Belt Tension Frequency Calculator
Calculate 3D printer belt resonant frequency from belt length and tension.
Find the target Hz for CoreXY and Cartesian axes to reduce ghosting.
Belt tension is one of the most overlooked tuning parameters on CoreXY and Cartesian printers. Too loose and the belt skips under rapid direction changes, producing ghosting artifacts on vertical surfaces. Too tight and you accelerate bearing wear, risk stretching the belt, and add unnecessary load to the steppers.
The belt behaves like a guitar string. Its resonant frequency follows:
f = (1 / (2L)) x sqrt(T / mu)
L is the free belt length in meters, T is tension in Newtons, and mu is the linear mass density in kg/m. For a GT2 6mm belt, mu is approximately 0.007 kg/m. The 9mm version runs about 0.011 kg/m.
Target range. Most CoreXY printers (Voron, RatRig, Bambu) target 50-80 Hz per belt. Bambu Lab specifies around 60-75 Hz for X and Y specifically. Cartesian printers typically run 45-65 Hz, as the belt paths are shorter and the gantry mass differs.
How to measure. Use a phone app. Gates Carbon Drive and Spectroid both work well. Pluck the belt firmly once and read the dominant frequency. Measure X and Y separately. If they differ by more than a few Hz, the gantry may not be sitting square.
Asymmetric tension between X and Y in CoreXY creates resonance at specific print speeds, showing up as diagonal banding or a ripple pattern that changes with speed but not with acceleration.
This calculator accepts tension in grams (from a luggage scale or fish scale). Clamp one end, hang a weight from the other at mid-span, and read the scale. The calculation converts grams to Newtons automatically.