# Belt tension calculator

URL: https://www.clove3d.com/tools/belt-tension/

Tension GT2 and GT3 timing belts by the pluck method. Measure the resonant frequency of the free belt span with a phone tuner app and convert to tension, or enter a target tension to find the target frequency to tune to.

## Formula

Frequency to tension: T = mu x (2 x L x f)^2
Tension to frequency: f = (1 / (2 x L)) x sqrt(T / mu)

Where:
  T   = tension in Newtons (N)
  L   = free span length in metres (m)
  f   = fundamental resonant frequency in Hz
  mu  = linear mass density of the belt in kg/m

## Belt reference

| Belt | Pitch | Typical width | mu (kg/m, 6 mm wide) |
|------|-------|---------------|----------------------|
| GT2  | 2 mm  | 6 mm, 9 mm    | approximately 0.0043 |
| GT3  | 3 mm  | 9 mm          | approximately 0.0100 |

Actual mu depends on belt brand and width. Use manufacturer data when available.

## Inputs

- Belt type (GT2 or GT3)
- Belt width (mm)
- Free span length (mm)
- Mode: measure frequency and get tension, or set target tension and get target frequency

## Outputs

- Tension in Newtons, or target frequency in Hz
- Comparison to typical target range for the belt type

## FAQ

Q: How do I measure belt frequency?
A: Pluck the free belt span like a guitar string and use a guitar tuner app or spectrum analyser on your phone. Read the fundamental frequency in Hz. Longer spans give lower, easier-to-measure frequencies.

Q: What counts as the free span?
A: The unsupported length between two pulleys or between a pulley and a guide. Do not include the part of the belt wrapped around a pulley.

Q: Why does belt tension matter?
A: Under-tensioned belts skip teeth and cause banding or layer shifting. Over-tensioned belts wear bearings faster. Correct tension gives consistent, repeatable motion.