Degrees Minutes Seconds to Decimal Degrees Converter

Convert coordinates between DMS (Degrees, Minutes, Seconds) and Decimal Degrees format instantly. Perfect for GPS navigation, surveying, mapping, and geographic coordinate conversion with step-by-step calculations.

DMS to Decimal Degrees Conversion

Degrees (°)

Minutes (')

Seconds ("")

Direction

Decimal Degrees Result:

Calculation Steps:

Decimal Degrees to DMS Conversion

Enter Decimal Degrees:

DMS Result:

Calculation Steps:

Quick Conversion Examples

Statue of Liberty
40° 26' 46" N
→ 40.446111°

Big Ben, London
51° 30' 26" N
→ 51.507222°

Eiffel Tower
48° 51' 30" N
→ 48.858333°

Sydney Opera House
-33.8688°
→ 33° 52' 7.68" S

Conversion Formulas

DMS to Decimal Degrees Formula

To convert coordinates from Degrees, Minutes, Seconds (DMS) format to Decimal Degrees (DD), use the following formula:

Primary Formula:

\[\text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} + \frac{\text{Seconds}}{3600}\]

Short form:

\[DD = D + \frac{M}{60} + \frac{S}{3600}\]

Example Calculation:

Convert 40° 26' 46" North to decimal degrees:

\[DD = 40 + \frac{26}{60} + \frac{46}{3600}\]
\[DD = 40 + 0.4333 + 0.0128\]
\[DD = 40.446111°\text{ N}\]

Decimal Degrees to DMS Formula

To convert from Decimal Degrees to DMS format, follow a step-by-step extraction process:

Step-by-Step Process:

1. Degrees: Take the integer part
2. Minutes: Multiply decimal part by 60, take integer
3. Seconds: Multiply remaining decimal by 60

Example Calculation:

Convert 40.446111° to DMS format:

Degrees: 40 (integer part)
Minutes: 0.446111 × 60 = 26.76666 → 26'
Seconds: 0.76666 × 60 = 46"
Result: 40° 26' 46"

Direction and Sign Convention

Geographic coordinates use directional indicators or sign conventions:

North (N) and East (E): Positive values
South (S) and West (W): Negative values
Latitude range: -90° (South Pole) to +90° (North Pole)
Longitude range: -180° (West) to +180° (East)

Important Note: When converting coordinates with South or West directions, the resulting decimal degrees should be negative. For example, 33° 52' S = -33.8667°.

Conversion Reference Tables

Common Coordinate Conversions

Location	DMS Format	Decimal Degrees
New York City	40° 42' 46" N	40.712778°
Los Angeles	34° 3' 8" N	34.052222°
London	51° 30' 26" N	51.507222°
Paris	48° 51' 24" N	48.856667°
Tokyo	35° 41' 22" N	35.689444°
Sydney	33° 52' 4" S	-33.867778°
Dubai	25° 15' 47" N	25.263056°
Singapore	1° 17' 21" N	1.289167°

Minutes to Decimal Conversion

Minutes	Decimal	Minutes	Decimal	Minutes	Decimal
5'	0.0833	25'	0.4167	45'	0.7500
10'	0.1667	30'	0.5000	50'	0.8333
15'	0.2500	35'	0.5833	55'	0.9167
20'	0.3333	40'	0.6667	60'	1.0000

Seconds to Decimal Conversion

Seconds	Decimal	Seconds	Decimal	Seconds	Decimal
10"	0.002778	25"	0.006944	40"	0.011111
15"	0.004167	30"	0.008333	45"	0.012500
20"	0.005556	35"	0.009722	50"	0.013889

Understanding Coordinate Formats

Geographic coordinates can be expressed in multiple formats, each serving different purposes and contexts. The two most common formats are Degrees Minutes Seconds (DMS) and Decimal Degrees (DD).

What is DMS Format?

Degrees, Minutes, Seconds (DMS) is the traditional format for expressing geographic coordinates. This sexagesimal (base-60) system divides each degree into 60 minutes, and each minute into 60 seconds, similar to how time is measured. The format is written as: D° M' S" (e.g., 40° 26' 46" N).

DMS Components:

Degrees (°): Whole number from 0 to 90 for latitude, 0 to 180 for longitude
Minutes ('): Whole number from 0 to 59
Seconds (""): Can be whole or decimal, from 0 to 59.9999
Direction: N/S for latitude, E/W for longitude

What is Decimal Degrees Format?

