Belt Tension Frequency Calculator

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. A frequency target only means something together with the span it was measured on, because f depends on L. The common reference point: the Voron docs call for about 110 Hz plucked on a 150 mm span of 6 mm GT2. That exact same healthy tension reads only about 40 Hz on a 400 mm span, so never compare your Hz to someone else’s without matching spans. In tension terms, which is span-independent, a 6 mm GT2 belt is usually happy around 4 to 9 newtons (roughly 400-900 grams); wider belts run toward the top of that band.

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). It answers: if you tensioned the belt to X grams while installing it, what pluck frequency should you expect on your span? Pull the belt to the target reading with the scale while fitting it, enter the grams here, then verify the predicted frequency with the phone app. The calculation converts grams to Newtons automatically.