Angle Converter - Convert Degrees, Radians, Gradians & More Units
Result:
1 ° = 0.01745329 rad
How Angle Conversion Works
Input Angle
Enter angle value
Convert to Degrees
Use conversion factor
Convert to Target
Apply target factor
Angle Conversion Formulas
Common Conversions
Degrees to Radians: rad = deg × (π/180)
Radians to Degrees: deg = rad × (180/π)
Degrees to Gradians: grad = deg × (10/9)
Gradians to Degrees: deg = grad × (9/10)
Key Constants
π (Pi): 3.14159265359
Full Circle: 360° = 2π rad = 400 grad
Right Angle: 90° = π/2 rad = 100 grad
Straight Angle: 180° = π rad = 200 grad
Angle Conversion Table
| Degrees | Radians | Gradians | Turns |
|---|---|---|---|
| 0° | 0.0000 | 0.00 | 0.0000 |
| 15° | 0.2618 | 16.67 | 0.0417 |
| 30° | 0.5236 | 33.33 | 0.0833 |
| 45° | 0.7854 | 50.00 | 0.1250 |
| 60° | 1.0472 | 66.67 | 0.1667 |
| 90° | 1.5708 | 100.00 | 0.2500 |
| 120° | 2.0944 | 133.33 | 0.3333 |
| 135° | 2.3562 | 150.00 | 0.3750 |
| 150° | 2.6180 | 166.67 | 0.4167 |
| 180° | 3.1416 | 200.00 | 0.5000 |
| 210° | 3.6652 | 233.33 | 0.5833 |
| 270° | 4.7124 | 300.00 | 0.7500 |
| 300° | 5.2360 | 333.33 | 0.8333 |
| 330° | 5.7596 | 366.67 | 0.9167 |
| 360° | 6.2832 | 400.00 | 1.0000 |
Angle Units Progression Chart
30°
45°
60°
90°
180°
360°
Practice Problems
Problem 1:
Convert 45° to radians
Solution: 45 × (π/180) = π/4 = 0.7854 rad
Problem 2:
Convert π/3 rad to degrees
Solution: (π/3) × (180/π) = 60°
Problem 3:
Convert 100 gradians to degrees
Solution: 100 × (9/10) = 90°
Problem 4:
Convert 0.25 turns to degrees
Solution: 0.25 × 360 = 90°
Problem 5:
Convert 120° to gradians
Solution: 120 × (10/9) = 133.33 grad
Daily Uses of Angle Conversion
Navigation systems convert compass bearings for GPS coordinates
Engineers calculate structural angles for building construction
Photographers adjust camera angles for perfect shot composition
Astronomers measure celestial object positions in the sky
Game developers program character rotation and movement angles
Export Options
What is an Angle?
An angle is the space between two lines that meet at a point. Think of it like opening a door - the wider you open it, the bigger the angle becomes. We measure angles to know exactly how much space is between these lines.
Angles are everywhere in our daily life. When you turn a steering wheel, adjust a laptop screen, or even slice a pizza, you are working with angles. Understanding angles helps us build things, navigate places, and solve many practical problems.
Common Angle Types
- • Right angle: 90 degrees (like a corner of a square)
- • Straight angle: 180 degrees (like a straight line)
- • Full circle: 360 degrees (complete rotation)
- • Acute angle: Less than 90 degrees
- • Obtuse angle: More than 90 but less than 180 degrees
Why Convert Angles?
- • Different fields use different units
- • Math problems often need radians
- • Engineering uses degrees mostly
- • Navigation systems use various units
- • International standards require conversions
Understanding Different Angle Units
Degrees (°)
Degrees are the most common way to measure angles. A full circle has 360 degrees. This system is very old and easy to understand.
Example: A right angle is 90°, half circle is 180°
Radians (rad)
Radians are used in advanced math and science. One radian is about 57.3 degrees. A full circle has 2π radians.
Example: π/2 radians = 90°, π radians = 180°
Gradians (grad)
Gradians divide a circle into 400 parts. This makes some calculations easier because 100 gradians = 90 degrees.
Example: Right angle = 100 grad, full circle = 400 grad
Turns
A turn is one complete rotation. It's simple - 1 turn = 360 degrees. Half turn = 180 degrees.
Example: Quarter turn = 0.25 turns = 90°
Minutes & Seconds
These are tiny parts of degrees. 1 degree = 60 minutes. 1 minute = 60 seconds. Used for very precise measurements.
Example: 30' = 30 minutes = 0.5°
Milliradians
Very small angle units used in military and surveying. 1 milliradian = 0.001 radians. Useful for long-distance measurements.
Example: 1000 mrad ≈ 57.3°
How to Convert Angles Step by Step
Method 1: Degrees to Radians
- Take your angle in degrees
- Multiply by π (3.14159)
- Divide by 180
- The result is in radians
Example: 90° × π ÷ 180 = 1.57 radians
Method 2: Radians to Degrees
- Take your angle in radians
- Multiply by 180
- Divide by π (3.14159)
- The result is in degrees
Example: π/2 × 180 ÷ π = 90°
Method 3: Degrees to Gradians
- Take your angle in degrees
- Multiply by 10
- Divide by 9
- The result is in gradians
Example: 90° × 10 ÷ 9 = 100 gradians
Real-World Uses of Angle Conversion
In Technology
- •Computer graphics use radians for smooth animations and rotations
- •GPS systems convert between different angle formats for accurate navigation
- •Robotics engineers program robot movements using precise angle calculations
- •Video game developers create realistic physics using angle conversions
In Daily Life
- •Carpenters measure angles when cutting wood for furniture and buildings
- •Photographers adjust camera angles for better composition and lighting
- •Athletes analyze body angles to improve their performance in sports
- •Architects design buildings with specific angles for stability and beauty
Common Mistakes to Avoid
❌ Common Errors
- • Forgetting to use π (pi) when converting to/from radians
- • Mixing up the conversion formulas
- • Using wrong calculator mode (degrees vs radians)
- • Not checking if the answer makes sense
- • Rounding too early in multi-step calculations
✅ Helpful Tips
- • Remember: π radians = 180 degrees
- • Use our calculator to double-check your work
- • Learn common angles: 30°, 45°, 60°, 90°
- • Practice with simple examples first
- • Keep more decimal places until the final answer
Frequently Asked Questions
Why do we need different angle units?
Different fields use different units because they work better for specific tasks. Degrees are easy to understand and visualize. Radians make math calculations simpler. Gradians divide circles into neat 100-unit quarters. Each unit has its place and purpose.
Which angle unit should I use?
Use degrees for everyday measurements and basic geometry. Use radians for advanced math, physics, and engineering. Use gradians for surveying and some European measurements. The choice depends on your field and what others in your area commonly use.
How accurate is this angle converter?
Our converter uses precise mathematical formulas and shows results up to 8 decimal places. This is more than enough accuracy for most practical uses. For scientific work requiring extreme precision, always verify with specialized software.
Can I convert negative angles?
Yes! Negative angles represent rotation in the opposite direction. Our converter handles negative values correctly. A negative angle simply means you're measuring clockwise instead of counterclockwise.
What's the difference between degrees and radians?
Degrees divide a circle into 360 equal parts - this is arbitrary but traditional. Radians are based on the circle's radius and are more natural for mathematics. One radian is the angle where the arc length equals the radius length.