Degrees Minutes Seconds (DMS) Calculator
Convert any angle between decimal degrees (DD), degrees-minutes-seconds (DMS), and degrees-decimal-minutes (DMM) instantly. Choose a conversion mode, enter your values, and get every format at once - plus total minutes, total seconds, and a step-by-step breakdown of the math. A DMS arithmetic mode lets you add or subtract two angles directly in DMS format.
What are degrees, minutes, and seconds?
A full circle contains 360 degrees. Each degree is divided into 60 arc-minutes (written with a single prime, like 23'), and each arc-minute is divided into 60 arc-seconds (written with a double prime, like 31.20"). So one degree equals 3,600 arc-seconds. This sexagesimal (base-60) system was inherited from ancient Babylonian mathematics and is still the standard for geographic coordinates, surveying, astronomy, and navigation. A GPS fix reported as 47° 23' 31.20" N means 47 whole degrees north, plus 23 minutes, plus 31.20 seconds - all three numbers together pinpoint the exact location.
How to convert decimal degrees to DMS
Start with your decimal degree value, for example 47.392. The whole number part (47) is your degrees. Multiply the decimal part (0.392) by 60 to get 23.52 - the whole part (23) is your minutes. Multiply the remaining decimal (0.52) by 60 to get 31.2 - this is your seconds. So 47.392° = 47° 23' 31.20". Going the other way (DMS to DD): divide minutes by 60, divide seconds by 3600, then add all three parts. For 103° 44' 12": DD = 103 + (44/60) + (12/3600) = 103 + 0.73333 + 0.00333 = 103.73667°.
Degrees-Decimal-Minutes (DMM) format
Some GPS devices and nautical charts use a hybrid format called Degrees Decimal Minutes (DMM or DDM), where degrees are whole numbers but minutes include a decimal fraction. For example, 47.392° becomes 47° 23.5200' in DMM. The NMEA sentences that GPS hardware outputs ($GPGLL, $GPGGA) use this format - the latitude field reads as DDMM.MMMM, meaning the first two digits are degrees and the rest are decimal minutes. If you are entering coordinates into a GPS unit or reading a chart, check which format it expects before entering values.
Adding and subtracting DMS angles
You cannot add 47° 23' 31" and 103° 44' 12" by simply adding columns the way you would with decimals, because seconds and minutes cap at 60, not 100. Instead, add the seconds column (31 + 12 = 43"), then the minutes column (23 + 44 = 67' - but 67' = 1° 7', so carry 1° and keep 7'), then the degrees column (47 + 103 + 1 carried = 151°). Result: 151° 7' 43". The arithmetic mode in this calculator handles all the carrying and borrowing automatically, including negative results when the minuend is smaller than the subtrahend.
Common angle reference values
| Angle description | Decimal Degrees (DD) | DMS | DMM |
|---|---|---|---|
| Right angle | 90° | 90° 0' 0" | 90° 0.0000' |
| Straight angle | 180° | 180° 0' 0" | 180° 0.0000' |
| Full rotation | 360° | 360° 0' 0" | 360° 0.0000' |
| 45 degrees | 45° | 45° 0' 0" | 45° 0.0000' |
| 30 degrees | 30° | 30° 0' 0" | 30° 0.0000' |
| 1 minute of arc | 0.016667° | 0° 1' 0" | 0° 1.0000' |
| 1 second of arc | 0.000278° | 0° 0' 1" | 0° 0.0167' |
| GPS precision example | 47.392° | 47° 23' 31.20" | 47° 23.5200' |
| Negative coordinate | -33.8688° | -33° 52' 7.68" | -33° 52.1280' |
Well-known angles expressed in all three formats. Use these to sanity-check your conversions.
Frequently asked questions
What is the difference between arc-minutes and time-minutes?
Arc-minutes are a measure of angle (1/60 of a degree), while time-minutes measure duration (1/60 of an hour). Although both subdivide their parent unit by 60 and share the same name, they are completely different quantities. In astronomy, the sky rotates 15 arc-degrees per time-hour (since 360 degrees / 24 hours = 15°/h), so 1 arc-minute corresponds to 4 time-seconds of apparent rotation - but that relationship is specific to the rotation rate of Earth and does not generalize.
Why do GPS coordinates use DMS?
DMS (and its cousin DMM) became the standard long before digital calculators made decimal degrees easy to work with. Mariners, surveyors, and astronomers all used paper tables and manual instruments that were natively calibrated in degrees, minutes, and seconds. That convention was baked into nautical charts, astronomy catalogs, and international standards. Today most software accepts both formats, but DMS remains preferred for human-readable coordinate display on maps, and decimal degrees are preferred for numeric computation.
How precise is one arc-second?
One arc-second of latitude on the Earth's surface is approximately 31 meters (about 101 feet). One arc-minute is roughly 1,852 meters - which is exactly how the nautical mile is defined. Consumer GPS receivers are typically accurate to about 3-5 meters, which corresponds to roughly 0.0001° or about 0.36 arc-seconds. When you see coordinates reported to 4 or 5 decimal places in decimal degrees, or to 2-3 decimal places in the seconds field of DMS, that level of detail is meaningful for navigation and survey work.
Can I enter negative angles?
Yes. Negative angles appear in two contexts: angles measured clockwise from a reference (such as bearing angles or negative longitudes in the Western Hemisphere), and angles below the horizontal (like negative declinations in astronomy). In DMS notation, the negative sign applies to the degrees value. For example, Sydney, Australia has a longitude of approximately 151.2093° E and a latitude of -33.8688° S (or 33° 52' 7.68" S). This calculator handles negative inputs in DD mode and negative degree entries in DMS mode.
How do I convert DMS to radians?
First convert DMS to decimal degrees using this calculator, then multiply the decimal degree result by pi/180 (approximately 0.017453293). For example, 47° 23' 31.20" = 47.392° in decimal degrees. Multiplying by pi/180 gives about 0.82726 radians. Radians are used in mathematics and physics; degrees (decimal or DMS) are used in navigation and geography.
Why does my seconds value sometimes exceed 59.9999?
Floating-point arithmetic can introduce tiny rounding errors when converting back and forth. For example, 60.000000000001 seconds would technically be invalid (60 seconds = 1 minute), but the error is below any meaningful precision threshold. This calculator normalizes the result so seconds always stay below 60 and any overflow carries into minutes, then degrees. If you notice a value of exactly 60 in a seconds field, it is a rounding edge case - the true value is 0 seconds with 1 extra minute carried.