GT2 Belt Tension Calculator
A tensioned belt span vibrates like a string when plucked, and the pitch it produces encodes its tension. The fundamental frequency depends on the tension, the free span length, and the belt's mass per unit length, by the standard vibrating-string relation. Rearranged, tension equals four times the linear mass density times the span length squared times the frequency squared. Measure the pluck frequency with a tuner or phone app, enter the free span and the belt's mass per meter, and this calculator returns the tension in newtons. The mass per meter stays editable because it depends on belt width and construction.
Belt tension formula
mu (kg/m) = mass per meter (g/m) / 1000
L (m) = span (mm) / 1000
Tension (N) = 4 * mu * L^2 * f^2
Tension (kgf) = tension (N) / 9.80665
This is the fundamental-mode vibrating-string relation rearranged for tension. Standard gravity is exactly 9.80665 m/s squared, used to convert newtons to kilograms-force.
Belt tension context
- The physics is exact for an ideal string; a real belt approximates it closely at the fundamental.
- Measure only the free span between pulleys or clamps, not the whole loop.
- Weigh a known belt length to find mass per meter, or use the manufacturer's spec.
- There is no universal target tension; follow your printer maker's recommendation.
- Use a tuner or microphone app to read the pluck frequency cleanly.
Belt tension: frequently asked questions
How does a plucked belt reveal its tension?
A tensioned belt span behaves like a vibrating string. The fundamental frequency f relates to tension T, span length L, and linear mass density mu by f equals one over two L times the square root of T over mu. Solving for tension gives T equals 4 times mu times L squared times f squared. Measure the pluck frequency with a tuner or phone app and compute the tension.
What is the linear mass density of a GT2 belt?
Linear mass density is the belt mass per unit length in kilograms per meter. It depends on belt width and reinforcement, so this calculator keeps it editable. Weigh a known length of your belt and divide mass by length, or use the manufacturer's specification.
What span length should I measure?
Use the free span: the unsupported length of belt between the two points where it leaves the pulleys or clamps. Only the freely vibrating section determines the pluck frequency, so measure that distance, not the total belt loop.
What tension should a 3D printer belt have?
There is no single official figure; recommended tension varies by machine, belt width, and frame stiffness. Use the value your printer manufacturer specifies and this tool to confirm you have reached it consistently across axes.
Why use frequency instead of a tension gauge?
A pluck-and-measure method needs only a microphone app, costs nothing, and is repeatable. The physics of a vibrating string is exact, so given an accurate frequency, span, and mass per meter, the tension follows directly.
Official sources
- National Institute of Standards and Technology: Fundamental Physical Constants (standard gravity).
- RepRap project documentation: reprap.org (belt and motion reference).
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.