Decimal Degrees to Degrees Minutes Seconds Converter

Convert decimal degrees to DMS (Degrees, Minutes, Seconds) format and vice versa. Perfect for GPS coordinates, navigation, surveying, mapping, and geographic data conversion with detailed step-by-step calculations.

Decimal Degrees to DMS Conversion

Enter Decimal Degrees:

DMS Result:

Calculation Steps:

DMS to Decimal Degrees Conversion

Degrees (°):

Minutes ('):

Seconds (""):

Decimal Degrees Result:

Calculation Steps:

Quick Conversion Examples

New York City
40.446111°
→ 40° 26' 46"

London
51.507222°
→ 51° 30' 26"

Paris
48.858333°
→ 48° 51' 30"

Sydney
-33.8688°
→ 33° 52' 7.68" S

Conversion Formulas

Decimal Degrees to DMS Formula

To convert from Decimal Degrees (DD) to Degrees, Minutes, Seconds (DMS) format, follow this sequential extraction process:

Step-by-Step Process:

1. Degrees (D): \(D = \lfloor|\text{DD}|\rfloor\) (integer part of absolute value)

2. Minutes (M): \(M = \lfloor(|\text{DD}| - D) \times 60\rfloor\)

3. Seconds (S): \(S = ((|\text{DD}| - D) \times 60 - M) \times 60\)

4. Direction: Negative DD = South (latitude) or West (longitude)

Example Calculation:

Convert 40.446111° to DMS format:

Step 1 - Degrees: \(D = \lfloor 40.446111 \rfloor = 40°\)
Step 2 - Decimal remainder: \(0.446111 \times 60 = 26.76666\)
Step 3 - Minutes: \(M = \lfloor 26.76666 \rfloor = 26'\)
Step 4 - Decimal remainder: \(0.76666 \times 60 = 46.0\)
Step 5 - Seconds: \(S = 46.0"\)
Result: 40° 26' 46"

DMS to Decimal Degrees Formula

To convert from DMS format to Decimal Degrees, use this straightforward addition formula:

Primary Formula:

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

Where:
• D = Degrees
• M = Minutes
• S = Seconds

Example Calculation:

Convert 51° 30' 26" to decimal degrees:

\[\text{DD} = 51 + \frac{30}{60} + \frac{26}{3600}\]
\[\text{DD} = 51 + 0.5 + 0.007222\]
\[\text{DD} = 51.507222°\]

Conversion Reference Tables

World Cities Coordinate Conversion

City	Decimal Degrees	DMS Format
New York, USA	40.712778°	40° 42' 46" N
London, UK	51.507222°	51° 30' 26" N
Paris, France	48.856667°	48° 51' 24" N
Tokyo, Japan	35.689444°	35° 41' 22" N
Sydney, Australia	-33.867778°	33° 52' 4" S
Dubai, UAE	25.263056°	25° 15' 47" N
Singapore	1.289167°	1° 17' 21" N
Rio de Janeiro, Brazil	-22.908333°	22° 54' 30" S

Decimal to Minutes/Seconds Quick Reference

Decimal	Minutes	Decimal	Seconds
0.0833	5'	0.00278	10"
0.1667	10'	0.00556	20"
0.25	15'	0.00833	30"
0.3333	20'	0.01111	40"
0.5	30'	0.01389	50"
0.75	45'	0.01667	60"

Precision Comparison Table

Format	Example	Precision	Typical Use
DD (2 decimals)	40.45°	~1.1 km	City-level location
DD (4 decimals)	40.4461°	~11 m	Building identification
DD (6 decimals)	40.446111°	~11 cm	Survey markers
DMS (whole seconds)	40° 26' 46"	~31 m	General navigation
DMS (0.1 seconds)	40° 26' 46.0"	~3.1 m	GPS navigation
DMS (0.01 seconds)	40° 26' 46.00"	~31 cm	Professional surveying

Understanding Coordinate Formats

Geographic coordinates use different formats to express location on Earth's surface. The two primary systems—Decimal Degrees and Degrees Minutes Seconds—serve different purposes and audiences, each with distinct advantages.

What is Decimal Degrees (DD) Format?

Decimal Degrees expresses geographic coordinates as decimal fractions of degrees. This format uses base-10 notation, making it compatible with modern computing systems, GPS devices, and mapping software. Example: 40.446111° represents a location's latitude or longitude as a single decimal number.

Decimal Degrees Characteristics:

Compact representation: Single number per coordinate component
Computational efficiency: Direct use in mathematical calculations
Database-friendly: Easy storage and indexing in digital systems
Sign convention: Negative values indicate South (latitude) or West (longitude)
Precision through decimals: More decimal places equal higher accuracy

What is DMS (Degrees Minutes Seconds) Format?

