in navigation, surveying, and astronomy.
When to Use DMS
- •Traditional navigation and marine charts
- •Astronomical observations and star charts
- •Land surveying and property boundaries
- •Aviation and maritime navigation
Note: Both formats represent the same angle, just expressed differently. The choice depends on your application and preference.