A Degrees Per Second to Radians Per Second Calculator converts angular velocity from degrees per second (°/s) to radians per second (rad/s). This conversion is widely used in physics, engineering, robotics, and rotational motion analysis, where angular velocity needs to be measured in standard units.
Importance of Degrees to Radians Per Second Conversion:
- Used in Physics & Engineering: Helps analyze rotational motion in mechanical systems.
- Essential for Robotics & Motion Control: Ensures precise angular speed calculations for automated systems.
- Crucial in Aerospace & Automotive Design: Converts rotational speed of gears, turbines, and wheels for accurate modeling.
- Applied in Computer Graphics & Game Development: Helps simulate realistic object rotations.
Formula of Degrees Per Second To Radians Per Second Calculator
The conversion from degrees per second (°/s) to radians per second (rad/s) follows the formula:
Radians per Second (ω) = Degrees per Second × (π / 180)
Where:
- π ≈ 3.1416
- 180 = Conversion factor between degrees and radians.
Since there are π radians in 180 degrees, multiplying degrees per second by (π / 180) converts the value to radians per second.
Degrees Per Second to Radians Per Second Reference Table
The table below provides pre-calculated conversions for common values:
| Degrees per Second (°/s) | Radians per Second (rad/s) |
|---|---|
| 1°/s | 0.0175 rad/s |
| 5°/s | 0.0873 rad/s |
| 10°/s | 0.1745 rad/s |
| 30°/s | 0.5236 rad/s |
| 45°/s | 0.7854 rad/s |
| 60°/s | 1.0472 rad/s |
| 90°/s | 1.5708 rad/s |
| 180°/s | 3.1416 rad/s |
| 360°/s | 6.2832 rad/s |
This table helps users quickly convert between degrees per second and radians per second without needing manual calculations.
Example of Degrees Per Second To Radians Per Second Calculator
Suppose an electric motor rotates at 90 degrees per second. To convert this to radians per second, use the formula:
Step 1: Apply the Formula
Radians per Second = 90 × (π / 180)
Step 2: Solve the Equation
Radians per Second = 90 × (3.1416 / 180)
Radians per Second = 90 × 0.0175 = 1.5708 rad/s
Thus, 90°/s is equivalent to 1.5708 rad/s.
Most Common FAQs
Radians per second is the standard unit in physics and engineering because it simplifies rotational motion equations and calculations.
Yes, this conversion is essential for calculating angular velocity, centripetal acceleration, and rotational kinetic energy.
The formula provides exact conversions, with slight variations depending on the precision of π used (3.1416 vs. 3.141592653…).