Need some help in the calculation of the torque multiplication if you use an extension.

I am referring to an extension that increase the length of the toque wrench AFTER to place where you normally attach a socket (not an extension in the same axis as the socket to reach into a deeper hole/gap).

In all this I am using a “click” type wrench and an extension (e.g. another spanner) that is connected to form a straight line with the wrench handle.

Now, if you apply turning force with your hand half way down the torque wrench handle, or add a “cheater” bar, the wrench will click at exactly the same applied torque at the nut. This logical, fits with my understanding of levers, and seems to be the accepted wisdom.

If I use an extension that increases the length after the torque wrench, this will increase the applied torque at the nut/bolt when the wrench “clicks”. Again no arguments

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However, in order to calculate the multiplication, most calculators/formulae take into account the original wrench handle length along with the extension length I can’t see why thee original handle has any bearing on the new value, especially as the effective handle length does not affect the setting in normal use.

If I set the wrench to 100Nm, and use a 1m extension, I assume I will get 200Nm at the bolt. Or do I need to use the original handle length in the calculation to get the ratio?