# How can I calculate force applied with a lever?

I am trying to understand how to calculate the amount of force applied using a given lever. I am by no means a physics expert and was unable to find an answer to this question online, or at least not one I could understand.

I am from the US and use imperial measurements so I have a basic understand that 1 pound of force applied to the end of a 1 foot lever will produce 1 lb-ft of torque, 2 pounds is 2 lb-ft, etc.

I want to know if that force is also increased linearly with length. For example would 1 pound applied to the end of a 2 foot lever produce 2 lb-ft, 1 pound applied to a 3 foot lever produce 3 lb-ft? If not is there some formula I can use to calculate how much force is being applied given an N length lever?

• Are you familiar with units like Newtons (N) and Metre (m)? Dec 5, 2021 at 7:21
• @IshaanManish I am but I am much more used to working with lb-ft Dec 5, 2021 at 13:47

I want to know if that force is also increased linearly with length.

Well, it isn't force, but instead torque that increases with increase in distance from the fulcrum, where you apply force.

If not is there some formula I can use to calculate how much force is being applied given an N length lever?

As your question isn't very clear, I am not sure if you want to find torque generated by force applied or force required to generate the torque. If you want to find torque generated by force applied, the formula is $$T = F\times d$$ $$T$$ is torque, $$F$$ is force applied, and $$d$$ is distance from fulcrum.

If you want to find force required to generate the torque, we can rearrange the previous formula to derive $$F = \frac{d}{T}$$

Again, $$T$$ is torque, $$F$$ is force applied, and $$d$$ is distance from fulcrum.

Just to be clear, I'll give an example.

In the above picture, assume the rod's length is $$1ft$$, and $$F_1$$ is $$10lb$$. Also assume that distance from $$F_1$$ and fulcrum is $$3in$$. In order to find torque generated, use the formula $$T = F \times d$$ Substituting the values, we get $$T = 10lb \times 3in$$ $$= 30lbin$$ In case you want to find force required to generate the torque, use the second equation $$F = \frac{d}{T}$$ Substituting the values, we get $$F = \frac{30lbin}{3in}$$ $$= 10lb$$

• This equation is correct $T=d\times F$
– Eli
Dec 5, 2021 at 8:23
• I am interested in the force generated and thinking more in terms of a breaker bar tightening bolts. If I push down on a 1 foot long breaker bar with 1 pound I would theoretically be applying around 1 lb-ft of torque to the bolt but what if that bar is two or three foot long? Dec 5, 2021 at 13:38
• I think this answers my question though since it's force multiplied by distance an increase in either should mean a linear increase in torque? Dec 5, 2021 at 13:45
• @jesse_b yes, increase in either will lead to linear increase in torque. (Probably, the term equivalent is better to use in this case.) Dec 5, 2021 at 14:00

Work out the force produced like this

$$F=\frac{3\times10}{0.1}$$

you can change the numbers as required.

• He isn't asking about static equilibrium. He is asking how to measure the force or torque on lever ( I am not sure if force or torque ). Dec 5, 2021 at 10:35
• The answer is about what the questioner wants to know. Dec 5, 2021 at 10:48