Degrees Minutes Seconds Calculator
Geometry & trigFreeNo sign-up
One degree is 60 minutes and one minute is 60 seconds. To convert 40.7484°: 0.7484 × 60 = 44.904′, and 0.904 × 60 = 54.24″, so 40.7484° = 40° 44′ 54.24″. Going back: degrees + minutes ÷ 60 + seconds ÷ 3600.
Negative for south or west.
| DMS | 40° 44′ 54.24″ |
| Compact | 40°44′54.24″ |
| Decimal degrees | 40.7484° |
| Radians | 0.7111937449 |
| Total arcseconds | 146,694.24″ |
| Total arcminutes | 2,444.904′ |
Show steps
- Degrees = whole part: 40°.
- Minutes = (decimal part) × 60 = 0.7484 × 60 = 44.904 → 44′.
- Seconds = (decimal part of the minutes) × 60 = 0.904 × 60 = 54.24″.
How to use the DMS calculator
- Choose the direction of the conversion.
- Enter decimal degrees, or degrees, minutes and seconds. Use a negative degree value for south latitudes and west longitudes.
- Press Convert to see the result with the working, radians and arcseconds.
Formulas
- Decimal → DMS: D = whole degrees; M = whole part of (decimal part × 60); S = (remaining decimal × 60).
- DMS → decimal: \(D + \frac{M}{60} + \frac{S}{3600}\)
1° = 60′ (minutes) = 3,600″ (seconds).
GPS coordinates
Latitude runs from −90° to 90° (negative = south); longitude from −180° to 180° (negative = west). The Empire State Building is at about 40.7484° N, 73.9857° W, which is 40° 44′ 54.24″ N, 73° 59′ 8.52″ W. On the ground, 1″ of latitude is about 31 m.
Adding and subtracting DMS angles
Add degrees, minutes and seconds separately, then carry: every 60″ becomes 1′ and every 60′ becomes 1°. Example: 25° 40′ 50″ + 10° 30′ 20″ = 35° 70′ 70″ = 36° 11′ 10″.
Degrees, minutes and seconds quiz: 10 questions
Test yourself with 10 multiple-choice questions. Choose an answer and press Submit to see if you are right and why. Your score appears at the end.
Quiz complete
Frequently asked questions
How do I convert decimal degrees to DMS?
The whole number is the degrees. Multiply the decimal part by 60: the whole number is the minutes. Multiply the remaining decimal by 60 to get the seconds.
How do I convert DMS to decimal degrees?
Add degrees + minutes ÷ 60 + seconds ÷ 3600. Keep the sign of the degrees for south or west.
What do the symbols ′ and ″ mean?
′ is minutes of arc and ″ is seconds of arc, not feet and inches.
How accurate is a GPS coordinate in seconds?
One second of latitude is about 31 meters, so 0.01″ is about 31 centimeters.
Can I enter negative coordinates?
Yes. A negative degree value gives a negative (south or west) decimal result, and the minutes and seconds stay positive.
Sources
Related calculators
- Degrees to Radians Calculator
- Coterminal Angle Calculator
- Time Calculator
- Unit Converter
- Quadrant Calculator
More geometry & trig calculators
Related to This Article
More math articles
- How to Find Slope? (+FREE Worksheet!)
- How to Write Inequalities from Number Lines?
- How to Read Your Paycheck: Gross, Net & Every Deduction
- 10 Most Common ATI TEAS 7 Math Questions
- Structural Reform: The Sixteenth and Seventeenth Amendments
- How to Identify Errors Involving the Order of Operations?
- Difference Quotient Calculator (Free)
- House of Representatives
- Best AI Math Solver for Students: Why StudyX Should Be Your Go-To Study Buddy
- FREE 5th Grade MAP Math Practice Test
What people say about "Degrees Minutes Seconds Calculator: DMS to Decimal and Back"?
No one replied yet.