Decimal Degrees (DD) expresses coordinates as decimal fractions of degrees, using a base-10 system. This format is more compact and easier to use in calculations, making it the preferred format for GPS devices, computer systems, and scientific applications. Example: 40.446111° N.

Decimal Degrees Characteristics:

Simpler format: Single decimal number per coordinate
Easier calculations: Direct mathematical operations without conversion
Computer-friendly: Native format for most mapping software and GPS devices
Sign convention: Positive for N/E, negative for S/W

Why Convert Between Formats?

Different applications and contexts require different coordinate formats:

Navigation charts: Traditional paper charts use DMS format for historical continuity
GPS devices: Modern devices typically display and work with decimal degrees
Surveying: Professional surveying often uses DMS for precision and tradition
Programming: Software applications prefer decimal degrees for mathematical operations
Data interchange: Converting between formats enables data sharing across platforms
Scientific research: Research papers may require specific coordinate formats

Step-by-Step Conversion Guide

Converting DMS to Decimal Degrees

Method: Mathematical Conversion

Step 1: Extract the degrees, minutes, and seconds values

Step 2: Divide minutes by 60 to convert to decimal degrees

Step 3: Divide seconds by 3600 to convert to decimal degrees

Step 4: Add all three components: Degrees + (Minutes/60) + (Seconds/3600)

Step 5: Apply negative sign if direction is South or West

Detailed Example:

Convert 51° 30' 26" N to decimal degrees:

Step 1: D = 51, M = 30, S = 26
Step 2: Minutes in decimal = 30 ÷ 60 = 0.5°
Step 3: Seconds in decimal = 26 ÷ 3600 = 0.007222°
Step 4: Total = 51 + 0.5 + 0.007222 = 51.507222°
Step 5: Direction is North, so result is positive: 51.507222° N

Converting Decimal Degrees to DMS

Method: Sequential Extraction

Step 1: Take the integer part as degrees (use absolute value if negative)

Step 2: Multiply the decimal remainder by 60

Step 3: Take the integer part as minutes

Step 4: Multiply the decimal remainder by 60 again to get seconds

Step 5: Determine direction based on sign (negative = S or W)

Detailed Example:

Convert -33.868889° to DMS:

Step 1: Degrees = 33 (take absolute value)
Step 2: Decimal part: 0.868889 × 60 = 52.13334
Step 3: Minutes = 52
Step 4: Decimal part: 0.13334 × 60 = 8.0004" ≈ 8"
Step 5: Original was negative, so: 33° 52' 8" S

Practical Applications

GPS Navigation

Modern GPS devices and smartphone navigation apps primarily use decimal degrees for coordinate display and calculation. However, users may need to input or read coordinates in DMS format when working with traditional maps or marine charts. Converting between formats ensures accurate waypoint entry and position sharing.

Surveying and Mapping

Professional surveyors often work with DMS coordinates for land boundary descriptions, legal documents, and property surveys. The DMS format provides high precision through decimal seconds and maintains compatibility with historical survey records. Conversion to decimal degrees facilitates computer-aided design (CAD) integration and GIS database management.

Aviation and Maritime Navigation

Pilots and mariners traditionally use DMS format on navigation charts and flight plans. Degrees, minutes, and seconds align with nautical mile measurements, where one minute of latitude equals approximately one nautical mile. Modern avionics may display both formats, requiring pilots to convert between them for cross-reference and verification.

Geographic Information Systems (GIS)

GIS software platforms like ArcGIS, QGIS, and Google Earth accept coordinates in multiple formats but internally work with decimal degrees for spatial calculations. Converting coordinate data to decimal degrees before importing ensures accurate spatial analysis, mapping, and data visualization. This conversion also simplifies mathematical operations like distance calculation and spatial queries.

Scientific Research

Researchers in geography, geology, ecology, and environmental science frequently work with coordinate data from various sources. Some field equipment outputs DMS coordinates, while data analysis software requires decimal degrees. Conversion enables data integration across instruments and platforms, ensuring consistency in spatial datasets.

Mobile Applications

Location-based mobile apps use decimal degrees for API calls and internal processing. However, displaying coordinates to users in DMS format can improve readability and alignment with traditional map reading skills. Developers implement bidirectional conversion to balance user experience with computational efficiency.

