Belt Tension Calculator | PrintCalcLab

Calculate 3D printer belt tension (N) using the vibration frequency method.

Loose belts cause layer shifts and sloppy dimensional accuracy; over-tight belts wear bearings and motor shafts. The frequency method gives you a repeatable way to hit a target tension: pluck the belt like a guitar string, measure the resonant frequency, and convert it to newtons. This calculator applies the string-vibration equation to your measured frequency, free belt span, and belt type, so both gantry belts of a CoreXY — or both Z belts — can be matched precisely instead of tuned by feel.

How It Works

Tension is calculated as T = 4 × span² × frequency² × linear density, with the span in meters, the frequency in hertz, and the density in kilograms per meter. Built-in density values cover GT2 belts: 0.006 kg/m for 6 mm width, 0.009 kg/m for 9 mm, and 0.010 kg/m for 10 mm. For example, a 6 mm GT2 belt with a 150 mm free span vibrating at 100 Hz carries 4 × 0.15² × 100² × 0.006 = 5.4 N. Because tension scales with the square of both span and frequency, measuring the free length accurately matters as much as the frequency reading.

FAQ

How do I measure my belt's vibration frequency?

Pluck the longest unsupported section and record it with a spectrum-analyzer or instrument-tuner app on a phone held close to the belt. Use the strongest low peak — harmonics show up at multiples of the true frequency.

What does the free span mean exactly?

It is the length of belt that can vibrate freely between two fixed points such as pulleys or clamps — not the total belt length. Measure only the section you pluck, and measure it carefully, since the result grows with the square of the span.

Why do my two belts read different frequencies at the same tension?

Frequency depends on the span as well as the tension. If the two belt runs have different free lengths, equal tension produces different pitches — convert each measurement to newtons using its own span instead of matching frequencies by ear.

Does belt width change the result?

Yes — a wider belt is heavier per meter, so the same span and frequency correspond to proportionally more tension. That is why the calculator uses 0.006, 0.009, and 0.010 kg/m for 6, 9, and 10 mm GT2 belts respectively.