Outside diameter of a synchronous (timing) pulley is computed as OD = PD - 2U, where PD is the pitch diameter and U is the distance between the tensile cord and the bottom of the timing belt tooth, a value tied to the belt's pitch profile [S1][S2].
Pitch diameter itself is a calculated, not measured, circle: PD = (belt pitch x number of teeth) / pi (3.14159), with belt pitch defined as tip-to-tip tooth spacing on the belt [S2][S4]. Because the tensile cord sits below the tooth tip, the OD you can measure with a micrometer is always smaller than the imaginary PD circle, a relationship repeated across every standard pitch profile from XL to GT [S3][S8].
Step 1: Compute Pitch Diameter from Teeth and Pitch
PD is a pure geometric construct defined as the pitch circle of the pulley, the circle tangent to the belt's pitch line, which is itself the constant-length neutral axis running through the belt body [S5]. The single governing equation is PD = (p x N) / pi, where p is the belt pitch and N is the number of pulley teeth [S2][S4]. For an XL-profile 36-tooth pulley on a 0.200 in (5.08 mm) pitch, that gives PD = (0.200 x 36) / 3.14159 = 2.292 in; the L-profile 24-tooth equivalent at 0.375 in pitch yields 2.864 in, illustrating how pitch changes the diameter more than tooth count does [S2]. FRC and automation pulleys typically run only 3 mm and 5 mm pitches for HTD/GT2 belts, so designers can pre-tabulate the full PD grid for stock tooth counts in those two profiles [S5].
Step 2: Look Up the PLD Constant U for the Pitch Profile
The PLD term U is not a universal number, it is a profile-specific offset, equal to the radial distance from the tensile cord (the pitch line) to the bottom of the belt's tooth root, which is the same as the height of the tooth above the neutral axis [S1][S8]. Each pitch family carries its own U: for example, the T2.5 / T5 / T10 trapezoidal (T) profiles, the AT-series curvilinear profiles, the XL/L/H trapezoidal profiles, and the HTD/GT/STPD curvilinear profiles each have a different U value, and that value is what Pfeifer, SDP-SI, and ContiTech publish in their respective pitch tables rather than encoding in the pulley part number [S1][S8]. Using the wrong U is the most common reason an "OD from chart" disagrees with a calipered pulley: a pulley ordered as HTD 5 mm will not give the same OD as the same tooth count in XL at 5.08 mm even though both are roughly "5 mm pitch" [S3].
Step 3: Apply OD = PD - 2U and Cross-Check Against the Chart
With PD and U both in hand, the subtraction is trivial: OD = PD - 2U, the exact relation reproduced verbatim in Pfeifer's diameter charts and the Model Engineer forum guidance [S1][S2]. For a 20-tooth HTD 5 mm pulley, PD = (5 x 20) / pi = 31.831 mm; the published U for HTD 5 mm is 1.49 mm, giving OD = 31.831 - 2.98 = 28.85 mm, the value that Illinois Pulley & Gear's table lists for that tooth count [S4][S5]. The 1-2 mm gap between calculated PD and measured OD is the practical signature of a timing pulley and is also the reason SDP-SI's handbook describes the OD as smaller than an "imaginary" PD circle [S8]. The SDP-SI datasheet also notes that the pitch line, and therefore PD, sits inside the belt body, so the PD is a theoretical reference used for length and center-distance math, not a physical surface you can put a ruler on [S5][S8].
Criteria Comparison: Common Pitch Profiles and Their U Values
Below is the comparison extract most often requested by engineers cross-referencing stock timing pulleys against belt catalog OD, derived from the same formula and profile tables referenced in the source material [S1][S2][S4][S8].
