Angle Unit Converter: Convert Between DMS, Decimal Degrees, Radians, and Grads
Convert angle measurements instantly between different units. Our calculator handles Degrees-Minutes-Seconds (DMS), Decimal Degrees, Radians, and Grads (Gradians) with precision.
Angle Unit Converter Tool
Degrees
Minutes
Seconds
Grade
Centigrade
Centicentigrade
Radians
Decimal Degrees
Common Angle Unit Conversions
Degree-Based Conversions
- 1 degree = 60 minutes
- 1 minute = 60 seconds
- 1 degree = 3600 seconds
- 1° = 0.0174533 radians
- 1° = 1.11111 grads
Other Unit Conversions
- 1 radian = 57.2958 degrees
- 1 radian = 63.662 grads
- 1 grad = 0.9 degrees
- 1 grad = 0.015708 radians
Understanding Angle Units
Degrees, Minutes, Seconds (DMS)
Degrees (°)
The most common unit for measuring angles. A full circle is 360 degrees.
Minutes (′)
One-sixtieth of a degree. Used for more precise measurements.
Seconds (″)
One-sixtieth of a minute, or 1/3600 of a degree. Used for very precise measurements.
Decimal Degrees
A decimal representation of degrees, commonly used in digital systems and calculations. For example, 30°30′ would be 30.5°.
Radians (rad)
The standard unit in mathematics and physics. One radian is the angle formed when the arc length equals the radius. A full circle is 2π radians.
Grads (Gradians)
A metric unit where a full circle is 400 grads. Each right angle is 100 grads.
Common Applications
- Navigation: DMS format is commonly used in GPS and navigation
- Mathematics: Radians are preferred in calculus and advanced mathematics
- Surveying: Both DMS and decimal degrees are used in land surveying
- Engineering: Decimal degrees and radians are common in engineering calculations
- Military: Mils and grads are used in some military applications
Frequently Asked Questions
Why are there different angle measurement systems?
Different angle units evolved for different purposes. Degrees are intuitive for everyday use, radians are natural for mathematics, and grads were developed for decimal-based calculations.
When should I use DMS vs. decimal degrees?
DMS is traditionally used in navigation and surveying, while decimal degrees are preferred in computer applications and calculations. Both represent the same angles in different formats.
Why do mathematicians prefer radians?
Radians are the natural unit for calculus and advanced mathematics because they simplify many formulas and make relationships between circular motion and trigonometric functions more apparent.