let's talk about horsepower and torque what is the difference between the two horsepower is a unit of measurement specifically it's a unit of power torque is related to a force but it's not exactly the linear force that we're familiar with you could think of torque as a rotational Force it causes objects to spin or rotate you could think of it as a Twist in or turn in force power is work divided by time and work has to do with the transfer of energy from one object to another so power is the rate at which energy is being transferred from one object to another and horsepower is simply a unit of power torque on the other hand is equal to force times the Leva arm so let's say you have an object that can rotate and if we apply a force here we're going to cause this object to turn so we're going to create a rotational torque the lever arm is perpendicular to the force and it's between the force which is the line of action and the axis of rotation which is here at the pivot now the level arm is also the radius of the circle that forms when this object rotates so R could be used as well so you can write this equation for torque two torque is force times the radius or force times the level arm now let's talk about the units of torque force is typically in Newtons and left is in meters so torque can be in newton meters also sometimes the force can be in pounds and the length of the radius can be in feet so torque can be measured in pounds times foot or foot pounds now work is very similar to torque in terms of the equation work is force times distance or force times displacement rather force is in Newton's displacement is in meters so notice that work and torque can have the same units newton meters now you can also report the force in pounds and the distance in feet so work can also be represented in foot pounds now when working with problems a lot of times you'll see work represented as foot pounds and torque as pounds times foot so if you have a problem that you're working on and the values aren't specified to be work or Torque if you see foot pounds typically that's associated with work if you see pounds times foot or pounds times feet that usually indicates torque so I just want you to be mindful of that now one horsepower is equal to 746 Watts for those of you who might be wondering what is a watt a watt is a unit of power and it's equal to one joule of energy being transferred in one second so that's what a watt is going back to this equation work equals force times displacement a force of one newton applied over a distance or displacement of one meter we'll do one joule of work so that's the equivalent of a joule one joule is equal to one newton times one meter now one horsepower is also 0.746 kilowatts and this also equals 550 foot pounds per second which also equals thirty three thousand foot pounds per minute so that's the equivalence of one horsepower now we know that work is force times displacement so you could describe power using this equation force times displacement divided by time now the idea of the horsepower came from James Watt and he coined this unit of power and he noticed that the average horse can exert 330 pounds of pulling Force over a distance of a hundred feet in one minute and so 330 times 100 this will give you 33 000 foot pounds per minute and that is equal to one horsepower so that's where the definition of the horsepower came from power exerted by the average horse now let's talk about how we can get these values from what we have here so using this equation we know that one horsepower so that's p is equal to 746 Watts which is also p now I'm going to use this equation here 746 watts is equivalent to applying a force of 746 Newtons over a distance of 1 meter in a time period of one second that will give us 746 Watts which is one horsepower now we're going to do some conversions here's some other conversion factors you want to be familiar with one pound is equal to 4.45 newtons and one meter is 3.2808 feet so converting Newtons to Pounds I'm going to put 4.45 newtons on the bottom and one pound on top so the unit Newtons will cancel next I'm going to convert meters to feet so 1 meter is 3.2808 feet so now the unit meters will cancel and what I have left over is foot pounds per second 746 divided by 4.45 times 3.2808 that's approximately 550 foot pounds per second so that's where we get this number so that's how you can prove that one horsepower is equal to this now let's convert seconds into minutes so we know that there's 60 seconds in one minute so now we can cross out the unit seconds 550 times 60 will give us 33 000 foot pounds per minute so that's how you can convert one horsepower into foot pounds per minute so make sure you know this one horsepower is 746 Watts which is 550 foot-pounds per second which is 33 000 foot-pounds per minute now there's another conversion factor that I want to give you and that is the conversion from newton meters to foot pounds So based on equation work is equal to force times displacement we know that one joule of work is equal to one newton times one meter but now let's convert the Newton meter to foot pounds so we know that one pound is 4.45 Newtons and there's 3.2808 feet per one meter so this is simply 3.2808 divided by 4.45 and we get our conversion factor which is point seven three seven three foot pounds so one joule of work is equivalent to one newton times one meter which is also equivalent to 0.7373 foot-pounds so now you have the conversion factor to go from foot pounds to joules to Newton meters now there's a formula that connects power with torque now we're also going to talk about how to derive the formula between horsepower torque and RPMs now we know that power is equal to work divided by time and work is equal to force multiplied by displacement and then we have t on the bottom now you know this equation displacement is equal to Velocity multiplied by the time