CALCULATOR · INSTANT · FREE
GT2 Belt Center Distance CalculatorGT2 CENTER DISTANCE
Enter a closed GT2 belt length and two pulley tooth counts to solve the centre distance numerically from the exact open-belt length formula, with speed ratio, wrap angles and teeth in mesh.
- PitchGT2 2 mm
- MethodExact formula, numeric
- OutputsCentre · wrap · ratio
RESULT
Live
Centre distanceC
80.00mm
Details
- Speed ratio z2 / z1i
- 1.0000
- Pulley 1 wrap angleθ1
- 180.0°
- Pulley 2 wrap angleθ2
- 180.0°
- Pulley 1 pitch diameterd1
- 12.732mm
- Pulley 2 pitch diameterd2
- 12.732mm
- Belt teethzb
- 100
- Teeth in mesh (small pulley)zm
- 10.0
Open in 3D generator
Opens the generator pre-filled with these values, ready to download STEP / STL.
HOW-TO
How to use the GT2 Belt Center Distance Calculator
- 1Pick or type the closed GT2 belt length (e.g. 200, 400, 610 mm).
- 2Enter both pulley tooth counts, e.g. 20T and 20T.
- 3Read the centre distance and check the wrap angle and teeth in mesh.
- 4Use the links to open the GT2 pulley generator with these tooth counts and download STEP / STL.
Worked example (default inputs)
| Item | Value |
|---|---|
| Belt length L (pitch length) | 200 mm |
| Pulley 1 teeth z1 | 20 |
| Pulley 2 teeth z2 | 20 |
| Centre distance(C) | 80.00 mm |
| Speed ratio z2 / z1(i) | 1.0000 |
| Pulley 1 wrap angle(θ1) | 180.0 ° |
| Pulley 2 wrap angle(θ2) | 180.0 ° |
| Pulley 1 pitch diameter(d1) | 12.732 mm |
| Pulley 2 pitch diameter(d2) | 12.732 mm |
| Belt teeth(zb) | 100 |
| Teeth in mesh (small pulley)(zm) | 10.0 |
The exact open-belt length formula
A two-pulley belt consists of two straight spans and two wrapped arcs: L = 2√(C² − e²) + π(d1+d2)/2 + 2e·asin(e/C) with e = (d2−d1)/2. There is no closed form for C, and the usual approximations lose accuracy at large ratios, so this tool solves it by bisection to better than 0.001 mm. With equal pulleys e = 0 and the formula reduces to L = 2C + πd.
Tips for 3D printers and CNC
GT2 is the standard timing belt for 3D printers and small CNC machines — typically 20T pulleys with 6 mm belt. Closed loops are used for Z-axis sync or reductions such as 20T→60T (1:3). Keep the small pulley at 16T or more with at least 6 teeth in mesh, and allow for tensioning. Generate the pulleys on this site and send them to Orinovate for printing in PETG, nylon or MJF.
Formulas
d = z × 2 / π L = 2√(C² − e²) + π(d1 + d2)/2 + 2e·asin(e/C), e = (d2 − d1)/2 C solved numerically from the formula above θ1 = 180° − 2·asin(e/C), θ2 = 180° + 2·asin(e/C) i = z2 / z1 teeth in mesh = z_small × θ_small / 360°
Results are for design reference only; confirm against supplier catalogues and the applicable standards before manufacturing.
FAQ
How do I calculate GT2 belt centre distance?
With equal pulleys it is simple: C = (L − teeth × 2) / 2. A 200 mm belt on two 20T pulleys gives C = (200 − 40) / 2 = 80 mm. For different pulleys this tool solves the exact open-belt length formula numerically.
What is the pitch diameter of a GT2 pulley?
d = teeth × 2 mm / π, so a 20T pulley has a 12.73 mm pitch diameter and an outside diameter about 0.5 mm smaller (≈ 12.22 mm).
Why do wrap angle and teeth in mesh matter?
A smaller wrap on the small pulley means fewer engaged teeth and less transmissible torque. Keep at least 6 teeth in mesh to avoid skipping.
How should I set the real centre distance?
The result is theoretical. Provide 1–3 mm of tension adjustment (slots or an idler) and tension until the belt gives a low twang when plucked; over-tensioning wears bearings.
Does this work for open-ended belt?
Open-ended belt is clamped at both ends and cut to any length, so the even-length rule does not apply. This tool targets closed loop belts.
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Further reading
Need a physical part?
Send the model straight to Orinovate's instant quote: FDM, SLA, SLS, MJF, metal printing and CNC, made in Hsinchu, Taiwan.
Standards
- GT2 2 mm pitch
- 2GT