DMS Calculations: Convert Degrees, Minutes, Seconds | CalcNova
Degree, Minute, Second (DMS) Calculations
To convert decimal degrees to DMS, keep the whole degrees, multiply the decimal by 60 for minutes, then multiply the leftover decimal by 60 for seconds. For example, 37.4625° is 37°27′45″. This guide also covers DMS to decimal, adding angles and the Casio key.
What DMS notation means
DMS splits an angle into degrees (°), minutes (′) and seconds (″). One degree is 60 minutes and one minute is 60 seconds, so one degree is 3,600 seconds. This is the same base-60 idea as hours, minutes and seconds on a clock. Maps, surveying and navigation often use DMS; most formulas use decimal degrees.
Decimal degrees to DMS
- The whole number is the degrees.
- Multiply the decimal part by 60. The whole number of that result is the minutes.
- Multiply the remaining decimal part by 60. That is the seconds.
Example: 37.4625°. Degrees = 37. Then 0.4625 × 60 = 27.75, so minutes = 27. Then 0.75 × 60 = 45, so seconds = 45. Answer: 37°27′45″.
DMS to decimal degrees
Use: decimal = degrees + minutes/60 + seconds/3600.
Example: 12°34′56″. 34/60 = 0.56667 and 56/3600 = 0.01556, so the angle is 12 + 0.56667 + 0.01556 = 12.58222° (rounded to five decimal places).
Adding and subtracting angles
Add each column, then carry: 60 seconds become 1 minute, 60 minutes become 1 degree.
Example: 1°45′30″ + 2°20′40″. Degrees: 1 + 2 = 3. Minutes: 45 + 20 = 65. Seconds: 30 + 40 = 70. Carry 70″ as 1′10″, giving 66′. Carry 66′ as 1°6′. Total: 4°6′10″.
For subtraction, borrow the other way: 1° becomes 60′ and 1′ becomes 60″. Example: 5°10′20″ − 2°30′45″. Borrow to get 4°69′80″ − 2°30′45″ = 2°39′35″.
Doing it on a Casio calculator
Casio’s fx-991ES PLUS manual includes a section titled “Degree, Minute, Second (Sexagesimal) Calculations”, so the feature exists on that model. Casio scientific calculators have a dedicated key marked °′″ used to type DMS values: enter the degrees, press the key, enter the minutes, press it again, enter the seconds and press it a third time. Pressing the same key on a displayed result converts it into DMS form, and the result toggles between decimal and DMS.
Exact key paths can differ between the fx-991ES PLUS, fx-991EX and fx-991CW, so confirm against your model’s manual and test with the examples above. A known answer such as 1.5° = 1°30′0″ is a good check.
The CalcNova online calculator has no DMS key. Convert by hand using the formulas above, or enter the decimal-degree value into the calculator.
Common mistakes
- Treating 0.5° as 50′. Half a degree is 30′.
- Forgetting to carry when seconds or minutes reach 60.
- Computing trig on a DMS value while the angle unit is set to radians.
- Rounding minutes too early; keep decimals until the final step.
Frequently asked questions
- How many seconds are in a degree?
- 3,600.
- Is DMS the same as degrees, minutes, seconds of latitude?
- Yes. Latitude and longitude are often written in DMS, such as 40°26′46″.
- How do I check my conversion?
- Convert back. 37°27′45″ → 37 + 27/60 + 45/3600 = 37.4625°.