DMS Calculator

By Calxy · Calculation methodology

Convert an angle or a latitude/longitude between decimal degrees and degrees-minutes-seconds (D° M′ S″), including negative values and hemisphere letters.

Printed from Calxy · https://www.calxy.net/math/dms-calculator

Degrees, minutes, seconds40° 26′ 46.30″
°

Negative values are south latitude, west longitude or a negative angle.

0 – 6

Degrees, minutes, seconds

40° 26′ 46.30″

  • Degrees and decimal minutes40° 26.7717′
  • Total arcseconds145,606.302000 ″
  • Radians0.70591927

Minutes and seconds here are arc units: 1° = 60′ and 1′ = 60″.

How this was calculated

Degrees = whole part of 40.446195 = 40°.

Minutes = 0.446195 × 60 = 26.7717 → 26′.

Seconds = 0.7717 × 60 = 46.302″, rounded to 2 decimal places.

Formulas

One degree is 60 arcminutes and one arcminute is 60 arcseconds. To go from DMS to decimal degrees: DD = D + M ÷ 60 + S ÷ 3600.

To go the other way, the whole part is the degrees. Multiply the remaining fraction by 60: the whole part is the minutes. Multiply that fraction by 60 again to get the seconds.

Worked example

40.446195°: the degrees are 40. 0.446195 × 60 = 26.7717, so the minutes are 26. 0.7717 × 60 = 46.302, so the seconds are 46.30″ to two decimals. The result is 40° 26′ 46.30″ N as a latitude.

Going back, 40 + 26 ÷ 60 + 46.302 ÷ 3600 = 40.446195°. A longitude of −73.9857° becomes 73° 59′ 8.52″ W.

Signs, hemispheres and rounding

Signed decimal degrees use positive values for north and east and negative values for south and west. Latitude must be within ±90° and longitude within ±180°; plain angles have no limit.

Rounding the seconds can reach 60. The calculator rounds on a whole grid of seconds first, so 10.9999999° shows as 11° 0′ 0.00″ rather than 10° 59′ 60.00″.

How to use the DMS Calculator

Pick the direction and value type, then enter the angle.

  1. Choose the direction

    Convert decimal degrees to DMS, or DMS to decimal degrees.

  2. Choose the value type

    Pick angle, latitude (N/S) or longitude (E/W).

  3. Enter the value

    Type decimal degrees, or degrees, minutes, seconds and the hemisphere.

  4. Read the result

    See the converted value, degrees and decimal minutes, and the steps.

References

Frequently asked questions

How do I convert decimal degrees to DMS?

Take the whole number as degrees, multiply the decimal part by 60 for minutes, then multiply the leftover decimal of the minutes by 60 for seconds.

Is a negative latitude south?

Yes. Negative latitude is south of the equator and negative longitude is west of the prime meridian, so −33.8° is 33.8° S.

How precise are the seconds?

Choose 0 to 6 decimal places. At the equator one arcsecond of latitude is about 31 meters, so two decimal places resolve roughly 30 cm.

Last updated . Results are estimates for informational purposes only.