Degrees To Radians Converter
Convert angles between degrees and radians, the two most common units in mathematics and physics.
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A Guide to Converting Degrees to Radians
What is a Degrees to Radians Converter?
A Degrees to Radians Converter is a tool for switching between the two primary units of angular measurement: degrees and radians. While degrees are commonly used in everyday life, radians are the standard unit of angular measure in many areas of mathematics and physics, especially in trigonometry and calculus.
- Degree (°): A unit of measure for angles, where a full circle is divided into 360 degrees.
- Radian (rad): An angle's measure in radians is the ratio of the length of a circular arc to the radius of the circle. A full circle is 2π radians.
How to Use the Degrees to Radians Converter
Our converter allows for instant, two-way conversions.
- Enter a value: Input a number into either the "Degrees" or "Radians" field.
- View the result: The other field will automatically update with the converted value.
The Conversion Formula
The conversion is based on the relationship that a full circle is 360° or 2π radians.
$$ 180° = \pi \text{ radians} $$
The formulas are:
$$ \text{Radians} = \text{Degrees} \times \frac{\pi}{180} $$
$$ \text{Degrees} = \text{Radians} \times \frac{180}{\pi} $$
Practical Example: Trigonometry Problem
A student is working on a trigonometry problem that involves the sine of 90°. However, most scientific calculators and programming languages require the angle to be in radians for trigonometric functions.
- Known Value: 90°
- Calculation: Radians = 90 × (π / 180) = π / 2 radians
- Using the calculator: Entering "90" in the degrees field instantly shows approximately 1.5708 (which is π/2) in the radians field.
This conversion is crucial for accuracy in higher mathematics and physics. For other angle conversions, you can use our general Angle Converter or the Degrees to Minutes Converter. To perform arithmetic on angles, the DMS Calculator is a valuable tool.
To learn more about radians and their use in mathematics, you can visit the Khan Academy. For applications in physics, resources like the Physics Tutorials website are very helpful.
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