๐ Angular Velocity Converter
Convert angular velocity in real time between radians per second (rad/s), degrees per second (deg/s), revolutions per minute (RPM), and hertz (Hz, revolutions per second). rad/s is the standard SI unit for angular velocity.
How to use
- Enter a value in whichever unit you want to convert from.
- The converted values in the other units are shown in real time.
How the calculation works
This tool converts between units of angular velocity (rotational speed). The value you enter is first converted to the SI unit, radians per second (rad/s), then to each of the other units. One revolution is 360ยฐ, or 2ฯ radians (about 6.283 rad), so the units relate as follows: 1 rpm (one revolution per minute) = 2ฯ รท 60 โ 0.1047 rad/s 1 ยฐ/s (one degree per second) = ฯ รท 180 โ 0.01745 rad/s 1 Hz (one revolution per second) = 2ฯ โ 6.283 rad/s = 60 rpm Motor, engine and hard-drive speeds are usually given in rpm, physics uses rad/s, and gyroscope sensors often report ยฐ/s, so this helps bring figures into the same unit.
Worked example
1000 rpm rad/s: 1000 ร 2ฯ รท 60 โ 104.72 rad/s ยฐ/s: 1000 ร 360 รท 60 = 6000 ยฐ/s Hz: 1000 รท 60 โ 16.67 Hz Typical speeds Hard drives: 5400 or 7200 rpm Washing machine spin: roughly 800โ1200 rpm LP records: 33โ rpm
Things to be aware of
- Hz here means revolutions per second. Angular frequency in rad/s (ฯ = 2ฯf) is 2ฯ times larger, so do not mix them up.
- To get the surface speed of a rotating object, use v = ฯ ร r (r is the radius, ฯ in rad/s).
- rpm stands for revolutions per minute and is sometimes written as minโปยน.
FAQ
What is the relationship between rad/s and RPM?
One revolution is 2ฯ radians, so to convert RPM (revolutions per minute) to rad/s, calculate "RPM ร 2ฯ รท 60".
Why is rad/s the standard unit?
The radian is a dimensionless ratio of arc length to radius, and physics formulas for circular motion (angular velocity, angular acceleration, torque, etc.) are simplest when expressed in radians, which is why SI adopted it as the base unit for angular velocity.
How is this different from Hz?
Hz (hertz) counts cycles (revolutions) per second, equivalent to RPM divided by 60. rad/s is Hz multiplied by 2ฯ.