Angular Velocity Converter
Convert between angular velocity units: rad/s, rpm, deg/s, rev/s, rev/h.
Conversion Results
Radian per second (rad/s)
0.1047197551
Degree per second (°/s)
6
Revolution per minute (rpm)
1
Revolution per second (rps)
0.01666666667
Revolution per hour (rph)
60
About this tool
Angular velocity measures how quickly something rotates or spins, expressing the rate of rotation in units like radians per second, revolutions per minute, or degrees per second. This is a fundamental concept in physics, engineering, and mathematics used to describe rotating machinery, planetary motion, gyroscopes, wheels, motors, and any system where circular motion matters. Understanding angular velocity is crucial for analyzing mechanical systems, calculating energy in rotating objects, predicting motion behavior, and designing equipment that operates smoothly and efficiently.
To use the converter, simply enter a value in any angular velocity unit—whether radians per second (rad/s), revolutions per minute (rpm), degrees per second (deg/s), revolutions per second (rev/s), or revolutions per hour (rev/h)—and the tool instantly converts it to all other supported units. This is invaluable when working across different industries and standards: automotive engineers may use rpm for engine specifications, physicists prefer rad/s in equations, astronomers track rev/h for orbital mechanics, and roboticists need deg/s for precise motion control.
The converter handles the complex mathematical relationships between angular units seamlessly, so you don't have to memorize conversion factors. Whether you're troubleshooting machinery, designing control systems, solving physics problems, or comparing specifications from different regions or manufacturers, this tool ensures accurate, instant conversions. It's equally useful for students learning rotational dynamics, technicians maintaining industrial equipment, engineers developing mechatronic systems, and anyone working with rotating systems where precision matters.
Frequently Asked Questions
Code Implementation
import math
# Angular velocity unit converter
UNITS = {
'rad_s': 1, # base unit
'deg_s': math.pi / 180, # 1 deg/s = π/180 rad/s
'rpm': (2 * math.pi) / 60, # 1 rpm = 2π/60 rad/s
'rps': 2 * math.pi, # 1 rev/s = 2π rad/s
'rph': (2 * math.pi) / 3600 # 1 rev/h = 2π/3600 rad/s
}
def convert_angular_velocity(value, from_unit, to_unit):
"""Convert between angular velocity units"""
in_rad_s = value * UNITS[from_unit]
return in_rad_s / UNITS[to_unit]
def linear_velocity(angular_rad_s, radius_m):
"""Calculate linear velocity from angular velocity"""
return angular_rad_s * radius_m # v = ω × r
# Motor shaft angular velocity
motor_rpm = 1800
omega = convert_angular_velocity(motor_rpm, 'rpm', 'rad_s')
print(f"{motor_rpm} rpm = {omega:.4f} rad/s")
print(f"{motor_rpm} rpm = {convert_angular_velocity(motor_rpm, 'rpm', 'deg_s'):.2f} deg/s")
# Linear velocity at wheel rim
radius = 0.3 # 30 cm
v = linear_velocity(omega, radius)
print(f"Wheel rim speed: {v:.2f} m/s = {v * 3.6:.2f} km/h")
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