So this is it, you just opened the box and pulled out your brand new superlight carbon frame, or not, and you want to mount your bike yourself.  Fair enough.  But what strength should you use to tighten the screws?

Introduction and precautions

For convenience, I’ll break down the screws into two broad categories: light and strong. I call light screws the ones with a thread under 5 mm, and strong ones the ones equal to or larger than 5 mm.

In the light screw set, I’m thinking of the very fragile ones, or applying on a fragile part, like the front derailleur braze on screw, or the 4 handlebar stem screws, which you’ll find very annoying to replace is you break one just before you get on your bike . . .

For the light set, I mostly recommend manual tightening, controlled by a torque wrench if you have one.
Remember that by construction, a torque wrench may get stuck and not trigger around the set torque.  It happened a couple of times with mine, and you could easily break a screw (best case scenario) or damage your frame irreversibly (worst case scenario).  That’s why when you use a torque wrench, you should always start well under the recommended torque, and make sure your wrench triggers off.  Then you progressively set the cut-off torque up.  After a few turns, if it doesn’t trigger, and you start to hear strain sounds in your material, you’d better stop and think twice.  That’s why if you only are to set a torque to about 6 Nm, you shouldn’t use a torque wrench you don’t trust at 100%, but rather the good old manual Allen key.

The strong set

Now, as far as the strong set goes, I have in mind the seat bolt, pedals, bottom bracket, and the cassette screws, it’s not so much that these screws are fragile, but rather that your“personal assessment”, or your more objectively your torque wrench may not go as high as 35 Nm for example.  You can only go by“tightened well enough”, with all its wake of subjectivity . . .
Your first reflex should be to read any possible specifications directly on the part to mount or on the target part that receives it.  Alternatively you may refer to the documentation that came with your part or frame.  Your last resort is to check the manufacturer website.

Once you know the cut-off torque to reach, how about measuring the torque you apply?
Let’s say in a high-torque scenario, like a cassette (a set of bicycle rear wheel sprockets).

3 rules

a) don’t apply your own strength with your arm, as you couldn’t measure it.  Apply a well known weight onto the wrench handle.

b) Determine the distance at which to exert the weight so that the corresponding torque equates the value you want to reach.

c) For the sake of simplicity, make sure the wrench is horizontal.

What weight corresponds to what torque?

By definition, torque is given by this formula:
T = F . r where F is the force exerted onto the wrench at the useful distance r from its centre O.  Here the force is the weight, so it is exactly vertical.
r is not always the length of the wrench.  We talked about useful distance.  It is if the force is exerted at a right angle from the wrench (α = 0), otherwise it’s more complicated to calculate, we’ll see that general case further down.  

A torque is always expressed in a unit of force multiplied by a unit of distance, such as the newton meter (N.m or Nm for short) in the International System (IS), used in this article.  Other units exist.  Attention, here it’s not newton per meter, it is a multiplication: newton by meter . . .

The newton is the unit of force in the IS.  It’s roughly equivalent to the horizontal, top down exertion made on Earth by a static mass of 100 grams.

In our case, if a static mass P exerts a force on a given point, that force is: F = P . g Where P is the mass in kilograms (in English we say weight, but it is subtly incorrect, it is actually mass), and g is the gravity.  Let’s consider g = 9.81 ms^-2.  Fundamentals being edicted, let’s apply them to a freeehub practical case.

Example

You want to tighten a cassette to 40 Nm, as specified on its screw.  We’ll say first that you apply a gym weight of 20 kg using an old clincher (you’ll see how convenient this is) to the tip of your cassette wrench (well you really need that one . . . ).
Let’s consider the wrench length is 21 cm from the axis to the middle of where the clincher applies.  You can now infer the torque applied when you lift the set so that the weight does not touch the ground anymore and the wrench is horizontal: T = F . r = 20 x 9.81 x 0.21 = 41.2 Nm 21 cm is converted in meters, as the unit used on the part is the Nm.

As you can see, 41 Nm is really close to the recommended 40 Nm, so I might not change a thing.  However, if you had to be more accurate, you might consider to get the rubber belt a tiny bit closer to the axis so that it reduces the torque.
The right distance to use is then:
r = T / F = 40 / (20 * 9.81) = 0.204 m = 20.4 cm

For the purists

If you really wanted to be accurate, you should add the own weight of the clincher tyre to the weight you use as a ballast, and also the contribution of the wrench itself, as if its weight added a torque applied at about half the length of its handle! Given the weights implied, the tyre and wrench contributions are called“second order terms” in Physics, hence negligeable before the main contributio: the weight of the ballast.

Remember, to use the torque formula, use the proper units.  A force should be expressed in newtons, and a distance in meters.

For further information, the general situation where a wrench makes an α angle with the horizontal leads to: T = F . r . cos(α) Reminder: cos(α) = 1 for α = 0, which is the remarkable case we used before, no calculator needed.