Angle Converter – Convert Between All Angle Units

Angle Converter

Convert between 15+ angle units including degrees, radians, gradians, minutes, seconds, and more.

Angle Conversion Calculator

Enter Value

From Unit

To Unit

Converting…

Conversion Result

Converted Value

Conversion Formula

1 ° = 1 °

Conversion Steps

Unit Details

Degree

Symbol:

Conversion Factor:

1 degree

A degree is a unit of angular measurement equal to 1/360 of a full rotation or circle. It is the most commonly used unit for measuring angles in everyday applications.

Radian

Symbol:

rad

Conversion Factor:

57.2957795131 degrees

A radian is the SI unit of angular measurement, defined as the angle subtended at the center of a circle by an arc equal in length to the radius. One radian equals approximately 57.3 degrees.

About Angle Conversion

History of Angle Measurement

Angle measurement has been essential to human civilization since ancient times. Early astronomers and mathematicians developed various systems to measure angles for navigation, construction, and astronomical observations. The Babylonians are credited with dividing the circle into 360 degrees, a system that remains widely used today.

The concept of radians emerged much later, in the 18th century, as mathematicians sought a more natural way to relate angles to the geometry of circles. Radians are now the standard unit in mathematics and physics because they simplify many formulas and calculations.

Understanding Angle Units

Angle units can be categorized into several systems:

Degrees: The most familiar unit, dividing a full circle into 360 equal parts.
Radians: The SI unit, based on the radius of a circle. A full circle equals 2π radians.
Gradians/Gons: A decimal system dividing a circle into 400 parts, developed in France during the metric revolution.
Minutes and Seconds: Subdivisions of degrees, where 1 degree = 60 minutes and 1 minute = 60 seconds.
Revolution-based Units: Including revolutions, turns, circles, and other units that represent full or partial rotations.

Practical Applications of Angle Conversion

Angle conversion is essential in numerous fields and everyday situations:

Engineering and Construction: Converting between different angle units for design specifications and manufacturing.
Navigation: Converting bearings and headings between different measurement systems.
Astronomy: Converting celestial coordinates for telescope positioning and calculations.
Mathematics and Physics: Converting angles for trigonometric calculations and wave analysis.
Computer Graphics: Converting angles for 3D modeling, animation, and game development.

How to Use This Converter

Our angle converter tool allows you to convert between 15 different angle units quickly and accurately. Simply enter the value you want to convert, select the original unit, choose the target unit, and click the Convert button. The tool will display the converted value, the conversion formula used, and step-by-step calculations showing how the conversion was performed.

This converter is particularly useful for students, engineers, scientists, navigators, and anyone who needs to work with different angle units. All conversions are based on the latest international standards to ensure accuracy.

Frequently Asked Questions

What is the relationship between degrees and radians?

The relationship between degrees and radians is defined by the fact that a full circle equals 360 degrees or 2π radians. Therefore, 1 radian equals approximately 57.2958 degrees, and 1 degree equals π/180 radians or approximately 0.0174533 radians.

Why are there 360 degrees in a circle?

The division of a circle into 360 degrees originated with the ancient Babylonians. They used a sexagesimal (base-60) number system and likely chose 360 because it has many divisors, making it convenient for calculations. Additionally, 360 is close to the number of days in a year, which may have influenced their choice.

What is a gradian and how does it compare to degrees?

A gradian (also called a gon) is a unit of angular measurement that divides a right angle into 100 parts. A full circle equals 400 gradians. One gradian equals 0.9 degrees. This system was developed in France during the metric revolution as a decimal alternative to degrees, but it never gained widespread acceptance outside of surveying in some European countries.

How do I convert degrees to minutes and seconds?

To convert degrees to minutes and seconds, first multiply the decimal part by 60 to get minutes. Then take the decimal part of the minutes and multiply by 60 to get seconds. For example, 45.75 degrees equals 45 degrees, 45 minutes, and 0 seconds (0.75 × 60 = 45 minutes).

What is the difference between a revolution and a radian?

A revolution represents a full rotation around a circle, equal to 360 degrees or 2π radians. A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. One revolution equals approximately 6.2832 radians (2π).

What is a mil and how is it used?

A mil is a unit of angular measurement used primarily in military contexts. There are different definitions: a NATO mil equals 1/6400 of a circle, while a Soviet mil equals 1/6000 of a circle. In our converter, we use the definition where 1 mil equals 0.05625 degrees (1/6400 of a circle).

How many radians are in a right angle?

A right angle equals π/2 radians, which is approximately 1.5708 radians. Since a full circle is 2π radians and a right angle is 1/4 of a circle, the calculation is (2π)/4 = π/2 radians.

What is a sextant and how does it relate to angle measurement?

A sextant is both a navigational instrument and a unit of angle measurement. As a unit, one sextant equals 60 degrees, which is 1/6 of a full circle. The instrument, also called a sextant, is used to measure the angle between two visible objects, typically for celestial navigation.

Why do mathematicians prefer radians over degrees?

Mathematicians prefer radians because they simplify many mathematical formulas. For example, the derivative of sin(x) is cos(x) only when x is in radians. Radians also make the formulas for arc length and sector area simpler: arc length = rθ and area = (1/2)r²θ, where θ is in radians.

How do I convert between gradians and degrees?

To convert from gradians to degrees, multiply by 0.9. To convert from degrees to gradians, multiply by 10/9 or approximately 1.1111. For example, 100 gradians equals 90 degrees, and 90 degrees equals 100 gradians.

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