Tridimensional microscopy and algorithms for automated segmentation and tracing are revolutionizing neuroscience through the generation of growing libraries of neuron reconstructions. Innovative computational methods are needed to analyze these neural traces. In particular, means to analyse the geometric properties of traced neurites along their trajectory have been lacking. Here, we propose a local tridimensional (3D) scale metric derived from differential geometry, which is the distance in micrometers along which a curve is fully 3D as opposed to being embedded in a 2D plane or 1D line. We apply this metric to various neuronal traces ranging from single neurons to whole brain data. By providing a local readout of the geometric complexity, it offers a new mean of describing and comparing axonal and dendritic arbors from individual neurons or the behavior of axonal projections in different brain regions. This broadly applicable approach termed nAdder is available through the GeNePy3D open-source Python quantitative geometry library.