Convert any value from / to revolution per minute [rpm] to miles per hour [mph], angular velocity to linear velocity. Fill one of the following fields, values will be converted and updated automatically.

revolutions per minute [rpm]

rpm

radius [m]

radius [m]

miles per hour [mph]

mph

\( rpm \) stands for revolutions per minute. The aim is to convert \(N\) (expressed in \(rpm\)) to \( \omega \) (expressed in \( rad/s \)). If \(N\) revolutions are performed in one minute, \( \frac {N}{60} \) revolutions are performed in one second. As one revolution is equal to \( 2\pi \) radians, the conversion can be done thanks to the following formula:

$$ N_{(rpm)} = \frac {60}{2\pi}.\omega_{(rad/s)} $$

Assume an object (or point) attached to a rotating wheel. The angular velocity of the wheel is defined by \( \omega \) expressed in \( rad/s \). This also means that the wheel rotates from \( \omega \) radians during one second. During that same second, the attached object (or point) travels a distance of \(r \times \omega \). It implies that the speed of the object is also equal to \(r \times \omega \). The conversion can be done thanks to the following formula:

$$ \omega_{(rad/s)}=\frac{v_{ (m/s) }}{r} $$

Assume that \( v_{(m/s)} \) is the velocity expressed in \( m/s \), i.e. the distance travelled during one second. To get the distance travelled during one minute, the previous value must be multiplied by 60. To get the distance in meters travelled during one hour, \( v_{(m/s)}\) must be multiplied by 60 x 60 = 3600. The result is a velocity expressed in \( m/h \). To convert this result in kilometers per hour, we now have to divide the previous velocity (expressed in \( m/h \)) by 1000 since one kilometer is equal to 1000 meters. The conversion can be done thanks to the following formula:

$$ v_{ (m/s) } = \frac {1000}{3600}.v_{(km/h)} $$

By convention, 1 mile exactly equal to 1.609344 kilometers, it becomes trivial to deduce the following formula:

$$ v_{(km/h)} = 1.609344 \times v_{(mph)} $$

From the previous demonstrations, we can conclude:

$$ N_{(rpm)} = \frac {60}{2\pi} \times \dfrac{1000}{3600} \times \frac{1.609344.v_{ (mph) }}{r} = \frac{965.6064}{72.\pi.r} \times v_{ (mph) } $$

and *vice-versa*:

$$ v_{(mph)} =\dfrac{72.\pi.r}{965.6064} \times N_{(rpm)} $$

- Convert binary, decimal and hexadecimal
- Convert cubic meters of topsoil to tonnes
- Convert from binary to decimal and vice-versa
- Convert newton-metre [N.m] to kilogramme-centimeter [Kg.cm] and vice-versa
- Convert newton-metre [N.m] to millinewton-metre [mN.m] and vice-versa
- Convert inches [in] to centimeters [cm] and vice-versa
- Convert meters per second [m/s] to kilometers per hour [km/h] and vice-versa
- Convert meters [m] to millimeters [mm] and vice-versa
- Convert miles per hour [mph] to kilometers per hour [km/h] and vice-versa
- Convert newton-meter [N.m] to newton [N] and vice-versa
- Convert kilometers per hour [km/h] to radians per second [rad/s] and vice-versa
- Convert radians per second [rad/s] to meters per second [m/s] and vice-versa
- Convert radians per second [rad/s] to miles per hour [mph] and vice-versa
- Convert revolutions per minute [rpm] to radians per second [rad/s] and vice-versa
- Convert revolutions per second [rps] to radians per second [rad/s] and vice-versa
- Convert radians [rad] to degrees [°] and vice-versa
- Convert revolutions per minute [rpm] to kilometers per hour [km/h] and vice-versa
- Convert revolutions per minute [rpm] to meters per second [m/s] and vice-versa
- Convert revolutions per second [rps] to meters per second [m/s] and vice-versa

Last update : 05/23/2021