Convert between various angle measurement units instantly. From degrees to radians, gradians to milliradians - all with precision and accuracy for mathematics, engineering, and navigation.
Formula: rad = deg × (π / 180)
Formula: deg = rad × (180 / π)
Formula: grad = deg × (10 / 9)
Formula: deg = grad × (9 / 10)
Formula: mrad = deg × (π / 180) × 1000
Formula: deg = mrad / 1000 × (180 / π)
Formula: grad = rad × (200 / π)
Formula: rad = grad × (π / 200)
Angles are fundamental measurements in mathematics, physics, engineering, navigation, and countless other fields. Understanding how to convert between different angle units is essential for professionals and students alike. This comprehensive angle converter supports the most commonly used angular units worldwide, providing instant and accurate conversions for all your calculation needs.
Degrees are the most widely recognized unit for measuring angles, dating back to ancient Babylonian mathematics. A complete circle contains 360 degrees, a convention that has endured for millennia. This system is particularly intuitive because 360 has many divisors, making it easy to work with fractions of a circle. A right angle measures 90 degrees, a straight line represents 180 degrees, and common angles like 30, 45, and 60 degrees appear frequently in geometry and everyday applications from construction to graphic design.
Radians are the standard unit of angular measure in mathematics and physics. One radian is defined as the angle subtended at the center of a circle by an arc equal in length to the radius. A complete circle measures 2π radians (approximately 6.28318 radians). Radians simplify many mathematical formulas, particularly in calculus and trigonometry. For example, the derivative of sin(x) equals cos(x) only when x is measured in radians. Most scientific calculators and programming languages default to radians for trigonometric functions.
Gradians (also called gons or grades) divide a right angle into 100 equal parts, making a full circle 400 gradians. This metric-compatible system was developed during the French Revolution as part of the metric system. Gradians are particularly useful in surveying and civil engineering in Europe and other regions using metric measurements. The decimal nature of gradians makes certain calculations more straightforward, especially when working with percentages of angles or slope calculations.
Milliradians (mrad) are one-thousandth of a radian and are extensively used in military applications, ballistics, and precision targeting. The practical advantage of milliradians is that at 1000 meters distance, 1 milliradian subtends approximately 1 meter. This makes range estimation and trajectory calculations intuitive. Military scopes, artillery systems, and precision optics commonly use milliradian measurements for their angular adjustments.