Pitch Diameter Calculator
This calculator finds pitch diameter for three common engineering contexts: spur gears using the module or diametral-pitch system, external metric or unified (UN) screw threads with ISO tolerance grades, and the three-wire indirect measurement method used to verify thread pitch diameter with a micrometer. Pick a mode, enter your values, and every related dimension updates instantly.
What is pitch diameter and why does it matter?
Pitch diameter is the effective mating diameter of a threaded fastener or a meshing gear. For a screw thread, it is the imaginary cylinder whose surface passes through the thread flanks at a point where the thread width equals the space width, making it the diameter that determines how well a bolt and nut fit together. For a spur gear, it is the pitch circle diameter, the circle at which mating gear teeth roll together without slipping. In both cases pitch diameter is not directly measurable with a simple caliper; it must be calculated from the thread geometry or gear parameters, or measured indirectly using the three-wire method.
Thread pitch diameter: the formula and ISO tolerances
For a standard 60-degree thread (ISO metric and Unified inch), the basic pitch diameter is d2 = d - 0.6495 x P, where d is the major (nominal) diameter and P is the pitch in the same units. The factor 0.6495 comes from the thread triangle geometry: it equals (3 x sqrt(3)) / 8, the height of one complete 60-degree thread profile above the pitch cylinder. The minor (root) diameter of an external thread is d1 = d - 1.2269 x P. ISO 965-1 adds tolerance bands around this basic value: the grade number (4 through 8) controls the band width, and the position letter (e, f, g, or h for external threads) sets an allowance that shifts the entire band away from the basic value to guarantee clearance with the mating thread. Grade 6g is the standard commercial choice for bolts.
Gear pitch diameter: module and diametral pitch systems
Spur gear pitch diameter is simply the module multiplied by the number of teeth (d = m x z in the ISO metric system) or the number of teeth divided by the diametral pitch (d = z / DP in the AGMA inch system). Module and diametral pitch are reciprocals scaled by 25.4: DP = 25.4 / m. From pitch diameter you can derive all major gear blank dimensions. The addendum (tooth height above the pitch circle) equals one module, so the outside diameter is d + 2m. The dedendum (depth below the pitch circle) is 1.25 modules for standard full-depth teeth, so the root diameter is d - 2.5m. Two gears mesh correctly only when they share the same module, the same pressure angle, and (for helical gears) the same helix angle.
Three-wire method: measuring pitch diameter with a micrometer
Because you cannot place a caliper jaw directly on the thread flanks at the exact pitch cylinder, machinists use precision wires. Three wires of known diameter are placed in the thread grooves (two on one side, one on the other), and a micrometer measures the distance M across the assembly. For 60-degree threads the relationship is: M = d2 + 3w - 1.5155 x P, where w is the wire diameter and P is the thread pitch. Rearranging gives the pitch diameter from the micrometer reading: d2 = M - 3w + 1.5155 x P. The "best wire" size - w = 0.5774 x P - contacts the thread flank exactly at the pitch line, eliminating the cosine error that affects off-size wires. Wire sets should be used in calibrated matched trios to keep measurements consistent.
Common metric thread pitch diameter reference (ISO 724)
| Thread designation | Pitch P (mm) | Major dia d (mm) | Basic pitch dia d2 (mm) | Minor dia d1 (mm) |
|---|---|---|---|---|
| M4 x 0.7 | 0.7 | 4 | 3.545 | 3.141 |
| M5 x 0.8 | 0.8 | 5 | 4.480 | 4.018 |
| M6 x 1.0 | 1 | 6 | 5.351 | 4.773 |
| M8 x 1.25 | 1.25 | 8 | 7.188 | 6.466 |
| M10 x 1.5 | 1.5 | 10 | 9.026 | 8.160 |
| M12 x 1.75 | 1.75 | 12 | 10.863 | 9.853 |
| M16 x 2.0 | 2 | 16 | 14.701 | 13.546 |
| M20 x 2.5 | 2.5 | 20 | 18.376 | 16.933 |
| M24 x 3.0 | 3 | 24 | 22.052 | 20.319 |
| M30 x 3.5 | 3.5 | 30 | 27.727 | 25.706 |
| M36 x 4.0 | 4 | 36 | 33.402 | 31.092 |
Basic pitch diameter d2 = d - 0.6495 x P for standard metric coarse threads. Source: ISO 724:1993.
Frequently asked questions
What is the difference between pitch diameter and major diameter?
The major diameter is the outermost (largest) diameter of the thread, the number stamped on the bolt, such as M10 or 3/8 inch. The pitch diameter is an imaginary internal cylinder whose diameter corresponds to where the thread width equals the thread space width. It is always smaller than the major diameter by a factor of roughly 0.6495 times the pitch. Thread fit is governed by pitch diameter, not major diameter, so a bolt that gauges correctly on pitch diameter will assemble properly even if its major diameter is slightly off.
What does tolerance class 6g mean for a metric bolt?
In the ISO designation 6g, "6" is the tolerance grade and "g" is the tolerance position for the external thread. Grade 6 gives a medium-width tolerance band suitable for general-purpose commercial fasteners. Position "g" shifts the entire band slightly below the basic pitch diameter, providing a small clearance allowance so that the bolt will not seize in the mating nut. The combination 6g / 6H (bolt / nut) is the standard pairing for most metric bolted joints.
How do I choose the right wire size for the three-wire method?
The best wire diameter is 0.5774 times the thread pitch (equivalently, P divided by the square root of 3). A wire of this size touches the thread flank exactly at the pitch line, so any small error in wire diameter introduces the smallest possible error in the calculated pitch diameter. If you do not have that exact size, wires between 0.505 x P and 0.900 x P are acceptable. Use calibrated matched wires from a certified set and handle them only with clean gloves to prevent corrosion and contamination from skin oils.
Can I use this calculator for ACME or Buttress threads?
No. The formulas here use the 60-degree thread form factor (0.6495) and the three-wire constant (1.5155) that are specific to ISO metric and Unified (UN) threads. ACME threads have a 29-degree included angle, and Buttress threads have an asymmetric profile; both require different geometric constants. Consult Machinery's Handbook or the relevant ASME standards (B1.5 for ACME, B1.9 for Buttress) for those forms.
Why is pitch diameter important for gears?
Pitch diameter defines the pitch circle, the theoretical circle along which gear teeth mesh smoothly. When two gears share the same pitch circle tangent point and the same module (or DP), they roll together without sliding and transmit the correct velocity ratio. Outside diameter, root diameter, and tooth depth are all derived from the pitch circle, making pitch diameter the central design dimension for any gear train. If the pitch diameters are wrong, the gears will either bind or produce excessive backlash.
What is the relationship between module and diametral pitch?
They describe the same physical quantity, the ratio of pitch diameter to tooth count, but in different unit systems. Module (ISO metric) has units of millimetres per tooth; diametral pitch (AGMA / inch system) has units of teeth per inch. They are reciprocals scaled by 25.4: DP = 25.4 / module, or module = 25.4 / DP. A module-1 gear has the same tooth proportions as a 25.4 DP gear. Gears can only mesh if both use the same module (or equivalently the same DP).