Profile (typical pitch) - U offset, mm - Tooth count example - PD, mm - OD, mm - Notes on use: XL (0.200 in / 5.08 mm), U approx 0.508, 36T, 58.32, approx 57.30, inch-system light drives; L (0.375 in / 9.525 mm), U approx 0.762, 24T, 72.77, approx 71.24, general industrial, higher torque than XL; T5 (5 mm), U approx 0.85, 20T, 31.83, approx 30.13, compact linear-actuator drives; HTD 5 mm, U approx 1.49, 20T, 31.83, approx 28.85, robotics, FRC, mid-load gear-replacement drives; GT2 5 mm, U approx 1.20, 20T, 31.83, approx 29.43, higher-precision positioning than HTD; T10 (10 mm), U approx 1.50, 12T, 38.20, approx 35.20, heavy conveyors, woodworking.
Numerical U offsets above for the 5 mm-class profiles are the most cross-referenced in automation and FRC work; the inch-system XL and L values are taken from the same manufacturer charts cited in the research and scale linearly with the belt's pitch [S1][S4][S5]. Where a manufacturer publishes a slightly different U for the same profile, the rule of thumb is to take the vendor's own U from their product datasheet rather than mixing the formula across catalogs [S1].
When to Use the Formula vs Reading the Chart
Use the formula when you are sizing a custom or non-stock pulley, when you are validating a vendor's chart, or when you need PD and OD for a center-distance calculation on a timing belt drive that you cannot directly measure [S5][S8]. Use the chart when you have a stock tooth count and a known pitch family, which is most of the time in maintenance work and small machine retrofits [S1][S4]. Pfeifer, SDP-SI, and ContiTech all publish side-by-side PD and OD columns indexed by tooth count, so the OD can be read directly without touching U at all, provided you stay inside one profile family [S1][S8]. If the belt profile is unknown, measure tip-to-tip across at least 10 teeth, divide by 10, and then pick the closest standard pitch from a manufacturer table before applying U [S4].
Common Failure Modes of the OD-from-PD Calculation
Three errors cause most of the disagreements seen on shop floors and engineering forums: (1) mixing profile U values, e.g. plugging an HTD U into an XL or T5 problem, which gives an OD off by 0.5 to 1.5 mm on a 30 mm-class pulley [S1][S3]; (2) confusing V-belt datum diameter, which is measured at the groove's top width, with timing-belt PD, which is a calculated neutral-axis circle and is not directly measurable on the part [S7]; (3) using PD as a physical surface for tolerancing or for press-fit decisions, when in reality the OD is the only dimension you can micrometer and it is the one that interacts with belt guide flanges and shaft-housing clearances [S3][S4][S8]. The OD is also the dimension that determines whether a timing pulley will physically clear a belt guide flange or an adjacent shaft collar, while the PD is what drives length and center-distance math, so each gets used in a different part of the drawing and they are not interchangeable [S4][S5].
Related Drive-Component Specs Worth Pinning Alongside OD
For a complete belt-drive data package, the OD/PD pair should sit next to the face width, the bore and keyway tolerance, the flange OD, and the material, because each of these gates a different failure mode and each is published in the same manufacturer table [S4]. The face width is matched to belt width to within the standard tolerance bands, the bore and keyway follow ISO or inch-key standards depending on the market, and the flange OD is typically PD plus 2 x flange height, a separate constant from the belt's U [S4][S8]. For linear or conveyor applications where the same pulleys feed into a wider construction machinery and equipment driveline, the same OD value is also the dimension used to size belt guides and shaft guards, so getting U right at the design stage prevents rework on assembly [S4].
Next data points worth tracking on the next refresh: (1) any 2026-vintage SDP-SI or ContiTech update to the U tables for HTD 5 mm, GT2 5 mm, and the T-series, which would re-rank the values in the comparison table above [S1][S8]; (2) the release of a public ISO or ISO-derived standard that names the U constant explicitly, since today the term is manufacturer-specific and varies by source [S1][S4]. Until then, the safe path is to compute PD from teeth and pitch, take U from the same vendor that supplies the belt, and subtract.
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