Here’s one of the most common technical mistakes in automotive publishing. Today, we fix it. Ha.
In your automotive reading down through the years, you may have noticed a small but curious thing. You will find engine torque quoted in either foot-pounds or pound-feet with apparent interchangeability, almost as if the two terms have the same meaning. Some sources use foot-pounds; some use pound-feet; some never quite make up their minds.
However, these two similar-looking units (and their abbreviations, ft.-lb. and lb.-ft.) are not interchangeable. While it may seem trivial, one is the correct term for torque in English units, and the other is a measure of something else altogether. For those fussy people who want to get it right, here is a brief rundown.
The foot-pound (also and originally known as foot-pound force) is a traditional English unit of work. It is equal to the work done by one pound of force acting through a distance of one foot. For example, when James Watt determined that a horse could lift 550 lbs. at a rate of one foot per second, he declared it one horsepower. The SI or international equivalent of the foot-pound is the Joule (J).
The pound-foot (also and originally known as pound-force foot) is a traditional English unit of torque. The angular equivalent of linear force, torque is the tendency of a force to produce a rotation. Torque is the product of the force and the distance from the center of rotation to the point where the force is applied. For example, if a one-pound force is exerted on a wrench with an effective length of one foot, one pound-foot of torque is applied to the fastener. The SI or international equivalent of the pound-foot is, naturally enough, the Newton meter (Nm).
In a similar way, when a brake and lever are fixed to the output shaft of an engine, if the measured resistance force is 100 pounds and the lever is one foot long, 100 pound-feet of torque is indicated. And that, in a nutshell, is how engine torque is actually measured. And this is the value you will find quoted as torque in car magazines and sales literature.
The takeaway: The proper term for torque in English units is the pound-foot, which we can find abbreviated any number of ways, such as lb.-ft., lb-ft, lb/ft, and so on. However, a foot-pound is a unit of work. Engines certainly do produce work as well as power, but in this case torque is the property in reference.
(For an amazing exploration of the wonderful world of measures, see A Dictionary of Units of Measurement by Russ Rowlett of the University of North Carolina at Chapel Hill. Be prepared to burn a few hours.)
But you’ve not addressed those messy plurals! It’s rarely 1 lb-ft. If you’re measuring the poundS of torque exerted at the end of a one-foot lever, it should be pounds-foot or lbs/ft, lbs-ft, etc. But the plural is usually rendered as pound-feet, as if it were a single pound at the end of a multi-foot lever. This is because the abbreviation for foot and feet are the same and everyone has agreed to use the singular lb-ft for everything…it may also be because pedants never actually win. It’s also possible that I’m just a permanently confused person…
As I see it, we say “50 pound feet,” not “50 pounds feet,” so the singular form lb. makes perfect sense to me. But really, lb. is both the singular and the plural form, being the abbreviation for libra as opposed to pound.
It’s just as you say, pedants never win. I came very close to killing this piece. The closer I got to the end, the more I wondered why I had cared in the first place. But then I thought what the heck, maybe someone will come along with an airtight case for foot-pound that was totally beyond my view.
I’ve been retired for 22 years. When I was an engineering student about 60 years ago the Society of Mechanical Engineers decided to call static torque pound-feet, and dynamic torque foot-pounds. Somehow this got lost.
In the end, it’s all about units and practicality.
The practicality is that in the shop, we know what foot pounds or pound feet are. But if you notice, it is the second definer that gets pluralized in speech. Unfortunate that it is backwards from the mathematical reality.
In torque, the force is usually expressed first as that is what we are interested in and will vary. To separate high torques from low torques in fasteners, we change the moment of the loading from foot to inch.
The notations of lb-ft and lb/ft are NOT equal. The / is very often used to denote the word “per” as in pressure lb/in^2 = pounds per square inch (pressure) which is represented by formula F (force) = A (area) x P (pressure). The pressure of say 30 pounds acted on a piston with a 4 square-inch area will produce 120 pounds force (lbf. which removes the force of gravity from consideration) MEANS that 30 pounds of force is acted on each square inch of the area. The / also implies divide.
Your prediction was correct. I spent the entire morning on the employers’ dime going through the systems of measures. What a magnificent web find! Ask me about hanks or rroods. Now I know how finger ring sizes work. Amazing!
