View source for Revolutions per minute

{{Short description|Unit of rotational speed}}
{{Other uses}}
{{redirect|rpm|other uses|RPM (disambiguation)}}
{{more citations needed|date=July 2016}}
{{Infobox unit
| bgcolor       = 
| name          = Revolutions per minute
| image         = File:Mitsubishi Carisma 1.8 GDI Tacho (cropped).jpg
| caption       = A car's [[tachometer]] marked in multiples of a thousand rpm
| standard      = 
| quantity      = Rotational speed, rotational frequency
| symbol        = rpm
| symbol2       = r/min
| namedafter    = 
| extralabel    = 
| extradata     = 
| units1        = SI accepted units
| inunits1      = 1&nbsp;min<sup>−1</sup>
| units2        = SI units
| inunits2      = {{sfrac|1|60}}&nbsp;Hz =&nbsp;0.01{{overline|6}}&nbsp;Hz
| units3        = SI base units
| inunits3      = 0.01{{overline|6}}&nbsp;s<sup>−1</sup>
}}

'''Revolutions per minute''' (abbreviated '''rpm''', '''RPM''', '''rev/min''', '''r/min''', or '''r⋅min<sup>−1</sup>''') is a unit of [[rotational speed]] (or [[rotational frequency]]) for rotating machines.
One revolution per [[minute]] is equivalent to {{sfrac|1|60}} [[hertz]].

== Standards ==
[[ISO 80000-3]]:2019 defines a [[physical quantity]] called [[rotation (quantity)|''rotation'']] (or ''number of revolutions''), [[dimensionless]], whose [[instantaneous rate of change]] is called ''[[rotational frequency]]'' (or ''rate of rotation''), with units of [[reciprocal second]]s (s<sup>−1</sup>).<ref>[https://www.iso.org/obp/ui/#iso:std:iso:80000:-3:ed-2:v1:en ISO 80000-3:2019].</ref>

A related but distinct quantity for describing rotation is ''[[angular frequency]]'' (or ''angular speed'', the magnitude of [[angular velocity]]), for which the SI unit is the [[radian per second]] (rad/s).

Although they have the same [[dimension (physics)|dimensions]] (reciprocal time) and base unit (s<sup>−1</sup>), the hertz (Hz) and radians per second (rad/s) are special names used to express two different but proportional [[International System of Quantities|ISQ]] quantities: frequency and angular frequency, respectively. The conversions between a frequency {{mvar|f}} and an angular frequency {{mvar|ω}} are
: <math>\omega = 2 \pi f, \quad f = \frac{\omega}{2 \pi}.</math>

Thus a disc rotating at 60&nbsp;rpm is said to have an angular speed of 2''π''&nbsp;rad/s and a rotation frequency of 1&nbsp;Hz.

The [[International System of Units]] (SI) does not recognize rpm as a unit. It defines units of [[angular frequency]] and [[angular velocity]] as rad&nbsp;s<sup>−1</sup>, and units of [[frequency]] as [[Hertz|Hz]], equal to s<sup>−1</sup>.

: <math>\begin{array}{rcrcr}
 1~\dfrac{\text{rad}}{\text{s}}                &=& \dfrac{1}{2\pi}~\text{Hz} &=& \dfrac{60}{2\pi}~\text{rpm} \\
 2\pi~\dfrac{\text{rad}}{\text{s}}             &=& 1~\text{Hz}               &=& 60~\text{rpm} \\
 \dfrac{2\pi}{60}~\dfrac{\text{rad}}{\text{s}} &=& \dfrac{1}{60}~\text{Hz}   &=& 1~\text{rpm}
\end{array}</math>

