Degrees, Minutes, Seconds Calculator
Convert angles accurately between decimal degrees and degrees – minutes – seconds notation.
Angle input
Live result
Conversion detail
| Component | Entered value | Contribution in degrees | Running total |
|---|---|---|---|
| Degrees | 103° | 103.00000000° | 103.00000000° |
| Minutes | 44′ | 0.73333333° | 103.73333333° |
| Seconds | 12″ | 0.00333333° | 103.73666667° |
How to use the degrees, minutes, seconds calculator
What this calculator does
This calculator converts a plane angle between decimal degrees and degrees – minutes – seconds (DMS). It is useful when coordinates, bearings, surveying notes, astronomy records, or mapping tools use different angle formats. The conversion is an exact base-60 identity apart from your chosen display precision; it does not transform coordinate datums, project map coordinates, or determine a physical location.
When to use it
Use it to rewrite a latitude or longitude before entering it into mapping software, to translate a survey bearing into a spreadsheet-friendly decimal value, to check a hand conversion, or to prepare a consistent coordinate list. NOAA's Coordinate Conversion and Transformation Tool also demonstrates that professional geodetic workflows commonly accept both decimal-degree and DMS formats.
How to calculate
- The calculator opens with the demonstration angle 103° 44′ 12″ and an immediately available Excel workbook. Choose DMS to decimal or Decimal to DMS.
- For DMS input, replace Degrees, Minutes, and Seconds. For decimal input, enter one signed Decimal degrees value. Results update as you type.
- Read the primary conversion, the total arcminutes and arcseconds, the normalized DMS form, and the row-by-row conversion detail.
- Select Download Excel to export the current validated model. Select Reset to clear the demonstration data; export is then disabled until a complete valid angle is entered again.
Input guide
Conversion direction is required and selects the active formula. Degrees accepts a finite signed number, such as 103 or – 73. The sign applies to the entire DMS angle, so keep Minutes and Seconds nonnegative. Minutes is required in DMS mode and must be at least 0 and less than 60; 44 is a valid example. Seconds is also required, may include decimals, and must be at least 0 and less than 60; 12 or 31.2 are valid. Do not enter 60 in either field – normalize it by carrying one unit into the next larger component. Decimal degrees is required in decimal mode and accepts a finite signed decimal such as – 73.985656. Commas, scientific notation, unit words, and mixed DMS symbols are intentionally rejected to avoid ambiguous parsing.
Output guide
Decimal degrees is the signed angle expressed as one base-10 number. DMS angle is the same value split into degrees, minutes, and seconds, with seconds rounded for display and carried correctly if rounding reaches 60. Total arcminutes equals the angle magnitude multiplied by 60 while preserving its sign. Total arcseconds equals the angle multiplied by 3,600. Normalized DMS always keeps minutes and seconds within 0 – 59.999..., making it suitable for clean data entry. The conversion-detail table shows each component, its degree contribution, and the running total. These outputs are exact conversions, not estimates.
Worked example
The startup values are 103 degrees, 44 minutes, and 12 seconds. Apply the identity decimal degrees = degrees + minutes ÷ 60 + seconds ÷ 3600: 103 + 44/60 + 12/3600 = 103 + 0.7333333333 + 0.0033333333 = 103.73666667° at eight displayed decimal places. The same angle contains 6,224.2 arcminutes and 373,452 arcseconds. NIST explains the conventional symbols for degree, minute, and second of plane angle, including the no-space style used in compact notation.
Understanding DMS notation
A degree is divided into 60 arcminutes, and each arcminute is divided into 60 arcseconds. The prime symbol (′) marks arcminutes and the double-prime symbol (″) marks arcseconds; these are angle units, not time units, even though the base-60 structure is similar. For geographic coordinates, the sign convention matters: north and east are commonly positive, while south and west are commonly negative when decimal degrees are used. Some systems instead use a hemisphere letter, so confirm the target format before pasting data.
At Earth's surface, an angular second corresponds to a real distance that varies by direction and latitude. The USGS explanation of degree, minute, and second map distances gives practical scale examples. This calculator only changes notation; it does not account for Earth shape, longitude convergence, elevation, or a map projection.
Formula and sign handling
For a nonnegative DMS angle, add the three contributions directly. For a negative DMS angle, the sign belongs to the whole angle: – (degrees magnitude + minutes/60 + seconds/3600). The interface follows the common convention that the Degrees field carries the sign while Minutes and Seconds remain nonnegative. When converting back, the whole-degree part is taken from the magnitude, the remaining fraction is multiplied by 60 for minutes, and the remaining minute fraction is multiplied by 60 for seconds.
Common mistakes
Do not treat 44 minutes as 0.44 degrees; it is 44/60 degrees. Do not place a negative sign on minutes or seconds. Avoid copying typographic symbols into numeric fields, because a value such as 44′ is intentionally rejected – the adjacent unit marker already supplies the meaning. Finally, remember that changing coordinate notation does not change the underlying datum. NOAA's latitude – longitude service documentation distinguishes accepted DMS and decimal-degree formats in a geodetic context.