Angle Converter
The Angle Converter on this page lets you instantly convert between 14 different units of angle measurement, including degrees, radians, gradians, minutes, seconds, and more. Whether you're working on geometry problems, surveying land, programming graphics, or navigating by celestial coordinates, this tool provides accurate conversions with a single click. Simply enter your value and select the units you want to convert from and to. The converter supports both decimal and fractional inputs, making it versatile for students, engineers, and hobbyists alike. No more manual calculations or memorizing conversion factors—just fast, reliable results.
How the Angle Converter Works
This converter uses precise mathematical relationships between angle units. For example, one full circle equals 360 degrees, 2π radians, 400 gradians, or 6400 mils. When you enter a value, the tool first converts it to a standard base unit (usually radians) and then multiplies by the appropriate factor to get the target unit. All conversions are based on internationally accepted definitions, ensuring accuracy to several decimal places.
Common Angle Units Explained
Understanding the units helps you choose the right one for your task:
- Degree (°) – The most familiar unit, with 360° in a full circle. Used in geometry, navigation, and everyday measurements.
- Radian (rad) – The SI unit, where 2π rad = 360°. Essential in calculus, physics, and trigonometry.
- Gradian (gon or ^g) – Divides a circle into 400 parts. Common in surveying and some European engineering.
- Mil (mil) – Used in military and shooting sports, with 6400 mils per circle (NATO standard).
- Minute (') and Second (") – Subdivisions of a degree: 1° = 60', 1' = 60". Used in astronomy and cartography.
Real-World Examples with Actual Numbers
Let's see the converter in action:
- Convert 90 degrees to radians: 90° × (π/180) = 1.5708 rad (π/2).
- Convert 1 radian to degrees: 1 rad × (180/π) ≈ 57.2958°.
- Convert 200 gradians to degrees: 200 gon × (360/400) = 180°.
- Convert 1 minute to degrees: 1' ÷ 60 = 0.0166667°.
- Convert 1 revolution to radians: 1 r × 2π = 6.2832 rad.
Common Mistakes to Avoid
Angle conversion errors often come from mixing units or forgetting key constants:
- Confusing degrees with radians – A common error in trigonometry. Always check if your calculator is in degree or radian mode.
- Using wrong conversion factors – For example, 1 gradian is not 1 degree; it's 0.9°.
- Forgetting minute/second subdivisions – 1 minute is 1/60 of a degree, not 1/100.
- Mixing mil standards – The NATO mil (6400 per circle) differs from the Soviet mil (6000 per circle). This converter uses NATO mils.
Everyday Uses for Angle Conversion
Angle conversion appears in many practical scenarios:
- Navigation – Converting between degrees and radians for GPS coordinates or bearing calculations.
- Construction – Using gradians for precise slope measurements in road building.
- Astronomy – Converting arcminutes and arcseconds to degrees for telescope pointing.
- Game development – Switching between degrees and radians for rotation functions in code.
- Shooting sports – Adjusting scopes in mils or minutes of angle (MOA).
For quick conversions between the two most common units, try our radians to degrees or degrees to radians dedicated tools.
Frequently Asked Questions
How do I convert 45 degrees to radians using this converter?
Enter '45' in the input field, select 'degree (°)' as the source unit, and choose 'radian (rad)' as the target unit. The result will be approximately 0.7854 rad (π/4).
What is the difference between a gradian and a degree?
A gradian (also called gon) divides a circle into 400 equal parts, while a degree divides it into 360 parts. So 1 gradian = 0.9 degrees, and 100 gradians = 90 degrees.
Can I convert minutes and seconds directly to radians?
Yes. First convert minutes and seconds to decimal degrees (1' = 1/60°, 1" = 1/3600°), then use the converter to change degrees to radians. Alternatively, you can enter the value in degrees with decimal places.
Why are there 6400 mils in a circle?
The NATO mil system uses 6400 mils because it provides a convenient approximation: 1 mil subtends about 1 meter at 1000 meters distance. This makes it useful for artillery and rifle scopes.
What is a 'sign' in angle measurement?
A 'sign' is an old unit equal to 30 degrees (1/12 of a circle). It was historically used in astrology and astronomy. For example, each zodiac sign spans 30 degrees of the ecliptic.
Complete List of Units for Conversion
- degree [°] (Base Unit)
- circle = 1 circle = 360.0 degree (circle to degree, degree to circle)
- gon [gon] = 1 gon = 0.9 degree (gon to degree, degree to gon)
- grad [^g] = 1 grad = 0.9 degree (grad to degree, degree to grad)
- mil [mil] = 1 mil = 0.05625 degree (mil to degree, degree to mil)
- minute ['] = 1 minute = 0.016667 degree (minute to degree, degree to minute)
- quadrant = 1 quadrant = 90.0 degree (quadrant to degree, degree to quadrant)
- radian [rad] = 1 radian = 57.29578 degree (radian to degree, degree to radian)
- revolution [r] = 1 revolution = 360.0 degree (revolution to degree, degree to revolution)
- right angle = 1 right angle = 90.0 degree (right angle to degree, degree to right angle)
- second ["] = 1 second = 0.000278 degree (second to degree, degree to second)
- sextant = 1 sextant = 60.0 degree (sextant to degree, degree to sextant)
- sign [sign] = 1 sign = 30.0 degree (sign to degree, degree to sign)
- turn = 1 turn = 360.0 degree (turn to degree, degree to turn)