Angle Converter
Instantly convert between Degrees, Radians, Gradians, and Arc Minutes. Includes advanced Trigonometry dashboard and Unit Circle visualizer.
Converter
Standard unit (360° = 1 Circle)
Current Formula
Enter a value to see the conversion formula.
Quick Reference
- π Radians180°
- 1 Full Circle360°
- 1 Gradian0.9°
- 1 Right Angle90°
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Master Geometry & Trigonometry
An angle measures the amount of turn between two lines meeting at a common point. While Degrees (360°) are common in daily life, Radians are essential for advanced math and physics. Our Angle Converter bridges these worlds instantly, visualized on a live Unit Circle.
Live Trigonometry
Instantly calculate Sin, Cos, Tan, Csc, Sec, and Cot values for any angle. Perfect for checking homework or physics problems.
Unit Circle Visualizer
See exactly where your angle lands. Our interactive Unit Circle shows the quadrant, coordinates (x,y), and rotation.
Precision Units
Need extreme accuracy? Convert down to Arc Minutes and Arc Seconds, or use Milliradians for ballistics.
Trigonometry Cheat Sheet
Standard Angles (Degrees)
- 0° sin=0, cos=1, tan=0
- 30° sin=0.5, cos=√3/2, tan=√3/3
- 45° sin=√2/2, cos=√2/2, tan=1
- 60° sin=√3/2, cos=0.5, tan=√3
- 90° sin=1, cos=0, tan=Undef
Standard Angles (Radians)
- 0 sin=0, cos=1, tan=0
- π/6 sin=0.5, cos=√3/2, tan=√3/3
- π/4 sin=√2/2, cos=√2/2, tan=1
- π/3 sin=√3/2, cos=0.5, tan=√3
- π/2 sin=1, cos=0, tan=Undef
Understanding Units
- Degrees (°)The most common unit. A full circle is 360°, arbitrarily chosen by ancient Babylonians (likely due to their 360-day calendar).
- Radians (rad)The SI unit for angles. It links the angle to the radius of a circle. A full circle is exactly 2π radians (approx 6.283).
- Gradians (grad)A metric attempt to decimalize angles. A right angle is 100 grads (vs 90°), making a full circle 400 grads.
Common Conversions
| Angle | Degrees | Radians |
|---|---|---|
| Full Circle | 360° | 2π (≈6.28) |
| Straight Line | 180° | π (≈3.14) |
| Right Angle | 90° | π/2 (≈1.57) |
| 45 Degree | 45° | π/4 (≈0.785) |
Common Pitfalls
- •Calculator Mode: The #1 reason for math errors is having your calculator in 'Rad' mode when you mean 'Deg', or vice versa.
- •Mixing Units: Never subtract Radians from Degrees without converting first. 180 - 3.14 is NOT ~177 degrees; it's nonsense.
Pro Tips
- •Memorize PI: Knowing that π ≈ 3.14159 helps you quickly estimate if a Radian answer looks right. 2 Rads should be around 114°.
- •Use Gradians for Slopes: In some engineering fields, gradians are easier because 100 grad = vertical, making percentages intuitive.
Frequently Asked Questions
How do I convert Degrees to Radians?
To convert Degrees to Radians, multiply the angle by π/180 (approximately 0.01745). For example, 180° × π/180 = π radians.
Why do we use Radians instead of Degrees?
Radians are the standard unit in mathematics and physics because they relate the angle directly to the arc length of a circle (Arc Length = Radius × Angle in Radians). This simplifies many calculus formulas.
What is a Gradian (gon)?
A Gradian is a unit where a right angle (90°) is defined as 100 gradians. This metric system attempt makes a full circle 400 gradians, simplifying calculations for land surveying.
What is a Reference Angle?
A Reference Angle is the smallest acute angle (less than 90°) formed by the terminal side of an angle and the x-axis. It is always positive and useful for finding trigonometric values.
What form coterminal angles?
Coterminal angles are angles that share the same initial and terminal sides. You can find them by adding or subtracting multiples of 360° (or 2π radians) to your original angle.
How do I use this tool for Excel formulas?
Excel uses Radians for trig functions. If you have degrees, use =RADIANS(angle) before using functions like =SIN(). Our tool converts these instantly so you can verify your Excel results.
What are Arc Minutes and Arc Seconds?
These are precision units used in astronomy and navigation. One degree is divided into 60 Arc Minutes ('), and one Arc Minute is divided into 60 Arc Seconds (").
What is a Milliradian (mrad)?
A Milliradian is 1/1000th of a radian. It is widely used in military scopes and artillery because 1 mrad subtends exactly 1 meter at a distance of 1000 meters.
How many degrees is 1 Radian?
1 Radian is approximately 57.2958 degrees. It is the angle formed when the arc length is equal to the radius of the circle.
Can I convert negative angles?
Yes, our tool supports negative angles. A negative angle represents clockwise rotation. The tool will also calculate the positive coterminal angle for you automatically.
Why is 360 degrees a full circle?
It is believed to come from ancient Babylonian astronomy. Their calendar had ~360 days, so the sun moved about 1 degree per day against the stars.
Does this tool work for Gaming rotations?
Yes! Game engines like Unity and Unreal use both Degrees (for Inspector) and Quaternions/Radians (for code). Use this tool to visualize the conversions.