== Examples ==
* For a wheel, a pump, or a crank shaft, the number of times that it completes one full cycle in one minute is given the unit revolution per minute. A revolution is one complete period of motion, whether this be circular, reciprocating or some other periodic motion.
* On many kinds of disc recording media, the rotational speed of the medium under the read head is a standard given in rpm. [[Phonograph record|Phonograph (gramophone) records]], for example, typically rotate steadily at {{frac|16|2|3}}, {{frac|33|1|3}}, 45&nbsp;rpm or 78&nbsp;rpm (0.28, 0.55, 0.75, or 1.3, respectively, in Hz).
* Air turbine rotating up to {{val|1500000|u=rpm}} (25 kHz)
* Modern air turbine [[dental drill]]s can rotate at over {{val|800000|u=rpm}} (13.3&nbsp;kHz).
* The [[second]] hand of a conventional analog clock rotates at 1&nbsp;rpm.
* [[Red Book (audio CD standard)|Audio CD]] players read their discs at a precise, constant rate (4.3218&nbsp;Mbit/s of raw physical data for 1.4112&nbsp;Mbit/s (176.4&nbsp;KB/s) of usable audio data) and thus must vary the disc's rotational speed from 8&nbsp;Hz (480&nbsp;rpm) when reading at the innermost edge to 3.5&nbsp;Hz (210&nbsp;rpm) at the outer edge.<ref name="MPEG DVD Spec">{{cite web |url=http://www.mpeg.org/MPEG/DVD/Book_A/Specs.html |title=Physical parameters |work=DVD Technical Notes |publisher=Moving Picture Experts Group (MPEG) |date=1996-07-21 |access-date=2008-05-30 |archive-date=2012-02-19 |archive-url=https://web.archive.org/web/20120219232931/http://www.mpeg.org/MPEG/DVD/Book_A/Specs.html |url-status=dead }}</ref>
* [[DVD]] players also usually read discs at a constant linear rate. The disc's rotational speed varies from 25.5&nbsp;Hz (1530&nbsp;rpm) when reading at the innermost edge, to 10.5&nbsp;Hz (630&nbsp;rpm) at the outer edge.<ref name="MPEG DVD Spec" />
* A [[washing machine]]'s drum may rotate at 500&nbsp;rpm to {{val|2763|u=rpm}} (8&nbsp;Hz – 46&nbsp;Hz) during the spin cycles.
* A [[baseball]] thrown by a [[Major League Baseball]] pitcher can rotate at over {{val|2500|u=rpm}} (41.7&nbsp;Hz); faster rotation yields more movement on [[breaking ball]]s.<ref>{{cite news |url=https://www.msn.com/en-us/sports/mlb/the-athletics-eno-sarris-talks-spider-tack-gerrit-cole-with-moose-andamp-maggie/ar-AAKSpVP |title=The Athletic's Eno Sarris talks Spider Tack, Gerrit Cole with Moose & Maggie |first=Ryan |last=Chichester |website=[[WFAN (AM)|WFAN]] |via=MSN.com |date=June 10, 2021 |access-date=June 14, 2021}}</ref>
* A power-generation turbine ([[Alternator#Synchronous speeds|with a two-pole alternator]]) rotates at 3000&nbsp;rpm (50&nbsp;Hz), 3600&nbsp;rpm (60&nbsp;Hz), and over 4000 rpm ({{frac|66|2|3}} Hz)
* Modern [[automobile]] [[engine]]s are typically operated around {{val|2000|u=rpm}} – {{val|3000|u=rpm}} (33&nbsp;Hz – 50&nbsp;Hz) when cruising, with a minimum (idle) speed around 750&nbsp;rpm – 900&nbsp;rpm (12.5&nbsp;Hz – 15&nbsp;Hz), and an upper limit anywhere from 4500&nbsp;rpm to up to {{val|10000|u=rpm}} (75&nbsp;Hz – 166&nbsp;Hz) for a road car, very rarely reaching up to {{val|12000|u=rpm}} for certain cars (such as the [[GMA T.50]]), or  {{val|22000|u=rpm}} for racing engines such as [[Formula One engines|those in Formula 1 cars]] (during the {{F1|2006}} season, with the 2.4&nbsp;L N/A [[V8 engine]] configuration; limited to {{val|15000|u=rpm}}, with the 1.6&nbsp;L [[V6 engine|V6]] [[Turbocharger|turbo]]-[[Hybrid electric vehicle|hybrid]] engine configuration).