Degrees Minutes Seconds (DMS) Converter Formula

Understand the math behind the degrees minutes seconds (dms) converter. Each variable explained with a worked example.

Use the Degrees Minutes Seconds (DMS) Converter

Formulas Used

Deg Part

deg_part = floor(abs(decimal_deg))

Min Part

min_part = floor(mod(abs(decimal_deg) * 60, 60))

Sec Part

sec_part = mod(abs(decimal_deg) * 3600, 60)

Radians

radians = decimal_deg * pi / 180

Variables

VariableDescriptionDefault
decimal_degDecimal Degrees(deg)45.7625

How It Works

Degrees, Minutes, Seconds (DMS)

Conversion

1 degree = 60 minutes = 3600 seconds

Decimal to DMS

1. Degrees = integer part of the decimal 2. Multiply the fractional part by 60 → Minutes = integer part 3. Multiply the remaining fraction by 60 → Seconds

Example: 45.7625°

  • Degrees: 45
  • 0.7625 × 60 = 45.75 → Minutes: 45
  • 0.75 × 60 = 45 → Seconds: 45
  • Result: 45° 45' 45"

    • Worked Example

    Convert 45.7625° to DMS.

    decimal_deg = 45.7625
    1. 01Degrees = floor(45.7625) = 45°
    2. 02Remaining = 0.7625 × 60 = 45.75
    3. 03Minutes = 45'
    4. 04Remaining = 0.75 × 60 = 45
    5. 05Seconds = 45"
    6. 06Result: 45° 45' 45"

    Frequently Asked Questions

    What is DMS format?

    DMS stands for degrees, minutes, seconds. One degree has 60 minutes, and one minute has 60 seconds. It is used in navigation, cartography, and astronomy.

    How do I convert DMS back to decimal?

    Decimal = Degrees + Minutes/60 + Seconds/3600. For example, 45° 30' 0" = 45 + 30/60 = 45.5°.

    Where is DMS format used?

    DMS is commonly used for GPS coordinates, maps, astronomy, and surveying. Decimal degrees are more common in computations and digital mapping.

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