DMS format divides degrees into 60 minutes, and each minute into 60 seconds, following a sexagesimal (base-60) system inherited from ancient Babylonian astronomy. This traditional format appears on navigation charts, survey documents, and property boundaries. Example: 40° 26' 46" N expresses the same location with hierarchical subdivision.

DMS Format Characteristics:

Historical continuity: Standard format for centuries of navigation and surveying
Hierarchical structure: Natural breakdown into progressively finer divisions
Chart compatibility: Matches traditional navigation charts and maps
Legal documentation: Required format for many property descriptions
Direction indicators: Uses N/S/E/W letters instead of positive/negative signs

Why Convert Between Formats?

Different applications, devices, and professional contexts require specific coordinate formats:

GPS devices: Most modern units display coordinates in decimal degrees for simplicity
Navigation charts: Marine and aviation charts predominantly use DMS format
GIS software: Geographic Information Systems work internally with decimal degrees
Surveying: Professional surveyors may use either format based on local standards
Property records: Legal land descriptions often require DMS format
Scientific research: Research papers and databases typically use decimal degrees
Mobile apps: Location-based services use decimal degrees for API integration
Data exchange: Converting between formats enables cross-platform compatibility

Step-by-Step Conversion Guide

Converting Decimal Degrees to DMS

Detailed Method: Sequential Extraction

Step 1: Take the absolute value of the decimal degrees (ignore sign temporarily)

Step 2: Extract degrees by taking the integer part: \(D = \lfloor\text{DD}\rfloor\)

Step 3: Calculate decimal remainder: Remainder₁ = DD - D

Step 4: Multiply remainder by 60 to get decimal minutes

Step 5: Extract minutes by taking the integer part: \(M = \lfloor\text{Remainder₁} \times 60\rfloor\)

Step 6: Calculate second decimal remainder: Remainder₂ = (Remainder₁ × 60) - M

Step 7: Multiply by 60 to get seconds: \(S = \text{Remainder₂} \times 60\)

Step 8: Apply direction based on original sign (negative = S or W)

Detailed Example:

Convert 51.507222° to DMS:

Step 1: Absolute value = 51.507222
Step 2: Degrees = 51
Step 3: Remainder₁ = 51.507222 - 51 = 0.507222
Step 4: Decimal minutes = 0.507222 × 60 = 30.43332
Step 5: Minutes = 30
Step 6: Remainder₂ = 30.43332 - 30 = 0.43332
Step 7: Seconds = 0.43332 × 60 = 25.9992 ≈ 26"
Step 8: Original was positive, so: 51° 30' 26" N (or E)

Converting DMS to Decimal Degrees

Detailed Method: Fractional Addition

Step 1: Identify degrees (D), minutes (M), and seconds (S) components

Step 2: Convert minutes to decimal degrees: \(M_{\text{decimal}} = \frac{M}{60}\)

Step 3: Convert seconds to decimal degrees: \(S_{\text{decimal}} = \frac{S}{3600}\)

Step 4: Add all components: \(\text{DD} = D + M_{\text{decimal}} + S_{\text{decimal}}\)

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

Detailed Example:

Convert 48° 51' 30" N to decimal degrees:

Step 1: D = 48, M = 51, S = 30
Step 2: Minutes in decimal = 51 ÷ 60 = 0.85°
Step 3: Seconds in decimal = 30 ÷ 3600 = 0.008333°
Step 4: Total = 48 + 0.85 + 0.008333 = 48.858333°
Step 5: Direction is North, so: 48.858333° N

Practical Applications

GPS Navigation and Waypoints

Consumer GPS devices and smartphone navigation apps predominantly display coordinates in decimal degrees for simplicity and screen space efficiency. However, users importing waypoints from traditional sources or sharing coordinates with mariners and pilots may need to convert between formats. Understanding both systems ensures accurate position recording and waypoint entry across different navigation platforms.

Geographic Information Systems (GIS)

GIS software like ArcGIS, QGIS, and Google Earth Pro accepts coordinate input in multiple formats but processes data internally using decimal degrees. When importing spatial datasets from various sources, converting all coordinates to a consistent format prevents positioning errors and ensures accurate spatial analysis. The conversion capability supports seamless integration of legacy survey data with modern mapping projects.

Professional Surveying

Land surveyors work with both coordinate formats depending on project requirements, client preferences, and legal documentation standards. Property boundary descriptions in legal documents traditionally use DMS format, while CAD software and modern survey equipment output decimal degrees. Surveyors must convert between formats to maintain workflow continuity from field measurement to final property plat.

Aviation and Marine Navigation

Pilots and mariners use DMS coordinates because aviation sectional charts and nautical charts display latitude and longitude in degrees, minutes, and seconds. However, modern avionics and electronic chart systems may internally calculate using decimal degrees. Flight planning and marine navigation require conversion skills to cross-reference positions between traditional charts and electronic flight bags or chartplotters.