Common Conversion Scenarios

Famous Landmarks Coordinates

Landmark	Location	DMS Latitude	Decimal Latitude
Statue of Liberty	USA	40° 41' 21" N	40.689167°
Eiffel Tower	France	48° 51' 30" N	48.858333°
Great Pyramid	Egypt	29° 58' 45" N	29.979167°
Sydney Opera House	Australia	33° 51' 31" S	-33.858611°
Taj Mahal	India	27° 10' 30" N	27.175000°
Christ the Redeemer	Brazil	22° 57' 7" S	-22.951944°

Tips and Best Practices

For GPS Users

Check coordinate format: Verify whether your GPS displays DMS or decimal degrees before recording positions
Maintain precision: Use at least 6 decimal places in decimal degrees for meter-level accuracy
Record direction: Always note N/S/E/W or +/- signs to avoid coordinate confusion
Cross-reference: Compare coordinates with known landmarks to verify conversion accuracy
Save both formats: When logging waypoints, record both DMS and decimal degrees for flexibility

For Surveyors

Preserve precision: Keep full decimal places during conversion to maintain survey-grade accuracy
Document conversions: Record conversion methods in survey reports for transparency
Verify boundaries: Check legal property descriptions match converted coordinates exactly
Use consistent datum: Ensure coordinate conversions maintain the same geodetic datum (WGS84, NAD83, etc.)
Quality control: Convert coordinates back to original format to verify calculation accuracy

For Programmers

Handle precision: Use appropriate data types (double, decimal) to preserve coordinate precision
Validate inputs: Check that degrees, minutes, and seconds fall within valid ranges
Account for edge cases: Handle 0°, 180°, ±90° latitude, and hemisphere boundaries correctly
Consistent formatting: Standardize output format for display (number of decimal places, symbols)
Unit testing: Test conversion functions with known coordinate pairs to ensure accuracy

For Cartographers

Match map format: Use coordinate format that aligns with map scale and intended audience
Grid references: Understand how DMS/DD relates to grid systems (UTM, MGRS)
Label clarity: Clearly indicate coordinate format on maps and legends
Projection awareness: Remember that coordinate conversion is separate from map projection transformation

Common Mistakes to Avoid:

• Forgetting to apply negative sign for South or West coordinates
• Confusing minutes (') with decimal minutes
• Rounding too early in multi-step conversions
• Using wrong divisor (60 vs 3600) for seconds
• Mixing coordinate formats in the same dataset
• Not validating that minutes and seconds are less than 60
• Dropping direction indicators during conversion
• Assuming DMS seconds are always whole numbers

Precision and Accuracy

Decimal Places and Precision

The number of decimal places in decimal degrees directly affects coordinate precision:

Decimal Places	Approximate Precision	Use Case
1 decimal place	11.1 km	Large regions, countries
2 decimal places	1.1 km	Cities, large features
3 decimal places	111 meters	Neighborhoods, fields
4 decimal places	11 meters	Individual buildings
5 decimal places	1.1 meters	Individual trees, precise positioning
6 decimal places	11 cm	Survey markers, precise mapping
7 decimal places	1.1 cm	Tectonic plate movement studies
8 decimal places	1.1 mm	Scientific research, specialized surveying

Seconds Precision in DMS

In DMS format, decimal seconds provide precision equivalent to decimal degrees:

Whole seconds (0.001°): Approximately 30 meters precision
0.1 seconds (0.0001°): Approximately 3 meters precision
0.01 seconds (0.00001°): Approximately 30 centimeters precision
0.001 seconds (0.000001°): Approximately 3 centimeters precision

Frequently Asked Questions

What's the difference between DMS and decimal degrees?

DMS (Degrees, Minutes, Seconds) uses a sexagesimal (base-60) system where each degree is divided into 60 minutes, and each minute into 60 seconds. Decimal Degrees uses a decimal (base-10) system expressing coordinates as decimal fractions of degrees. DMS format: 40° 26' 46" N. Decimal format: 40.446111°. Decimal degrees are easier for calculations and computer processing, while DMS is traditional and used in navigation charts.

How do I convert latitude and longitude from DMS to decimal?

Use the formula: Decimal Degrees = Degrees + (Minutes/60) + (Seconds/3600). For example, to convert 40° 26' 46" N: DD = 40 + (26/60) + (46/3600) = 40 + 0.4333 + 0.0128 = 40.446111°. If the direction is South or West, make the result negative. Apply this formula separately to latitude and longitude coordinates.

Why do some coordinates have negative values?

