The formula is: Decimal Degrees = Degrees + Minutes/60 + Seconds/3600.

For example: 30°15'50" = 30 + 15/60 + 50/3600 = 30 + 0.25 + 0.013888... = 30.263889°.

For negative angles, the degrees portion carries the sign: −30°15'50" = −(30 + 15/60 + 50/3600) = −30.263889°.

Use our converter above — simply enter your DMS values and the decimal degree result updates instantly.

Step 1: Take the integer part as Degrees.

Step 2: Multiply the decimal remainder by 60. The integer part is Minutes.

Step 3: Multiply the new decimal remainder by 60. This gives Seconds.

Example: 30.263889° → Degrees = 30, remainder = 0.263889 × 60 = 15.83334 → Minutes = 15, remainder = 0.83334 × 60 = 50.0004 → Seconds ≈ 50″. Result: 30°15'50″.

The conversion formula is: Radians = Degrees × π / 180.

Key reference values:

• 180° = π rad ≈ 3.141593 rad
• 90° = π/2 rad ≈ 1.570796 rad
• 45° = π/4 rad ≈ 0.785398 rad
• 60° = π/3 rad ≈ 1.047198 rad
• 30° = π/6 rad ≈ 0.523599 rad
• 360° = 2π rad ≈ 6.283185 rad
• 1° ≈ 0.017453 rad

You can also reverse this: Degrees = Radians × 180 / π.

Due to floating-point arithmetic in computers, converting decimal degrees to DMS can sometimes produce results like 59.999999″ instead of 60″. Our converter handles this by applying smart rounding at your chosen precision level.

If seconds round to 60.000 at your selected precision, the converter automatically carries over: seconds reset to 0, and 1 minute is added. If minutes reach 60, they carry over to degrees. This ensures accurate, clean DMS output.

Tip: Increase the precision setting (e.g., 8–10 decimals) to see the raw calculated values before rounding.

DMS (Degrees-Minutes-Seconds) is a sexagesimal notation that divides each degree into 60 minutes and each minute into 60 seconds. It's commonly used in cartography, navigation, astronomy, and surveying.

Decimal Degrees expresses the angle as a single decimal number (e.g., 34.567890°), which is easier for computation and is the standard format for most software, GPS systems, and APIs.

DMS is more human-readable for precise geographic coordinates (e.g., 40°26'46"N 79°58'56"W), while decimal degrees are preferred for calculations and data storage.

Decimal degree precision and their approximate ground distance at the equator:

• 1 decimal place (0.1°) ≈ 11.1 km
• 2 decimal places (0.01°) ≈ 1.11 km
• 3 decimal places (0.001°) ≈ 111 m
• 4 decimal places (0.0001°) ≈ 11.1 m
• 5 decimal places (0.00001°) ≈ 1.11 m
• 6 decimal places (0.000001°) ≈ 11.1 cm
• 7 decimal places (0.0000001°) ≈ 1.11 cm

For most consumer GPS applications, 5–6 decimal places provide sufficient precision. Surveying and scientific applications may require 7–8 decimal places or more.

A radian is defined as the angle subtended by an arc equal in length to the radius of the circle. Since the circumference of a circle is 2πr, a full circle contains 2π radians (≈ 6.283185 rad), which equals 360°.

Common radian values expressed as π multiples:

• π/6 ≈ 0.523599 rad = 30°
• π/4 ≈ 0.785398 rad = 45°
• π/3 ≈ 1.047198 rad = 60°
• π/2 ≈ 1.570796 rad = 90°
• π ≈ 3.141593 rad = 180°
• 3π/2 ≈ 4.712389 rad = 270°
• 2π ≈ 6.283185 rad = 360°

Our converter automatically detects when the radian value is close to a common π fraction and displays it below the radian input.

Yes! This converter is perfect for geographic coordinates. Latitude ranges from −90° to +90° (or 90°S to 90°N), and longitude ranges from −180° to +180° (or 180°W to 180°E).

For geographic DMS notation, negative degrees correspond to South (latitude) or West (longitude), while positive values correspond to North or East. Example: −33°51'28"S = 33°51'28" South can be entered as −33 in the degrees field.

The converter handles the full range of angles, including values beyond ±360° for multi-turn rotations.

Angle conversion is essential in many fields:

• GPS & Navigation: Converting between DMS coordinates and decimal degrees for maps and devices.
• Engineering & CAD: Precise angle measurements for mechanical design and architecture.
• Astronomy: Celestial coordinates are often given in DMS (Right Ascension, Declination).
• Mathematics & Physics: Radians are the standard unit for trigonometric functions, calculus, and angular velocity calculations.
• Surveying: High-precision DMS measurements for land boundaries and construction.
• Aviation & Maritime: Navigation bearings and course plotting.