so solving for V if we divide both sides by T we get D over t is equal to V so what we can do is we can replace D over t with v so we get that power is equal to force times velocity so if you have a linear Force causing an object to move by some velocity V you can calculate the power that that force is exerted on the object now what about its rotational equivalent the rotational equivalent of force is the torque and the rotational equivalent of linear velocity is angular velocity represented by the symbol Omega and here's how we can derive that we know that torque is force times the radius linear velocity is angular velocity times the radius now in this equation we could solve for Force if we divide both sides by R we get that torque divided by radius is the force so I'm going to replace f with torque over the radius and V is just Omega r is going to cancel and we get that the power is equal to the torque times the angular speed or the angular velocity now in this equation power is measured in watts torque is measured in newton meters and the angular speed or the angular velocity that is in radians per second but we want to modify this equation such that P is going to represent horsepower instead of the power and Watts and we want the torque to be in foot pounds and instead of Omega we want the angular speed in RPMs because when you're dealing with engines the angular speed is usually not reported in radians per second it's reported in rotations per minute or revolutions per minute so how can we modify this equation to fit those units well let's start with Omega we know the RPMs are in revolutions per minute and one revolution around a circle is 2 pi radians which represents 360 degrees and we can convert minutes into seconds one minute is equal to 60 Seconds so notice that the unit minutes cancel and revolutions cancel so we get radians per second which represents Omega so this is going to equal Omega now this doesn't have to be a one in front of it this could be two thousand four thousand five thousand revolutions per minute 6 000 RPMs but this quantity here represents the RPMs the angular speed this part is just equal to 2 pi and this is another conversion which we divide by 60. so to go from RPMs to get Omega you need to multiply the RPMs by 2 pi and divided by 60 and that'll give you the angular speed in radians per second so let's write this equation here Omega is 2 pi times the RPMs divided by 60. now we need to convert watts into horsepower let's say if we had a thousand watts of power and we want to convert it to horsepower we know that one horsepower is 746 Watts so in order to convert from watts to horsepower we need to divide by 760. I mean by 746. that's the only way the units will cancel so what this tells us is that the power in Watts divided by 746 will give us the power in horsepower multiplying both sides by 746 we get that the power in watts is 746 times the horsepower so I'm going to save that equation for later now let's do the same thing for the torque let's say we have a torque of 100 newton meters and we want to convert it to foot pounds we know one Newton meter is equal to 0.7373 foot-pounds so in order to convert it we need to multiply by that number so the torque in newton meters multiplied by 0.7373 that will give us the torque in foot pounds so in order to get this by itself we need to divide this by this number so the torque in newton meters is equal to the torque in foot pounds divided by this number 0.7373 so I'm going to rewrite this equation so here we have power is equal to torque multiplied by the angular velocity in this equation the power is in Watts the torque is in newton meters and the angular speed is in radians per second so I'm going to replace the power in Watts with 746 times the horsepower because they equal each other now the torque in newton meters I'm going to replace that with the torque in foot pounds divided by the conversion factor of 0.7373 now Omega I'm going to replace with this it's 2 pi times the RPM over 60. now I need to get horsepower by itself so I need to do something with that 746 number in front of it so I'm going to multiply both sides by 1 over 746. so 746 times 1 over 746 they'll cancel on the left I'm just going to have horsepower on the right I have the torque in foot pounds times the RPM so that's the angular velocity but in RPMs times 2 pi divided by now I'm going to multiply these three numbers on the bottom 0.7373 times 60 times 746 will give us 33 000. that's a familiar number now what I'm going to do is I'm going to divide these two numbers backwards not 2 pi over 33 000 but 33 000 divided by 2 pi and you want to put 2 pi in parentheses 33 000 divided by 2 pi is 5252. now because I divide it backwards the 52 52 is going to be on the bottom of the fraction so we're going to get this equation the horsepower is equal to the torque in foot pounds 9 newton meters but foot pounds times the angular speed in revolutions per minute or rotations per minute divided by 52-52 so this formula shows the relationship between horsepower torque and RPMs so if you need to calculate the horsepower the torque or the RPMs if you know the other two you could use this formula so let's go ahead and work on some practice problems so you can see how to put this formula in in practice or how to put it in use let's start with this problem how much horsepower can be produced by an engine and that exerts a torque of 500 foot-pounds or pounds feet at a RPM of 2500. so with this problem all we need to do is use this formula the horsepower is going to equal the torque times the RPMs divided by 5252. so we have 500 foot pounds of torque 2500 rpm and then let's divide that by 5252. so you should get a power of 238 horsepower and you could easily convert this to Watts by multiplying this number by 746. so this is equivalent to a hundred seventy seven thousand 555 1 Watts and if you divide that by