Decimal Degrees to Degrees Minutes Seconds Calculator

The formulas are: degrees = the whole number part; minutes = the whole number part of (decimal part × 60); seconds = (the remaining decimal of the minutes) × 60.

Worked example: 12.345° → 12°, then 0.345 × 60 = 20.7 → 20′, then 0.7 × 60 = 42″, giving 12° 20′ 42″.

Many calculators return angles in decimal degrees: the Arctangent Calculator, the Arcsine Calculator, and the Rectangular to Polar Coordinates Calculator all do, and this page turns those results into degrees, minutes, and seconds.

1. Take the whole number as the degrees: 40.7128° gives 40°.
2. Multiply the decimal part by 60: 0.7128 × 60 = 42.768, so the minutes are 42′.
3. Multiply the remaining decimal by 60: 0.768 × 60 = 46.08, so the seconds are 46.08″.
4. Combine them and add the direction: 40° 42′ 46.08″ N.

Latitude and Longitude Converter for GPS Coordinates

For a coordinate, choose Latitude or Longitude above so the result ends in N, S, E, or W. Write latitude first, as Google Maps expects. Use either a minus sign or a direction letter, never both: 33° 52′ 7.68″ S is already south, so it takes no minus. A latitude must be between -90 and 90 and a longitude between -180 and 180, and the calculator flags anything outside that range. A few well known city coordinates, converted:

Decimal Degrees to DMS in Excel

With the decimal value in cell A1, use one formula per part:

• Degrees: =TRUNC(A1)
• Minutes: =INT(MOD(ABS(A1),1)*60)
• Seconds: =ROUND(MOD(ABS(A1)*60,1)*60,2)

Use TRUNC rather than INT for the degrees: INT rounds down, so INT(-30.51) gives -31 instead of -30. For a value between 0 and -1, TRUNC returns 0, so add the minus sign, or S or W, by hand. If the seconds round up to 60, add one to the minutes and set the seconds to 0.

Latitude measures distance north or south of the equator. It starts at 0° on the equator and rises to 90° at the North and South Poles, and its lines, called parallels, run east to west and stay evenly spaced.

Longitude measures distance east or west of the prime meridian. Its lines, called meridians, run from pole to pole, sit farthest apart at the equator, and meet at the poles. Longitude runs to 180° east or west. Both are traditionally written in degrees, minutes, and seconds, which is why this conversion comes up so often.

Common decimal values and their DMS equivalents:

Latitude and longitude are traditionally written in degrees, minutes, and seconds, while software and spreadsheets work with one decimal number per coordinate, so readings move back and forth between the two. Official records can use DMS too: the US FCC, for example, publishes its own converter for broadcast station coordinates. For the reverse, from a DMS reading back to one decimal number, use the companion converter below.

For angles that wrap past 360° or go negative, the Coterminal Angle Calculator finds the equivalent angle between 0° and 360°, and the Sector Area Calculator uses a decimal degree angle to work out an arc length.

Every converter in the angle family, starting with the reverse of this one:

• DMS to Decimal Degrees Calculator: turn 30° 30′ 36″ back into 30.51°
• Degrees to Radians Converter: multiply by π/180
• Degrees to Arcminutes Converter: 1° = 60 arcminutes
• Degrees to Arcseconds Converter: 1° = 3,600 arcseconds
• Angle Converter: every angle unit at once, including gradians, turns, and milliradians