Scientific Research

Researchers collecting spatial data across different instruments and platforms encounter both coordinate formats. Field equipment may output DMS coordinates, while data analysis software and scientific publications require decimal degrees. Converting coordinates to a standardized format ensures dataset compatibility and enables collaborative research across institutions and disciplines.

Real Estate and Property Management

Property records, title documents, and survey certificates often specify boundaries using DMS coordinates for legal precision and historical consistency. Real estate professionals using online mapping tools to visualize properties must convert these coordinates to decimal degrees for input into Google Maps, GIS software, or property management systems.

Precision and Accuracy Considerations

Decimal Places Impact

The number of decimal places in decimal degrees directly determines coordinate precision and real-world accuracy:

Decimal Places	Precision	Real-World Distance	Application
1	0.1°	~11.1 km	Large regions, countries
2	0.01°	~1.1 km	Cities, large features
3	0.001°	~111 m	Neighborhoods
4	0.0001°	~11 m	Individual buildings
5	0.00001°	~1.1 m	Trees, precise positions
6	0.000001°	~11 cm	Survey markers
7	0.0000001°	~1.1 cm	Scientific research
8	0.00000001°	~1.1 mm	Specialized surveying

Seconds Decimal Places in DMS

In DMS format, decimal places in the seconds component provide equivalent precision:

Whole seconds (46"): ≈ 31 meters precision
One decimal (46.0"): ≈ 3.1 meters precision
Two decimals (46.00"): ≈ 31 centimeters precision
Three decimals (46.000"): ≈ 3.1 centimeters precision

Conversion Precision Loss

When converting between formats, rounding at intermediate steps can introduce errors. To maintain precision:

Preserve all decimal places during calculation steps
Round only the final result to required precision
Use appropriate data types (double-precision floating point) in software
Document the precision level in shared coordinate data
Verify conversions by converting back to original format

Tips and Best Practices

For GPS Users

Check device settings: Verify coordinate display format in GPS settings before recording positions
Record full precision: Save coordinates with maximum available decimal places
Note hemisphere: Always record N/S/E/W or verify sign convention
Backup coordinates: Store waypoints in both formats for compatibility
Verify accuracy: Cross-reference critical waypoints with known landmarks

For Programmers and Developers

Use appropriate data types: Double-precision floating point for coordinate storage
Validate inputs: Check that minutes and seconds are within 0-59 range
Handle edge cases: Test with 0°, 180°, ±90° latitude, and both hemispheres
Preserve precision: Avoid intermediate rounding during multi-step conversions
Implement bidirectional conversion: Allow conversion in both directions
Unit test thoroughly: Test with known coordinate pairs to verify accuracy
Document format assumptions: Clearly specify input/output format expectations

For Surveyors

Maintain precision: Use full decimal precision throughout all calculations
Document conversions: Record conversion methods in survey reports
Verify legal descriptions: Ensure converted coordinates match property documents
Consistent datum: Maintain the same geodetic datum (WGS84, NAD83) during conversion
Quality control: Convert coordinates back to original format to verify accuracy
Software calibration: Ensure survey software uses correct conversion algorithms

For Mariners and Pilots

Chart compatibility: Convert waypoints to match chart coordinate format
Double-check positions: Verify critical navigation points in both formats
Electronic system settings: Configure navigation equipment for correct display format
Record conversions: Note original and converted formats in logs
Cross-reference: Compare electronic and paper chart positions

Common Mistakes to Avoid:

• Rounding too early in multi-step conversions, causing precision loss
• Forgetting to convert negative degrees to South/West direction
• Allowing minutes or seconds to equal or exceed 60
• Using incorrect divisors (60 vs 3600) for minutes vs seconds
• Mixing coordinate formats within the same dataset
• Not verifying conversion accuracy through back-conversion
• Dropping direction indicators when converting to/from DMS
• Assuming all applications use the same coordinate format

Frequently Asked Questions

How do I convert decimal degrees to degrees, minutes, and seconds?

Extract the integer part as degrees, multiply the decimal remainder by 60 to get minutes (take the integer part), then multiply the remaining decimal by 60 again to get seconds. For example, 40.446111° becomes: Degrees = 40, then 0.446111 × 60 = 26.76666, so Minutes = 26, then 0.76666 × 60 = 46, so Seconds = 46. Final result: 40° 26' 46". If the original number is negative, the location is South (latitude) or West (longitude).

What's the difference between decimal degrees and DMS format?

Decimal degrees express coordinates as single decimal numbers (e.g., 51.507222°) using base-10 notation, making them ideal for computer calculations. DMS format divides degrees into 60 minutes and each minute into 60 seconds (e.g., 51° 30' 26"), using base-60 notation inherited from ancient astronomy. Decimal degrees are more common in modern GPS and software, while DMS remains standard for navigation charts and legal documents.