My maintenance manual (English) uses the abbreviations lbf ft and lbf in – also supplied as Nm and kgf (c)m
So, when I go to buy my new torque wrench, I now look at lb/ft instead of ft/lb. When did all of this come about? In maintenance manuals I have always read “torque nut B on bolt A to x number of ft/lbs. So the manuals are wrong? Now I must torque my cylinder head bolts and exhaust header bolts to lbs/ft?
The values themselves should be correct; they are simply using the wrong terminology.
I am sorry, but to use the notation lb/ft or ft/lb for energy (or torque) is wrong. When units are given “/” means “divided by” and cannot be interpreted as multiplication. The units of both energy and torque are force times distance, which means ft-lb or lb-ft (here the “-” means multiplication and does not mean “minus” (you cannot meaningfully subtract ft from lbs or lbs from feet– i.e., terms with different units). A physicist (such as myself), would not distinguish ft-lb from lb-ft (they both have units of feet times pounds). Sometimes “-” is replaced with “.”, as in “ft.lb” to more directly suggest multiplication and not subtraction.
There is sometimes a suggestion that “ft-lb” is used to connote energy, while “lb-ft” is used to connote torque. This might be a convention in certain shop manuals, but a physicist would view ft-lb and lb-ft as equivalent to each other (and not at all the same as ft/lb or lb/ft).
In this case the forward slash is not a division sign but a virgule. A lb-ft is not the same quality as a ft-lb, just as a Newton meter is not the same quality as a joule.
(Nice distinction between division sign and virgule!)
One wonders: why not just use SI nomenclature…
Indeed…though there is a similar issue in that the joule and the Newton meter are the same quantity algebraically but represent two different properties.
Nice deflection away from the argument against the use of a division sign by highlighting that it is indeed a virgule. However, a virgule itself is not appropriate since it is either i) a short oblique stroke between two words indicating that whichever is appropriate, e.g. his / her, ii) a dividing line, as in dates or fractions, or iii) a forward slash as used in computing. In this case the virgule is being used as in a fraction, i.e. a dividing line, and is wholly inappropriate and incorrect for use in a multiplying term such as ft-lbs or lbs-ft.
It is interesting to note that the unit definitions for Work and Torque are as such. But if you consider their mathematical definitions, you would think the units would be reversed.
I will use LaTeX notations for this, but it should still be follow-able. Let’s start with Work:
W = \int F \cdot dr
Notice that the order of the terms in then integrand is not interchangeable, we cant take dr \cdot F and compute anything meaningful. By dimension analysis, the units should follow the order of the formulas, i.e. a unit of Force then a unit of lenth. N.m or lb.ft are possible candidates.
As for Torque
\tau = r \times F
Again the order of the terms makes it seem the units should follow the same pattern, m.N or ft.lb. But from the property of cross product you may also get
\tau = -F \times r
But seeing the negative sign as inconvenience, the former equation should hold better.
I myself use the dimension analysis as a way to remember corresponding units. Maybe there were other factors in history that I don’t know that led to these conventions, but I think it is unfortunate that the conventions for Work and Torque are as such.
I am a retired mechanical engineer, and I distinctly remember that approximately fifty years ago the Society of Mechanical Engineers decided to make static torque pound-feet, and dynamic torque foot-pounds.
For the engineers and physicists.. A lowly mechanic asks: is two pounds of force upon a one foot lever the same torque as one pound of force on a two foot lever? If the formula is force times arm length then I see it would have to be so.
Good article. Per SAE AS1310, Fastener Torque for Threaded Applications, Defenitions of, it states “Torque is the force or turning moment tending to produce rotation. It is expressed in terms of applied load and the length of the moment arm applying it, usally in pound-inches, pounf-feet, or Newton-meters (lb-in, lb-ft, N-m).
Are ANY of you (expletive deleted by MCG) going to actually ANSWER THE QUESTION IN ENGLISH that DOES NOT REQUIRE a MASTER’S DEGREE in ENGINEERING ) for the AVERAGE GUY ATTEMPTING to TOURQUE DOWN the CYLINDER HEAD of his FORD , CHEVY or TRIUMPH ( Motorcycle ) !?!?!?!?!?
