Angle converter

Metric Conversions.

Angle converter

Select the unit you wish to convert from


The angle converter is a tool for anyone working with angles in various fields such as mathematics, engineering, and physics. It allows for easy conversion between different units of angle measurement, ensuring accuracy and consistency in calculations and data analysis.

The angle converter supports a wide range of units, including degrees, radians, gradians, minutes, and seconds. With just a few clicks, users can effortlessly convert angles from one unit to another, saving time and effort. This tool is particularly useful when working with angles in different contexts or when collaborating with individuals who use different units of measurement.

For example, if you have an angle measured in degrees and need to convert it to radians, simply enter the value in the degrees field and select radians as the desired unit. The angle converter will instantly provide you with the equivalent value in radians. This feature is especially handy when dealing with trigonometric functions that often require angles to be expressed in radians.

Units of Angle

The most commonly used unit of angle is the degree (°), which divides a circle into 360 equal parts. However, the site also covers other units such as radians (rad), which are widely used in mathematics and physics. Radians are based on the radius of a circle and are defined as the angle subtended by an arc equal in length to the radius. This unit is particularly useful in trigonometry and calculus.

In addition to degrees and radians, the site also covers other units of angle, including gradians (gon) and minutes/seconds of arc. Gradians divide a circle into 400 equal parts, making calculations involving right angles more straightforward. Minutes and seconds of arc are smaller units of angle that are commonly used in navigation and astronomy.

Variations of Milliradians

Milliradians, also known as mils, are a unit of measurement commonly used in military and engineering applications to express small angles. One milliradian is equal to one-thousandth of a radian, which is approximately 0.057 degrees. The milliradian system is advantageous because it allows for easy and precise calculations when dealing with angular measurements.

There are variations of milliradians that are used in different contexts. One such variation is the NATO mil, which is commonly used by military forces. The NATO mil divides a circle into 6,400 equal parts, with each part representing one NATO mil. This system is particularly useful for artillery and long-range shooting, as it allows for accurate adjustments in aiming and target acquisition.

Another of these variations is the Swedish mil, also known as the artillery mil. In this system, a circle is divided into 6,000 equal parts, with each part representing one Swedish mil. The Swedish mil is often used in artillery and fire control systems, providing a precise and standardized unit for angular measurements.

About Degrees

Degrees (symbol: °) are a unit of measurement used to quantify angles in geometry and trigonometry. An angle is formed when two lines or rays intersect, and degrees are used to measure the amount of rotation between these lines or rays. The concept of degrees dates back to ancient civilizations, with the Babylonians being credited with the development of the sexagesimal system, which divided a circle into 360 equal parts.

In the sexagesimal system, a full circle is divided into 360 degrees, with each degree further divided into 60 minutes (symbol: '). Each minute is then divided into 60 seconds (symbol: "). This system allows for precise measurement of angles, with smaller units providing greater accuracy. Degrees are commonly used in various fields, including mathematics, physics, engineering, and navigation.

Degrees are a versatile unit of measurement, allowing for easy conversion between different angular units. For example, radians, another commonly used unit for measuring angles, can be converted to degrees by multiplying the value by 180/π (approximately 57.3°). Similarly, degrees can be converted to radians by multiplying the value by π/180. This flexibility makes degrees a convenient choice for expressing angles in everyday life and scientific calculations.

About Radians

Radians are a unit of measurement used in mathematics and physics to quantify angles. Unlike degrees, which divide a circle into 360 equal parts, radians divide a circle into 2π (approximately 6.28) equal parts. This unit is particularly useful in trigonometry and calculus, as it simplifies many mathematical calculations involving angles.

The concept of radians is based on the relationship between the length of an arc and the radius of a circle. One radian is defined as the angle subtended by an arc that is equal in length to the radius of the circle. In other words, if we were to take a circle with a radius of 1 unit and measure an arc along its circumference that is also 1 unit long, the angle formed at the center of the circle would be 1 radian.

Radians are advantageous because they allow for more straightforward calculations involving angles in trigonometric functions and calculus. Many mathematical formulas and equations involving angles become simpler when expressed in radians. Additionally, radians are dimensionless, meaning they do not have any units associated with them. This property makes it easier to perform calculations and conversions involving angles in various systems of measurement.

About Gradians

Gradians, also known as gons or grads, divide a circle into 400 equal parts. This means that a right angle is equal to 100 gradians, a full circle is 400 gradians, and so on. Gradians were introduced as an alternative to degrees and radians, aiming to provide a more convenient and decimal-based system for measuring angles.

While gradians are not as commonly used as degrees or radians, they do have their applications. For example, they are often used in surveying and navigation, where angles need to be measured and calculated with high precision. Additionally, gradians can be easily converted to degrees or radians, making them a versatile unit of measurement.

While radians are the standard unit for measuring angles in mathematics and physics, gradians offer an alternative system that can be useful in specific fields. Whether it's for precise measurements in surveying or for converting between different angle units, gradians provide a decimal-based approach to quantifying angles.