<ref>{{cite web |url=http://www.formula1.com/inside_f1/rules_and_regulations/sporting_regulations/12877/|title=2014 season changes|publisher=Formula One |access-date=2014-08-18}}</ref> The exhaust note of [[V8 engine|V8]], [[V10 engine|V10]], and [[V12 engine|V12]] [[F1 car]]s has a much higher pitch than an [[straight engine|I4 engine]], because each of the [[Cylinder (engine)|cylinders]] of a [[four-stroke engine]] fires once for every two revolutions of the [[crankshaft]]. Thus an eight-cylinder engine turning 300 times per second will have an exhaust note of {{val|1200|u=Hz}}.
* A piston [[aircraft engine]] typically rotates at a rate between {{val|2500|u=rpm}} and {{val|10000|u=rpm}} (42&nbsp;Hz – 166&nbsp;Hz).
* Computer [[hard drive]]s typically rotate at {{val|7500|u=rpm}} – {{val|10000|u=rpm}} (125&nbsp;Hz – 166&nbsp;Hz), the most common speeds for the [[Advanced Technology Attachment|ATA]] or [[Serial ATA|SATA]]-based drives in consumer models. High-performance drives (used in fileservers and enthusiast-gaming PCs) rotate at {{val|10000|u=rpm}} – {{val|15000|u=rpm}} (160&nbsp;Hz – 250&nbsp;Hz), usually with higher-level SATA, [[SCSI]] or [[Fibre Channel]] interfaces and smaller platters to allow these higher speeds, the reduction in storage capacity and ultimate outer-edge speed paying off in much quicker access time and average transfer speed thanks to the high spin rate. Until recently, lower-end and power-efficient laptop drives could be found with {{val|4200|u=rpm}} or even {{val|3600|u=rpm}} spindle speeds (70&nbsp;Hz or 60&nbsp;Hz), but these have fallen out of favour due to their lower performance, improvements in energy efficiency in faster models and the takeup of [[solid-state drive]]s for use in slimline and ultraportable laptops. Similar to CD and DVD media, the amount of data that can be stored or read for each turn of the disc is greater at the outer edge than near the spindle; however, hard drives keep a constant rotational speed so the effective data rate is faster at the edge (conventionally, the "start" of the disc, opposite to a CD or DVD).
* [[Floppy disc]] drives typically ran at a constant 300&nbsp;rpm or occasionally 360&nbsp;rpm (a relatively slow 5&nbsp;Hz or 6&nbsp;Hz) with a constant per-revolution data density, which was simple and inexpensive to implement, though inefficient. Some designs such as those used with older Apple computers (Lisa, early Macintosh, later II's) were more complex and used variable rotational speeds and per-track storage density (at a constant read/record rate) to store more data per disc; for example, between 394&nbsp;rpm (with 12 sectors per track) and 590&nbsp;rpm (8 sectors) with Mac's 800&nbsp;kB double-density drive at a constant 39.4&nbsp;kB/s (max) – versus 300&nbsp;rpm, 720&nbsp;kB and 23&nbsp;kB/s (max) for double-density drives in other machines.<ref>{{cite web |url=http://support.apple.com/kb/TA39910?viewlocale=en_US |title=Double-Density Versus High-Density Disks |publisher=Apple |access-date=2012-05-05}}</ref>
* A [[Zippe-type centrifuge]] for enriching uranium spins at {{val|100000|u=rpm}} ({{val|1666|u=Hz}}) or faster.<ref>{{cite web |url=http://www.electricityforum.com/news/mar04/centrifuge.html |title=Slender and Elegant, It Fuels the Bomb |publisher=The Electricity Forum |access-date=2006-09-24}}</ref>
