 When calculating torque you probably have used most of the time this equation here. Torque is equal to the length of the lever times the force times sine of the angle in between. For example in our little setup here on the left, we have the force down here and we have the length of the lever here and the angle which is here. Now quite often you don't know the lever exactly, but you might know information like this. This is a length of five meters, so let's say this one is a length of three meters. Instead of calculating our square root of five squared plus three squared and the angle, so the theta here is the same as here. Theta is the inverse of the tan of opposite over adjacent, so five over three, and then plug it into equation. There is another way to get the torque much quicker. To do so, let me change a little detail here in my equation above. What I'm doing is I'm changing the position of r and f. I'm absolutely allowed to do that. sine theta times f. And now what is r times sine theta? If you look at my triangle, r times sine theta is the opposite side of my right angle triangle. I have one here. So my formula here becomes the r perpendicular to f. It's the shortest distance from the pivot point, which I assume here to be up here, to the axis along which my force is acting. So my force is acting along this axis and the shortest distance in this case is five. So I can just do five times whatever my force is and I have the answer and I don't even need to calculate any sine functions. Now this works for any random situation. Let's say I have a pivot here and I have a force acting like this. Instead of trying to figure out what is my r, I can also just make a line where my force is going and find the shortest distance, the shortest distance. So it's perpendicular. So if I could know this value here, I could calculate my torque as what the shortest distance times whatever the force it is here, which is exactly the same as if I go the long way and they do r times f, r being that one here times sine of the angle. Angle here being that one here. Now, this is my first shortcut. There is another one that I could use. So again, I have a pivot point here. I have an r that's around like this, should be a straight line and I have a force at the random angle, theta. Now instead of doing torque is r times sine theta times f. I'm now regrouping sine theta times f. Basically, I'm regrouping this part here. If we go and draw here another triangle, this line here is my f perpendicular, which is nothing else than sine theta theta times f. That means if I can easily find the part of the force that is perpendicular to my r, I can use the following new equation. So torque is f perpendicular times the force at length of the lever. So this is one shortcut formula and the other one from before is r perpendicular times f, which adds to our general equation. Just torque is r times f times sine of the angle. If you go with vectors, there's actually another way to calculate torque. That is torque as a vector. Simply r cross f. But only use this if you actually have learned how to use the cross product properly. Because this cross here is not just a multiplication. It's the cross product which has its own definition. So only use that one if you know what you're doing, otherwise use one of the other ones. If you can, this one here, number one, number two, or number three. And which one is the best? Depends on the situation of what you are given. All three of them will work all the time. So worst case, you just pick one and you go with one.