Involute Spur Gear Center Distance, Gear Ratio & GT2/HTD Timing Belt Length Calculator (ISO 53)
Involute Spur Gear Center Distance, Gear Ratio & GT2/HTD Belt Length Calculator
How This Gear Center Distance & Belt Length Calculator Works
Designing a laser-cut or CNC-machined gear train or synchronous timing belt drive requires exact shaft center-to-center spacing so gears mesh along their tangent pitch circles without binding or excessive backlash, and timing belts match standard closed-loop tooth counts. Our dual-mode ISO 53 / ISO 5294 calculator computes driving and driven pitch diameters (d = m × Z), outside tip diameters, exact mounting center distance (a), speed/torque ratio, and required GT2 (2mm), HTD 3M (3mm), or HTD 5M (5mm) timing belt length and tooth count.
Governing Mathematical Equations (ISO 53 Cylindrical Gears & ISO 5294 Synchronous Belt Drive Standard)
Multiplies metric module (m) by tooth count (Z) to find tangent pitch circles and outer addendum tip circles.
Defines the exact distance between the two shaft bore centers on your mounting plate.
Computes total belt pitch circumference and exact belt tooth count (N_belt = L_belt / Pitch) for a given shaft center distance C.
Standard Metric Gear Modules & Synchronous Timing Belt Pitches
| Drive Profile | Linear Pitch (P) | Module Equivalent | Min Tooth Count | Typical Application |
|---|---|---|---|---|
| GT2 Synchronous Belt | 2.00 mm | m ≈ 0.6366 | 16 – 20 Teeth | 3D printers, laser engraver X/Y axes, light robotics |
| HTD 3M Synchronous Belt | 3.00 mm | m ≈ 0.9549 | 18 – 24 Teeth | Desktop CNC routers, camera motion rigs, automation |
| HTD 5M Synchronous Belt | 5.00 mm | m ≈ 1.5915 | 20 – 28 Teeth | High-torque CNC gantries, e-bikes, industrial conveyors |
| ISO 53 Spur Gear (m = 1.5 – 3.0) | 4.71 – 9.42 mm | m = 1.5, 2.0, 2.5, 3.0 | 14 – 18 Teeth (20° PA) | Laser-cut Delrin/plywood gearboxes, mechanical clocks |
Apply These Calculations in 1:1 Parametric CAD Studios
Parametric Involute Spur Gear & Center Bore CAD Generator (1:1 DXF & SVG)
Parametric NEMA 17 / 23 / 34 Stepper Motor Mount & Bolt-Circle Flange CAD Generator
Synchronous Timing Belt Pulley & Keyed Shaft Sprocket Generator (GT2 / HTD DXF)
Frequently Asked Questions — Gear Center Distance & Belt Length
How much clearance should I add to the theoretical gear center distance (a)?
For laser-cut Delrin (POM), acrylic, or plywood gears, adding +0.15mm to +0.25mm to the theoretical center distance a = m(Z1+Z2)/2 prevents tight tooth binding caused by slight material thermal expansion.
What happens if my calculated timing belt tooth count is not a whole integer?
Closed-loop timing belts are manufactured with an integer number of teeth (e.g., 200mm = 100 teeth on GT2). Our calculator rounds to the nearest whole tooth count and shows the exact adjusted shaft center distance required to tension the belt.
Can I launch the 1:1 DXF gear or pulley generator directly with my calculated diameters?
Yes! Click the 'Open Gear Studio' or 'Open Pulley Studio' button inside the calculator to pre-populate the exact Pitch Diameter (L) and Tooth Count (H) into our 1:1 CAD generator.