a thousand that's 177 0.55 kilowatts so that's how you can quickly convert horsepower into watts and kilowatts so remember to go from horsepower to watts multiply by 746 and to go from watts to kilowatts divide by a thousand now let's move on to number two how many RPMs will a 133.3 horsepower engine generate at a torque of 200 foot-pounds so let's start with our original equation horsepower is equal to torque times RPMs divided by 52 52. so what we want to do in this problem is we want to isolate RPMs so I'm going to multiply both sides by 5252. so the horsepower times 5252 is going to equal the torque times the RPMs now to get RPM by itself I need to divide both sides by the torque so these will cancel so now we get this equation to calculate the RPM it's going to be the value of the horsepower times 5252 so I'm going to write this way 5252 times HP and then divided by the torque so it's 5252 times the horsepower of 133.3 divided by a torque of 200 foot-pounds so this will give us an RPM of 3 500. so that's how you can calculate the RPM if you know how much power is exerted by the engine in horsepower and if you know the torque that the engine produces in foot pounds now let's move on to example three how much torque will a 500 horsepower engine produce at 3000 RPMs so let's begin with our original formula HP is equal to torque times RPM divided by 5252 now this time we want to solve for torque so what we could do is cross multiply so here we have one I put HP over 1 so 1 times the torque times RPM it's going to equal 5252 times the horsepower now I want to get torque by itself so I'm going to divide both sides by RPM so to calculate the torque we could use this formula it's 52 52 times the horsepower divided by RPM so we have a 500 horsepower engine and the RPMs are at 3000. so 3 000 revolutions per minute which is pretty fast 5252 times 500 over 3000 that will give us a torque of 875.3 foot pounds or pound feet so that's the answer for this problem now let's work on one more problem how much horsepower can be produced by an engine that exerts a torque of 75 000 inches times ounces at a RPM of 4000. feel free to pause the video if you want to work on this example problem now this problem is similar to number one the only difference is the units of torque instead of foot pounds it's inches times ounces so we need to do a conversion here so we have seventy five thousand inches times ounces we know that there's 12 inches in a foot and one pound is equivalent to 16 ounces you could do a Google search on that if you type in pounds to ounces you see that one pound is 16 ounces now we set this up in such a way that the unit ounces will cancel and the unit inches will cancel by the way for those of you who are confused about how to do this unit conversion stuff I do have a video entitled converting units on YouTube so if you type in converting units organic chemistry tutor and a YouTube search bar that video is going to come up and it has a ton of examples that will explain how you can convert from one unit to another because if you know how to do that a lot of problems that you'll deal with in physics and even chemistry become a lot easier if you could understand how the units relate to each other so if this is a topic that you struggle with you need conversion I highly recommend that you watch that video so this is going to be 75 000. divided by 12. divide that result by 16. so the torque is 390 0.625 foot pounds so now that we have the torque and the appropriate unit we can now use this formula to calculate the horsepower so the horsepower is going to be the torque times the RPMs divided by 5252. so this is 390.625 and we have an angular speed of 4 000 revolutions per minute or rotations per minute and then we'll divide that by 5252. so 390.625 times 4000 divided by 5252 and you should get 297.5 so that's how much horsepower this engine can produce at an RPM of four thousand when it exerts a torque of 75 000 inches times ounces now let's get the power in Watts so if we take 297.5 and multiply by 746 we'll get 221 935 Watts and if we divide that by a thousand this is 221.9 kilowatts because sometimes you need to convert horsepower to kilowatts and that's a quick way of how you can do it so that's basically it for this video hopefully it gave you a good understanding where you could see the relationship between horsepower and torque so remember horsepower is simply a unit of measurement it is a unit of power and power is the rate at which energy can be transferred from one object to another by means of a force torque is a rotational Force torque is the twist-in or rotational force that causes objects to spin or rotate so horsepower and torque they're completely different one is a rotational Force One is the unit of power now there's something else I do want to mention so we said that power is force times velocity and it's also equal to rotational power which is torque times angular velocity work is force times displacement rotational work is torque times angular displacement notice the similarities so just as a force when applied on an object can do work on that object by moving it through some displacement if you apply a force on an object that can turn or rotate you're creating a torque and as you move this object by some angular displacement Delta Theta where this is Theta 1 this is Theta two Delta Theta is the difference between those two angles as that rotational force or that torque caused the object to spin you're doing rotational work on that object and that's the formula for rotational work it's torque times angular displacement much in the same way as linear work is force times linear displacement and we can see that power is force times velocity rotational power is torque times angular velocity so I want to make sure you see the similarities between work and power for objects in linear motion versus objects with rotational motion