Belt Tension Calculator
Pluck the belt, read the frequency with a tuner app, and see the tension in newtons — or start from a target tension and get the frequency to aim for. It also converts a documented target ('110 Hz at 150 mm') to whatever span your belt actually has.
The physics
A belt under tension between two fixed points behaves like a guitar string. Its fundamental frequency depends only on the free length, the tension and the belt's mass per unit length:
L in meters, T in newtons, μ in kg/m
Two consequences worth knowing. Tension goes with the square of frequency, so 10% more Hz is 21% more tension. And at the same tension, frequency is inversely proportional to span, which is why a target quoted for one printer can't be used on another without converting — a 400 mm Ender 3 X-belt at the same tension as a 150 mm Voron span rings at less than half the frequency.
Worked example
6 mm fiberglass GT2 belt (8 g/m), 150 mm free span, plucked at 110 Hz.
- T = 4 × 0.15² × 110² × 0.008 = 4 × 0.0225 × 12100 × 0.008 = 8.7 N (about 890 grams-force)
- The same 8.7 N on a 200 mm span: f = 110 × 150 ÷ 200 = 82.5 Hz
Measuring it
- Move the carriage so a long, unobstructed section of belt is exposed — on a CoreXY, park the toolhead at a front corner and use the long back run; on an i3-style printer, the X belt with the head at one end.
- Measure the free span between the two points where the belt is clamped or leaves a pulley or idler. This is the number people get wrong; it isn't the axis length.
- Open a tuner or spectrum app. Guitar tuners work if the frequency is in their range (most accept 60–400 Hz); Spectroid or any FFT app shows the peak directly.
- Pluck the belt in the middle of the span and read the fundamental. Ignore the higher harmonics; the lowest strong peak is the one.
- Adjust the tensioner and repeat. On CoreXY, do both belts and match them within 1–2 Hz.
A belt-tension gauge or a luggage scale hooked to the belt gives the tension directly, but the frequency method is free and usually more repeatable.
Where the string model breaks down
The formula treats the belt as an ideal string with no stiffness of its own. Real toothed belts have steel or glass cords and a rubber body, and both resist bending. On a long span that contribution is negligible and the model is good. On a short span — roughly under 80–100 mm — bending stiffness adds to the restoring force, so the belt rings higher than tension alone would explain and the calculated tension reads high.
Two practical consequences. Measure the longest free span you can reach rather than a convenient short one. And when comparing against a published figure, match the span length where you can, because converting a short-span measurement to a long span inherits that error.
Matching the two belts on a CoreXY
On a CoreXY both belts drive both axes together, so their relative tension matters more than the absolute number. A mismatch means the two diagonal motions have different stiffness, which shows as skewed prints, dimensions that differ between X and Y, and ringing that appears on one axis but not the other. If your X and Y measurements disagree on a test square, unequal belts are a prime suspect.
Aim to get both within about 2 Hz of each other at the same span. Equal belts at a slightly wrong tension beat one perfect belt and one loose one.
What tension to aim for
There's no universal number, and the honest answer is: use your manufacturer's figure if one exists. Some that are commonly cited:
| Printer / source | Target | ≈ Tension |
|---|---|---|
| Voron 2.4 / Trident (6 mm GT2, 150 mm span) | 110 Hz | 8.7 N |
| Prusa MK3S/MK4 (via Prusa's belt tuning app) | ≈ 85 Hz X, ≈ 75 Hz Y at their spans | varies |
| Bambu Lab (X1/P1, via built-in tension routine) | firmware-guided | — |
| Generic desktop, 6 mm belt | — | 5 – 15 N |
| Generic desktop, 9 mm belt | — | 8 – 20 N |
Symptoms guide you from there. Too loose: ringing/ghosting after corners, dimensions that vary with direction, belt teeth skipping on fast moves. Too tight: a hum or whine from the motors, warm idler bearings, accelerated wear on the belt teeth, and on flimsier frames, a frame that flexes measurably. If a belt has been over-tightened for a long time, check the idlers before assuming the belt is the problem.
Converting a documented target
Most published figures are given as a frequency at a specific span, because that's what people measure. If your span differs, convert with:
| 110 Hz at 150 mm becomes… | 100 mm | 150 mm | 200 mm | 250 mm | 300 mm | 400 mm |
|---|---|---|---|---|---|---|
| same tension at this span | 165 Hz | 110 Hz | 82.5 Hz | 66 Hz | 55 Hz | 41 Hz |
The belt mass cancels out of the conversion, so it works for any belt as long as both figures refer to the same belt type. When they don't — a 9 mm belt on your printer versus 6 mm in the docs — use the tension figure instead and let the calculator work out the frequency for your belt.
Frequently asked questions
How tight should 3D printer belts be?
Tight enough that the belt doesn't skip or ring, loose enough not to load the bearings: for 6 mm GT2 belts on desktop printers that's typically 5–15 N of tension. As a frequency, the widely used Voron figure is 110 Hz measured over a 150 mm span, which is about 8–9 N. Your printer's documentation beats any generic number.
How do I measure belt tension with my phone?
Install a tuner or spectrum app (any guitar tuner, or Spectroid on Android), hold the phone near the middle of a free belt span, and pluck the belt like a guitar string. Read the fundamental frequency. Measure the span length between the two points where the belt is fixed or wraps a pulley, and enter both here.
What's the formula relating frequency and tension?
For a vibrating string: f = (1 ÷ 2L) × √(T ÷ μ), where L is the free span in meters, T the tension in newtons and μ the belt's mass per meter. Rearranged, T = 4 × L² × f² × μ. A 6 mm GT2 belt weighs about 8 g per meter.
Why do the two belts on a CoreXY need to match?
On CoreXY both belts drive both axes. If one is tighter, the X and Y motions have different stiffness, which shows up as skewed prints, uneven ringing and mismatched dimensions along the two diagonals. Matching them within 1–2 Hz matters more than the absolute value.
My printer's docs give a frequency for a different span. What do I do?
Frequency scales inversely with span at the same tension. If the docs say 110 Hz at 150 mm and your free span is 200 mm, the equivalent is 110 × 150 ÷ 200 = 82.5 Hz. The bottom section of the calculator does this conversion.
Last reviewed September 8, 2026. Spotted an error or want another calculator? Tell us.