No worries at all. Simply use the spec listed in the manual or other technical literature. The numerical value is not affected.
I have been laughing at the big car companies for the last few years saying “pounds feet” in their TV and magazine adds. I have read the great article at the beginning and the reply’s. In some cases the folks making comments used the wrong nomenclature which actually disproves their own point. I have built many racing cars and tested many engines on dynos. I even worked for the famous Smokey Yunick for a while on the dual turbo Chevy Indy car project. In all my years all the amateur and professionals I ever came in contact with said, “foot pounds”, but that is not what makes it right, What makes it right is the fact that we are dealing with a one foot lever.
That one foot lever connects the absorption/brake unit to the load cell or scales for measuring, The length is “one foot” , If you noticed, one foot indicates that it is not plural. A person might say they have two feet but keep one foot in their mouth. We all understand exactly what they meant and I especially know because I practice this behavior often. If you say the word feet then the lever must be longer so your “pounds feet would become a different unknown length of measurement that would need a correction factor added to have any comparative value. Maybe the car companies have found a new way of stretching the truth about their product and a clever way to hide the true power of their product and plead ignorance when caught. As a few pointed out in their comments the abbreviation is what may confuse folks who do not know how torque is measured.
As a note: The article at the beginning of all this contradicts it’s self in the sentence copied an pasted here. The writer wrote, ” if the measured resistance force is 100 pounds and the lever is one foot long, 100 pound-feet of torque is indicated.” Wrong. First it correctly stated that it is measured with a one foot lever but then the writer incorrectly calls out the torque value claiming the lever used for the test is longer. How much longer? Feet is the plural form of foot. Torque is measured one foot from the center of the load absorbing device that must be one foot long not one feet long. I enjoyed and admired all those who took the time to write their opinions.
I came to this article via a Google search after listening to some of the guys on Power Nation say “Pound Feet” of torque, I have to say it’s been bothering me. As I read the article and the replies I am thinking to myself “What would Smokey say”? I was ready to scour the internet and look for a quote or two, until I read your reply. I read his book on SBC tuning I believe it was years ago when most of these guys were just a glimmer in their Daddy’s eye, he never referred to it as “Pound Feet”. Over my years of racing and building I’ve NEVER heard it pronounced “Pound Feet” until recently. This is what happens when a young fella with a pocket protector gets involved. Right, wrong or indifferent “Foot Pounds” is how it’s pronounced in the trenches. So for the young whipper snapper engineers splitting hairs saying that the likes of Smokey Yunick was mispronouncing ft/lbs, stop. Your only embarrassing yourself.
Yeah….and that is why I prefer the world measurements of Joule (J), Horse power (HP) and Newton meter (N.m). To me it is a clear difference although one must say Joules and Newton meter are in bed together. Being German I seem to like the complication to convert “N m” into an actual weight resting (~10N.m = 1KG) on a 1 meter long lever. It is the EXACT same idea of the lbs.ft. (and this should be the ONLY abbreviation, not “-” not “/” or what ever). But you ALWAYS know it is a WEIGHT acting upon a (1ft)lever, end of discussion, no if’s or but’s about it.
Think of X-amount of pounds resting on a lever of 1 foot length, perfect, makes sense.
So Lbs.ft. (POUNDS FOOT) is the one and only thing that should EVER exist and describe a torque in imperial, although it sounds retarded).
As for work, fts.lb. just is ridiculous in any case, as it completely changes the measurement (beside the fact it also sounds stupid, “FEET POUND”).
You now travel over a distance x with 1 lb in you lap WITH the addition of a time frame (assuming it is a second).
Example 1000 fts.lb means you travel 1000 ft. with 1lb of weight in one second…riiiight.
How realistic does that even sound?
VS: 2HP = 1100 lbs are being moved 1 foot in one second.
Is it just me or does that seem less ridiculous?
[Everybody knows HP refers to a second and either
1) 550lbs per one foot
2) 75 KG per one meter]
Watts and Kilowatts are even more precise, but less imaginable as WORK imho.
75kg*1meter/1second=750Watts (0.75KW)
But the cool thing here is to imagine the work it takes to light a bulb.
People hate the Metric system, but it makes more sense at times than Imperial.
