Convert degrees to radians
Please provide values below to convert deg to rad, or vice versa.
Convert degrees to radians
The degrees to radians converter helps you quickly convert angle values from degrees (°) to radians (rad). This is useful in mathematics, geometry, trigonometry, engineering, physics, computer graphics, and many technical applications where radians are commonly used instead of degrees.
Degrees are a familiar way to measure angles in daily life. For example, a full circle is 360 degrees. Radians, however, are often preferred in mathematics and science because they are directly related to the geometry of a circle and make many formulas easier to use. Converting degrees to radians helps bridge the gap between intuitive angle measurements and technical calculations.
What Is a Degree?
A degree (symbol: °) is a unit used to measure angles. One full circle contains 360 degrees. Degrees are commonly used in education, navigation, construction, drafting, and everyday descriptions of direction or rotation.
What Is a Radian?
A radian (symbol: rad) is a unit of angle based on the radius of a circle. One radian is the angle created when the length of an arc is equal to the radius of the circle. A full circle is equal to 2π radians, which means 180 degrees is equal to π radians.
When You May Need to Convert Degrees to Radians
- Solving trigonometry or geometry problems
- Using scientific calculators or math software
- Working with physics, engineering, or programming formulas
- Understanding graphing functions such as sine, cosine, and tangent
- Converting rotation angles in animation, modeling, or game development
Degrees to radians Formula
radians = degrees × π / 180
To convert degrees to radians, multiply the number of degrees by π and divide by 180.
Example: Convert 90° to radians:
90 × π / 180 = π/2 ≈ 1.5708 rad
Common degrees to radians Conversion Table
| Degree [°] | Radian [rad] |
|---|---|
| 0° | 0 rad |
| 30° | π/6 ≈ 0.5236 rad |
| 45° | π/4 ≈ 0.7854 rad |
| 90° | π/2 ≈ 1.5708 rad |
| 180° | π ≈ 3.1416 rad |
| 360° | 2π ≈ 6.2832 rad |
Why Convert Degrees to Radians?
Converting degrees to radians is important because many advanced formulas in mathematics and science use radians by default. Trigonometric functions, calculus, angular velocity, wave motion, and rotation formulas are often easier to express and calculate in radians.
For example, while degrees are more familiar for describing an angle visually, radians are the standard form in many textbooks, programming languages, graphing tools, and engineering calculations. Understanding both units helps improve accuracy and makes it easier to work across different fields.
Why Radians Are Common in Math and Science
Radians are directly tied to the properties of circles, which makes them more natural for many equations. In calculus, derivatives and integrals of trigonometric functions work cleanly when the angle is expressed in radians. In physics, rotational motion and oscillation formulas also commonly use radians.
Because of this, students and professionals often need to convert between degrees and radians when moving from introductory geometry to higher-level technical work.
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Frequently Asked Questions
What is the formula for converting degrees to radians?
Use the formula: radians = degrees × π / 180.
What is 180 degrees in radians?
180 degrees is equal to π radians.
What is 90 degrees in radians?
90 degrees is equal to π/2, or approximately 1.5708 radians.
Why do calculators sometimes use radians?
Many scientific and graphing calculations are based on radians, especially in trigonometry and calculus.
Are radians more accurate than degrees?
Radians are not more accurate, but they are often more convenient and mathematically natural in formulas.
When should I use degrees instead of radians?
Degrees are often easier for everyday understanding, drawing angles, navigation, and basic geometry, while radians are preferred for technical and scientific work.