In decimal degree format, negative values indicate direction: negative latitude values represent South hemisphere (below the equator), and negative longitude values represent West of the Prime Meridian. For example, Sydney, Australia is at -33.8688° latitude (South) and 151.2093° longitude (East). This sign convention eliminates the need for N/S/E/W direction indicators while maintaining full geographic information.

Can minutes and seconds be greater than 60 in DMS format?

No, minutes and seconds must be less than 60 in proper DMS format. If you encounter values of 60 or greater, they need to be converted: 60 seconds = 1 minute, and 60 minutes = 1 degree. For example, 40° 62' 15" is incorrect and should be written as 41° 2' 15". This is similar to time measurement where 60 seconds make a minute and 60 minutes make an hour.

How accurate are GPS coordinates in DMS vs decimal degrees?

The accuracy is equivalent between formats - it depends on the precision of the numbers, not the format itself. In DMS, using decimal seconds (e.g., 46.0128") provides the same precision as more decimal places in DD format. Consumer GPS devices typically provide accuracy of ±3-5 meters, which corresponds to about 0.00003-0.00005° in decimal degrees or 0.1-0.2 seconds in DMS format. The choice of format doesn't affect the underlying measurement accuracy.

Which coordinate format should I use for my application?

Use decimal degrees for software development, scientific calculations, GIS applications, and database storage because they simplify mathematical operations. Use DMS format for aviation, maritime navigation, traditional surveying, legal property descriptions, and when compatibility with navigation charts is required. Many modern applications support both formats, allowing users to choose based on preference or context.

How do I handle coordinate conversion for the Prime Meridian and Equator?

Locations exactly on the Equator have 0° latitude, and locations on the Prime Meridian have 0° longitude. These coordinates convert the same way: 0° 0' 0" = 0.0°. Locations west of the Prime Meridian use negative longitude or West designation, and locations east use positive or East. Similarly, locations south of the Equator use negative latitude or South designation. The conversion formula remains the same for all locations including these reference lines.

What is DDM format and how does it relate to DMS and DD?

DDM (Degrees Decimal Minutes) is a hybrid format between DMS and DD. It expresses coordinates as degrees and decimal minutes, omitting seconds. For example: 40° 26.7667'. To convert DDM to DD, use: DD = Degrees + (Decimal Minutes/60). To convert DMS to DDM, first convert seconds to decimal minutes: DDM Minutes = Minutes + (Seconds/60). Many marine GPS units use DDM format as a compromise between traditional DMS and modern DD formats.

How many decimal places should I use in decimal degrees?

Use 6 decimal places for most applications, providing precision of about 11 centimeters. For general GPS navigation, 4-5 decimal places (11-1.1 meters) suffice. For survey-grade accuracy, use 7-8 decimal places (1-11 millimeters). For city-level precision, 2-3 decimal places are adequate. Avoid excessive precision that exceeds your measurement device's actual accuracy - consumer GPS cannot deliver millimeter precision even if you use 8 decimal places.

Can I convert coordinates using Excel or spreadsheet formulas?

Yes, you can easily convert coordinates in Excel. For DMS to DD: =Degrees+(Minutes/60)+(Seconds/3600). For DD to DMS degrees: =INT(ABS(DecimalDegrees)). For minutes: =INT((ABS(DecimalDegrees)-INT(ABS(DecimalDegrees)))*60). For seconds: =((ABS(DecimalDegrees)-INT(ABS(DecimalDegrees)))*60-INT((ABS(DecimalDegrees)-INT(ABS(DecimalDegrees)))*60))*60. Replace cell references with your data cells. These formulas handle the mathematical conversion accurately for large datasets.

Historical Context

Origin of DMS System

The Degrees, Minutes, Seconds system originated with ancient Babylonian astronomers around 2400 BCE. They developed a sexagesimal (base-60) number system that proved remarkably effective for astronomical calculations and angular measurements. This system persisted through Greek and Arabic astronomy, eventually becoming the international standard for geographic coordinates.

Development of Decimal Degrees

Decimal degrees gained prominence with the advent of computers and digital mapping in the late 20th century. The decimal system simplified programming calculations and database storage, eliminating the need for complex base-60 arithmetic. GPS technology, introduced in the 1980s and opened for civilian use in 2000, accelerated adoption of decimal degrees as the standard format for electronic navigation.

Modern Usage

Today, both formats coexist with specific applications preferring each. Aviation and maritime operations maintain DMS for compatibility with existing charts and international standards. Digital mapping, GIS software, and mobile applications predominantly use decimal degrees for computational efficiency. Professional surveyors may use either format depending on local regulations and client requirements.