How many decimal places should I use for accurate GPS coordinates?

Use 6 decimal places for most applications, providing approximately 11 centimeters of precision. For general GPS navigation, 4-5 decimal places (11 meters to 1.1 meters precision) suffice. Professional surveying requires 6-7 decimal places (11 cm to 1 cm), while scientific research may use 8 decimal places (1 mm). However, don't use more precision than your measurement device can actually deliver—consumer GPS typically provides 3-5 meter accuracy.

Why do some coordinates show negative numbers?

In decimal degree format, negative values indicate direction without requiring N/S/E/W letters. Negative latitude indicates South of the Equator, and negative longitude indicates West of the Prime Meridian. For example, -33.8688° represents a latitude in the Southern Hemisphere. When converting to DMS format, take the absolute value for the conversion and add the appropriate direction letter (S or W) to the result.

Can minutes and seconds exceed 60 in DMS coordinates?

No, proper DMS format requires minutes and seconds to be less than 60. If calculations result in 60 or more, convert to the next higher unit: 60 seconds = 1 minute, and 60 minutes = 1 degree. For example, 40° 63' 15" is incorrect and should be converted to 41° 3' 15". This is similar to time notation where 60 seconds make a minute. Always validate DMS coordinates to ensure minutes and seconds stay in the 0-59 range.

Which coordinate format is better for my application?

Use decimal degrees for software development, databases, GIS applications, scientific research, and any situation requiring mathematical calculations. Use DMS format for aviation navigation, maritime charts, traditional surveying, legal property descriptions, and when compatibility with existing navigation charts is essential. Many modern applications support both formats, allowing users to choose based on context. If interfacing with legacy systems or regulatory requirements, check which format is mandated.

How do I handle coordinates at the Equator or Prime Meridian?

Coordinates exactly on the Equator have 0° latitude, and coordinates on the Prime Meridian have 0° longitude. Convert these the same way: 0° 0' 0" = 0.0°. For locations just east or west of the Prime Meridian, use positive (East) or negative (West) values in decimal degrees, or E/W directions in DMS. Similarly, for locations north or south of the Equator, use positive (North) or negative (South) in decimal degrees, or N/S in DMS. The conversion formulas work identically for zero values.

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

DDM (Degrees Decimal Minutes) is a hybrid format expressing coordinates as degrees and decimal minutes without seconds. For example: 40° 26.7667'. To convert DD to DDM: take integer degrees, then multiply the decimal part by 60 for decimal minutes. To convert DMS to DDM: keep the degrees, then convert seconds to decimal minutes by dividing by 60 and adding to minutes. Many marine GPS units use DDM as a compromise between traditional DMS and modern DD formats.

How accurate are coordinate conversions between DD and DMS?

Conversions between DD and DMS are mathematically exact when proper precision is maintained. Accuracy depends on how many decimal places you preserve during conversion. If you convert 40.446111° to 40° 26' 46" and back, you should get 40.446111° again. However, premature rounding or limiting decimal places introduces error. To maintain accuracy, use at least 6-8 decimal places in intermediate calculations and round only the final result to your required precision level.

Can I convert coordinates using Excel or Google Sheets?

Yes. For DD to DMS: Degrees = INT(ABS(A1)), Minutes = INT((ABS(A1)-INT(ABS(A1)))*60), Seconds = ((ABS(A1)-INT(ABS(A1)))*60-INT((ABS(A1)-INT(ABS(A1)))*60))*60. For DMS to DD: =D1+(M1/60)+(S1/3600), where D1, M1, and S1 are cells containing degrees, minutes, and seconds. Apply negative sign if direction is S or W. These formulas handle the arithmetic accurately for large datasets and can be copied down for batch conversion.

Historical Context

Origin of Sexagesimal System

The DMS format traces its origins to ancient Babylonian mathematics and astronomy around 2400 BCE. Babylonians developed a base-60 (sexagesimal) 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 and time measurement.

Adoption of Decimal Degrees

Decimal degrees gained prominence with the digital revolution and the development of GPS technology. The Global Positioning System, launched by the U.S. Department of Defense in the 1970s and opened for civilian use in 2000, accelerated the adoption of decimal notation. Computer systems naturally process base-10 decimals more efficiently than base-60 calculations, leading to widespread adoption in GIS software, mapping applications, and location-based services.

Modern Coexistence

Today, both formats serve distinct purposes. Aviation and maritime operations maintain DMS for compatibility with international charts and regulations. Digital mapping, GPS devices, and scientific research predominantly use decimal degrees. Professional surveyors may use either format depending on project requirements, local standards, and client preferences. Understanding both systems remains essential for professionals working across traditional and modern mapping domains.