The DMS Calculator is a tool used to convert between different angular measurement formats, such as Degrees, Minutes, and Seconds (DMS), Decimal Degrees, Radians, and Gradians. This calculator helps professionals, students, and hobbyists accurately convert angles for navigation, surveying, astronomy, and engineering applications.
Formulas DMS Calculator
Decimal Degrees to DMS
Degrees = Floor(Decimal Degrees)
Minutes = Floor((Decimal Degrees - Degrees) × 60)
Seconds = ((Decimal Degrees - Degrees) × 60 - Minutes) × 60Where:
Floor()represents the integer part of a decimal numberDecimal Degreesis the angle in decimal form (e.g., 45.5°)Degreesis the whole degree valueMinutesranges from 0 to 59Secondsranges from 0 to 59.999...
DMS to Decimal Degrees
Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)Where:
Degreesis the whole degree valueMinutesranges from 0 to 59Secondsranges from 0 to 59.999...Decimal Degreesis the resulting angle in decimal form
Radians to DMS
Decimal Degrees = Radians × (180 / π)Then apply Decimal Degrees to DMS conversion.
DMS to Radians
Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)
Radians = Decimal Degrees × (π / 180)Where:
π (pi)is approximately 3.14159265359Radiansis the angle in radian form
Gradians to DMS
Decimal Degrees = Gradians × (9 / 10)Then apply Decimal Degrees to DMS conversion.
DMS to Gradians
Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)
Gradians = Decimal Degrees × (10 / 9)Where:
Gradiansis the angle in gradian form (400 gradians in a full circle)
Conversion Table for Quick Reference
| Measurement Type | Formula | Example |
|---|---|---|
| Decimal to DMS | Degrees = Floor(Decimal) Minutes = Floor((Decimal - Degrees) × 60) Seconds = ((Decimal - Degrees) × 60 - Minutes) × 60 | 45.75° = 45° 45' 00" |
| DMS to Decimal | Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600) | 45° 45' 00" = 45.75° |
| Radians to DMS | Decimal Degrees = Radians × (180 / π) | 1 rad = 57.2958° |
| DMS to Radians | Radians = Decimal Degrees × (π / 180) | 180° = π rad |
| Gradians to DMS | Decimal Degrees = Gradians × (9 / 10) | 100 grad = 90° |
| DMS to Gradians | Gradians = Decimal Degrees × (10 / 9) | 90° = 100 grad |
Example of DMS Calculator
Convert 48.2564° to DMS
Degrees = Floor(48.2564) = 48°
Minutes = Floor((48.2564 - 48) × 60) = 15'
Seconds = ((48.2564 - 48) × 60 - 15) × 60 = 23.04"
Result: 48° 15' 23.04"Most Common FAQs
DMS notation is commonly used in navigation, surveying, and astronomy because it provides a more precise and understandable format for angles, particularly when measuring land or celestial bodies.
The conversion is highly accurate as long as all calculations maintain precision up to at least six decimal places, which is standard for scientific applications.
Yes, the DMS Calculator can convert GPS coordinates between DMS and Decimal Degrees formats, which is essential for mapping and navigation applications.