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Convert between degrees and radians.
Everything you need to know
Angles measure the amount of rotation or the space between two intersecting lines. While we interact with angles daily—from parking a car to adjusting a computer monitor—different scientific and mathematical fields require entirely different units of measurement for these rotations.
The Angle Converter seamlessly translates values between Degrees (used in everyday navigation), Radians (used in higher mathematics and physics), and Gradians (used in some surveying and construction applications).
Converting angles manually requires memorizing irrational numbers like Pi ($\pi$). Our tool does it instantly:
Why do we have so many different ways to measure a circle?
The most common measurement. A full circle is divided into 360 degrees. This system originated in ancient Babylon, likely because their calendar had 360 days in a year, and 360 is easily divisible by many numbers (2, 3, 4, 5, 6, 8, 9, 10, 12, 15, etc.).
The standard unit of angular measure in calculus and physics. One radian is the angle created when the arc length equals the radius of the circle. A full circle is exactly $2\pi$ radians.
1 Full Circle = 360° = 2π rad
Created during the French Revolution to align angles with the metric system (base 100). A right angle is exactly 100 gradians, making a full circle 400 gradians.
If you need to perform the math yourself, use these core formulas:
Multiply the degrees by Pi and divide by 180.
Radians = Degrees * (π / 180)
Multiply the radians by 180 and divide by Pi.
Degrees = Radians * (180 / π)
Scenario 1: Engineering Calculus You are writing a physics simulation and your trigonometric function requires radians, but the user inputted 45 degrees.
45 * (π / 180) = 45 * 0.01745 = 0.7854 Radians
Scenario 2: Surveying Land A European surveyor provides a measurement of 50 gradians, and you need it in standard degrees. Since 100 gradians = 90 degrees:
Degrees = Gradians * 0.9
50 * 0.9 = 45 Degrees
Understanding how to translate between degrees, radians, and gradians is the key to unlocking advanced geometry, programming, and physics. Use this converter to ensure total precision in your angular mathematics.
Disclaimer: While this calculator provides conversions to extremely high decimal precision, standard floating-point computer arithmetic may result in microscopic rounding differences at the 15th decimal place.