ESPECIALLY when they clearly distinguish the use of forces, work and distances.
Time to combine all the good units 😛
Conclusion: Newton meter (N.m) sounds cooler than Pounds foot (lbs.ft.)
Foot pounds (ft.lbs.) sounds the best, but seems to be most confusing when the amount X refers to the “lbs.” and not the “ft.”
Sorry about the rant.
I’m so happy to see your post. I think, out of all that replied to the original post, your explanation suits me the best. It also gives me more insight into my humble knowledge of electronics. I gather in your statements that, by inference, 1 HP = 750 watts for 1 second. So, by that, a 750 watt bulb burning for 1 minute has basically used 60 HP. Fascinating. Thanks for the time you spent on this.
Actually, a 750W bulb burning for 1 minute consumes the same energy as a 60hp motor would use in 1 second. That’s the best way to compare energy usage.
Just a clarification…1 HP = 746 watts no matter how much time has elapsed. Example: An ideal 1HP electric motor consumes 746 watts (a unit of power) while running. So one would express the total amount of energy consumed in terms of watt/sec or watt/min or most commonly watt/hr for consumer products. Your home electric costs are based on units of watt/hrs. Suppose your electric rate was 20 cents per kilowatt hour and your ideal 1HP motor ran for 15 minutes. Then, your total cost to run that motor would be 0.746 kw * 0.25hr * 20cents/kw/hr = 3.73 cents. Hope that helps!
Your clarification requires clarification. A forward slash is most commonly used to denote division in the United States. As such, energy consumed would be watt-second, watt-minute or watt-hour, NOT watt/sec, watt/min or watt/anything.
In algebra, there is an implied 1 before any unit of measure, and you can divide or multiply anything by 1 and get the same answer. I believe that is why units and operators move around on these compound units. So 20kW/hr should be the same as 20kW•hr (or 20kW^hr, for that matter). The problem is those operators don’t represent what you are actually measuring (Watts over a period of 1hr, usually accumulating rather than an average, which is better represented by a multiplication operator, rather than division)
This discussion was food for a question to another person, and my ideas of the meanings Differed, of course, when t=(time) is considered. This then caused me some consternation, because as I envisioned the comparison of the net Participation, believing in the Heat Death of the universe (“entropy” of sorts) causes a different result.
Without confusing the Reader with possibly defective arithmetic and the subsequent entree of fowl, I politely ask another to ruminate for a second and see if this phenomenon is at least viable, or is it an hallucination?
Sometime ago, when learning of the Plurality situation in cases where mere observation affects Results, my grounding in this physical world seemed ever more ephemeral. Am I here? Is there a “here” where I’m Not? Are all these measurements tangible?
Or what are the numbers? Is there or are there realms where Torque and Work
coincide, and does doing one figuring-up versus another spur the Heat Death of
the Universe, or stave it off for a moment or so………?
I respect and enjoy the purity of the intent and the engineering creed for the correct definition of the measurement of torque and/or work. However, it is more than obvious to most that intuitively most know and/or understand both terms as listed. It never ceases to amaze me how anal some are about thing of this kind or how un-tolerant they are. I guess they just have so some much free time to debate what I consider semantics. Most are becoming desensitized to many terms like “Motorsports” when in fact cars have engines, not motors. Some marketing manager most likely felt that “Enginesports” didn’t sound as good as “Motorsports” — so Motorsports it was.
You Guys are not smart. It is ONE FOOT( singular)distance from the center of rotation and the application of ONE or MANY (multiple) POUNDS of Force.Now see if you can say it in the ENGLISH language. FOOT-POUNDS. WE (every mechanic in AMERICA( you know, the ones who kicked the asses off the rest of the world) were not incorrect in using this term for Hundreds of years. You are incorrect because you don’t have command of the proper syntax of the English language, and like so many Dweebs, think that pound-feet sounds sophisticated.OH PUKE! please stick to your little 2 litre( properly pronounced “leetree”) putt-putt cars,and we will continue to blow you away with affordable FOOT-POUNDS of TORQUE! Even Airbus builds their Airplanes to the INCH(not foot) system of Imperial measure. 2 is easier than .5 x 4 and the term Motor was around a long time before we understood electricity.