Calculation
dw = z · p / π
Pitch circumference equals tooth count times tooth pitch; the resulting pitch circle is not the measurable outside diameter.
Zahnriemen-Geometrie
Timing-belt pulley pitch diameter
Pitch circumference equals tooth count times tooth pitch; the resulting pitch circle is not the measurable outside diameter.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Pitch diameter dw — Diameter of the timing belt's pitch line around the pulley.
- Pulley teeth z — Number of equally spaced pulley teeth or grooves.
- Tooth pitch p — Spacing of adjacent tooth profiles along the pitch line; must match the belt profile.
Example
20 teeth at 5 mm pitch give dw = 20·5/π = 31.831 mm.
Assumptions and limits
Matching timing-belt profile with uniform pitch; outside, root, flange and bore diameters are not calculated.
Understand Timing-belt pulley pitch diameter
This calculator converts timing-pulley tooth pitch and tooth count into pitch diameter. That geometric diameter controls ratio, belt speed and center distance but cannot simply be measured at the outside of a real tooth profile.
What does this quantity describe?
Along the pitch circle, each tooth occupies one pitch p. Pitch circumference is therefore z·p and also π·dw. From πdw = zp follows dw = z·p/π.
Wrap a marked tape around the invisible pitch circle. One revolution must contain exactly z intervals of length p, and diameter is circumference divided by π.
Formula and variables
dw = z · p / π
π·dw = z·pdw = z·p/πz = π·dw/pp = π·dw/z
| Symbol / input | Meaning |
|---|---|
| Pitch diameter dw | Diameter of the timing belt's pitch line around the pulley. |
| Pulley teeth z | Number of equally spaced pulley teeth or grooves. |
| Tooth pitch p | Spacing of adjacent tooth profiles along the pitch line; must match the belt profile. |
Choose the inputs correctly
z is whole pulley tooth count. p is nominal pitch of the selected belt profile, such as 5 mm or 8 mm. Belt and pulley pitch and profile must match.
How to use the calculator
Read pitch and tooth count from the product designation or drawing and calculate dw. Solving for z may produce a fraction; select an available whole tooth count and recheck the layout.
Worked example
At z = 20 and p = 5 mm, pitch circumference is 100 mm, so dw = 100/π = 31.831 mm.
Understand the result and units
31.831 mm is the kinematically effective diameter. Profile-specific outside diameter must come from a manufacturer drawing. dw can then be used in v = πdw·n.
p and dw are lengths, commonly millimetres in catalogs; z is dimensionless. The app converts through SI internally.
Why is pitch diameter different from outside diameter?
The pitch line lies in the belt tensile member rather than on visible tooth tips. Its position depends on profile. Kinematic diameter still follows z·p/π, while tooth tip and root manufacturing dimensions come from profile-specific drawings.
Typical applications
Use it for CAD envelope work, pulley selection, ratio and speed calculations, and as geometry input for timing-belt length and wrap.
Assumptions, limits and common mistakes
The equation gives only pitch circle. Tooth profile, outside diameter, flanges, minimum teeth, bore, width and rating remain product-specific. It does not define a manufacturable tooth contour.
Common mistake: Do not use the chain-sprocket p/sin(π/z) formula. Do not confuse pitch with tooth height or mix metric and inch profiles.
Frequently asked questions
How is timing-pulley pitch diameter calculated?
Use dw = z·p/π from tooth count z and pitch p.
Is pitch diameter the outside diameter?
No. The pitch circle lies at the belt tensile member; visible outside diameter is profile-specific.
Can any tooth count be used?
Geometrically yes, but profile-specific minimum teeth, available catalog sizes and ratings apply.
What do 5M and 8M mean?
For many metric timing-belt profiles the number indicates nominal pitch in millimetres, but verify the complete profile designation.
Why is the chain-sprocket equation different?
A timing belt follows a continuous pitch line of circumference z·p; roller-chain links form a polygon of pitch-length chords.