* [[Gas turbine]] engines rotate at tens of thousands of rpm. JetCat model aircraft turbines are capable of over {{val|100000|u=rpm}} ({{val|1700|u=Hz}}) with the fastest reaching {{val|165780|u=rpm}} ({{val|2763|u=Hz}}).<ref>{{cite web |url=http://www.jetcatusa.com/p60.html |title=P60-SE Special Edition |publisher=JetCat USA |access-date=2006-07-19 |archive-date=2012-04-19 |archive-url=https://web.archive.org/web/20120419105441/http://www.jetcatusa.com/p60.html |url-status=dead }}</ref>
* A [[Flywheel energy storage]] system works at {{val|60000|u=rpm}} – {{val|500000|u=rpm}} (1&nbsp;kHz – 8.3&nbsp;kHz) range using a passively magnetic levitated flywheel in a vacuum.<ref>{{cite journal |title=A New Look at an Old Idea: The Electromechanical Battery |last=Post |first=Richard F. |journal=Science & Technology Review |date=April 1996 |publisher=University of California |pages=12–19 |url=http://www.llnl.gov/str/pdfs/04_96.2.pdf |issn=1092-3055 |access-date=2008-05-30}}</ref> The choice of the flywheel material is not the most dense, but the one that pulverises the most safely, at surface speeds about 7 times the speed of sound.
* A typical 80&nbsp;mm, 30&nbsp;CFM computer fan will spin at {{val|2600|u=rpm}} – {{val|3000|u=rpm}} (43&nbsp;Hz – 50&nbsp;Hz) on 12&nbsp;V DC power.
* A [[millisecond pulsar]] can have near {{val|50000|u=rpm}} (833&nbsp;Hz).
* A [[turbocharger]] can reach {{val|1000000|u=rpm}} (16.6&nbsp;kHz), while {{val|100000|u=rpm}} – {{val|250000|u=rpm}} (1&nbsp;kHz – 3&nbsp;kHz) is common.
* A [[supercharger]] can spin at speeds between or as high as {{val|50000|u=rpm}} – {{val|100000|u=rpm}} (833&nbsp;Hz – 1666&nbsp;Hz)
* [[Molecular biology|Molecular microbiology]] – molecular engines. The rotation rates of bacterial [[Flagellum|flagella]] have been measured to be {{val|10200|u=rpm}} (170&nbsp;Hz) for ''[[Salmonella enterica subsp. enterica|Salmonella typhimurium]]'', {{val|16200|u=rpm}} (270&nbsp;Hz) for ''[[Escherichia coli]]'', and up to {{val|500000|u=rpm}} ({{val|1700|u=Hz}}) for polar flagellum of ''[[Vibrio alginolyticus]]'', allowing the latter organism to move in simulated natural conditions at a maximum speed of 540&nbsp;mm/h.<ref>{{cite journal |title=Very fast flagellar rotation |journal=Nature|first1=Y.|last1=Magariyama |first2=S.|last2=Sugiyama|first3=K.|last3=Muramoto|first4=Y.|last4=Maekawa|first5=I.|last5=Kawagishi|first6=Y.|last6=Imae|first7=S.|last7=Kudo |date=October 27, 1994 |volume=371 |issue=6500|pages=752 |bibcode=1994Natur.371..752M|doi=10.1038/371752b0|pmid=7935835 |doi-access=free}}</ref>
* The sample in [[magic angle spinning]], a [[nuclear magnetic resonance]] technique, typically rotates between {{val|300000}} and {{val|6000000|u=rpm}} (5–{{val|100|u=kHz}}), with experimental instruments reaching speeds as high as {{val|12000000|u=rpm}} ({{val|200|u=kHz}}).

== See also ==
*[[Constant angular velocity]] (CAV) – used when referring to the speed of gramophone (phonograph) records
*[[Constant linear velocity]] (CLV) – used when referring to the speed of audio CDs
*[[Radian per second]]
*[[Rotational speed]]
*[[Compressor map]]
*[[Turn (geometry)]]
*[[Idle speed]]
*[[Overspeed (engine)]]
*[[Redline]]
*[[Rev limiter]]
*[[RPM gauge]]

== Notes ==
{{notelist}}

== References ==
{{reflist}}

[[Category:Units of frequency]]
[[Category:Rotation]]