Angle Converter
Convert angle measurements between different units quickly and accurately
Angle Conversion Calculator
Popular Angle Conversions
Quickly convert between the most commonly used angle units.
Understanding Angle Measurements
Angle measurement is fundamental in geometry, navigation, and various technical fields. The radian (rad) is the base unit of angle in the International System of Units (SI), while degrees (°) and gradians (grad) are commonly used in different applications. Understanding angle conversions is essential for mathematics, engineering, and navigation.
Common Angle Units
SI Units
- Radian (rad) - Base unit
- Milliradian (mrad) - 1/1000 of a radian
- Degree (°) - π/180 radians
- Minute (') - 1/60 of a degree
Other Units
- Gradian (grad) - 400 gradians = 360°
- Second ('') - 1/60 of a minute
- Turn (rev) - 360° or 2π radians
- Quadrant - 90° or π/2 radians
Common Applications
| Field | Common Units | Typical Uses |
|---|---|---|
| Mathematics | Radians, degrees | Trigonometry, calculus |
| Engineering | Degrees, gradians | Design, construction |
| Navigation | Degrees, compass points | Marine, aviation navigation |
| Astronomy | Degrees, arcminutes, arcseconds | Star positions, telescope pointing |
| Military | Milliradians | Artillery, ballistics |
| Surveying | Gradians, degrees | Land measurement, mapping |
Conversion Tips
- π radians = 180 degrees (exact relationship)
- To convert degrees to radians: multiply by π/180
- To convert radians to degrees: multiply by 180/π
- Gradians are useful in surveying: 100 gradians = 90 degrees
- Milliradians are practical for military use: 1 mrad ≈ 0.057 degrees
- For navigation: 32 compass points = 360 degrees (11.25° per point)
Angle Conversions
| Conversion | Formula | Quick Answer |
|---|---|---|
| degrees to radians | degrees × π/180 | Multiply degrees by 0.017453 |
| radians to degrees | radians × 180/π | Multiply radians by 57.2958 |
| degrees to gradians | degrees × 10/9 | Multiply degrees by 1.1111 |
| gradians to degrees | gradians × 9/10 | Multiply gradians by 0.9 |
| degrees to arcminutes | degrees × 60 | Multiply degrees by 60 |
| arcminutes to degrees | arcminutes ÷ 60 | Divide arcminutes by 60 |
| degrees to arcseconds | degrees × 3600 | Multiply degrees by 3600 |
| arcseconds to degrees | arcseconds ÷ 3600 | Divide arcseconds by 3600 |
| radians to gradians | radians × 200/π | Multiply radians by 63.662 |
| gradians to radians | gradians × π/200 | Multiply gradians by 0.015708 |
Our angle conversion tool provides precise conversions between all common units of angle measurement. Whether you're working in mathematics, engineering, navigation, or astronomy, our converter ensures accuracy for both everyday calculations and precise scientific work.
Angle Conversion Questions
Everything you need to know about angle measurements and conversions
What is the difference between degrees and radians?
Degrees divide a circle into 360 equal parts, while radians are based on the radius of the circle. One radian equals approximately 57.3 degrees. Radians are the standard unit in mathematics and physics because they create simpler formulas in calculus and trigonometry.
What are gradians and when are they used?
Gradians (also called gons) divide a circle into 400 equal parts, making a right angle exactly 100 gradians. They're primarily used in surveying and some European countries because they allow for easier decimal calculations when measuring land and construction angles.
How do I convert between degrees and radians?
To convert degrees to radians: multiply by π/180 (≈ 0.017453). To convert radians to degrees: multiply by 180/π (≈ 57.2958). Remember that π radians = 180 degrees exactly. Common conversions: 30° = π/6 rad, 45° = π/4 rad, 90° = π/2 rad.
What are milliradians and why do militaries use them?
Milliradians (mrad) are 1/1000 of a radian. Military forces use them because they provide a convenient relationship between angle and distance: at 1000 meters, 1 milliradian subtends approximately 1 meter. This makes range estimation and artillery calculations much easier.
How many compass points are in a full circle?
A traditional compass rose has 32 points, making each point equal to 11.25 degrees. The main points are North, Northeast, East, Southeast, South, Southwest, West, and Northwest, with additional half-points and quarter-points for more precise navigation.
What is a turn or revolution?
A turn (also called a revolution) is a complete rotation around a circle, equal to 360 degrees, 2π radians, or 400 gradians. It's useful in engineering and physics when describing rotational motion, gear ratios, or motor speeds.
When should I use different angle units?
Use degrees for everyday measurements and basic geometry, radians for calculus and advanced mathematics, gradians for surveying and construction, milliradians for military applications, and arcminutes/arcseconds for astronomy and precise navigation.
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