How is the E argument calculated for a given G1 command?

Question

I'm working on building a tool to generate G-code (a simpler slicer), and I'm trying to calculate how much filament should be extruded per movement.

Is there a standard calculation for this? Something like:

layer height * flow % * extruder diameter * distance 

How does Ultimaker Cura calculate this?

Answer 1

Basically, all movements are (small) straight lines, the volume of a straight line is easily calculated as you already guessed.

To calculate the volume to be extruded you multiply the following parameters:

• the layer height (h)
• flow modifier (e.g. as percentage) (SF)
• extruder nozzle diameter (d_n) (or extruder line width if different from nozzle diameter)
• distance of the straight line (l)

With this volume you can calculate how much filament you need to extrude. To get the length (thus the length defined by the E parameter), divide the obtained volume by surface area of your used filament by:

• π * (filament radius)² or alternatively π /4 * (filament diameter)² = (π /4 * d_f²)

To sum up, the value of E is given by:

$$ E_{value} = \frac{h \times {SF} \times d_{n} \times l}{\frac{\pi}{4}d_{f}^2} = \frac{4 \times h \times {SF} \times d_{n} \times l}{\pi \times d_{f}^2} $$