How to Calculate PCD (Pitch Circle Diameter)?

PCD is the short form of Pitch Circle Diameter; the Pitch Circle Diameter (PCD) is the diameter of that circle which passes through the center of all the bolts hole or wheel bolts or wheel rim holes or stud.  The best example is Flanges, there are multiple holes in Flanges, the circle through the center of these holes is known as pitch circle and the diameter of this circle is known as Pitch Circle Diameter, in short PCD. Look at the figures and find PCD of different stud arrangement circle.

Studs: from the definition of stud is “a large-headed piece of metal that pierces and projects from a surface, especially for decoration”, shown in figure as different form of stud arrangement, such- 3 stud means 3 holes; 4 stud means 4 holes; 5 stud means 5 series of holes and so on.  

Pitch circle: The transverse section of the pitch cylinder normal to the axis.

Pitch, Circular: The distance measuring along the pitch circle between the centers of two adjacent teeth (holes) on a plane at right angles to the axis of rotation.

The easiest way calculate the PCD for different number of studs is as follows:
Fig: PCD of Different Numbers of Studs

For calculation hole to hole distance H is an important to calculation. Distance H may be hole’s center to center or same side to side. R is the diameter of the pitch circle.

PCD_Calculation_Multiple_StudAs per circle and triangle theory, total angle of circle= 360o total angle of triangle =180o


For 3 stud, PCD= 258mm, what would be the holes distance?

360o /number of holes

= 360o /3 =120 o , half of 120o is 60o.

Using Sin rules in triangle,

SIN = Perpendicular/Hypotenuse= (H/2)/R= H/2R= H/D (Diameter or PCD)


Or, Sin60o=H/258

Or, H= 258x Sin60o= 223.45mm, hole to hole distance.

Similarly, for 8 holes:

360o /8 =45o, half is (45o/2)

Sin (45o/2) = H/258

Or, hole to hole distance, H= 258x Sin (45o/2) =98.73mm;

So, the common formula is,

Hole to hole distance, H= Sin [(360o/hole number)/2]*PCD


How Measure Pitch Circle Diameter of Gear?

In order to design, build and discuss gear drive systems it is necessary to understand the terminology and concepts associated with gear systems. Good designers and engineers have experience and knowledge and the ability to communicate their thoughts and ideas clearly with others. The students and teachers who participate in this unit will learn the gear terms and concepts necessary to design, draw and build gear drive systems, and improve their “Gear literacy”. 

How calculate PCD of a Gear?
Fig: Pitch Circle Diameter of a Gear Tooth

The length in mm of the pitch circle diameter per tooth.

Number of Teeth

The number of teeth on the gear.

Pitch Circle Diameter

The diameter of the pitch circle.

Outside Diameter

The outside diameter of the gear.
OD = (N + 2) x MOD

Center Distance

The distance between the axes of two gears in mesh.
C = PCD(g) + PCD(p)
Circular Pitch
The distance between adjacent teeth measured along the arc at the pitch circle diameter.
CP = pi x MOD

Circular Tooth Thickness

The width of a tooth measured along the arc at the pitch circle diameter.
CTT = CP / 2


The height of the tooth above the pitch circle diameter.


The depth of the tooth below the pitch circle diameter.
D = H - A

Whole Depth

The total depth of the space between adjacent teeth.
Finer than 1.25 MOD:
H = 2.4 x MOD

1.25 MOD and coarser:

H = 2.25 x MOD

If you interested to know more details about PCD calculation of gear tooth, you may read the full article or even download the pdf file for free from the link below:

PCD-Pitch Circle Diametear Calculation of Gear Tooth


How Calculate PCD (Pitch Circle Diameter) of a Flange?

The PCD of a flange is one of the most critical dimensions. Now we will try to make easy to find the PCD (Pitch Circle Diameter) of a flange in our daily work.

PCD (Pitch Circle Diameter) is the diameter of a circle that goes through each of the bolt holes. Let's see the 8 holes flange at figure below:

How Calculate PCD of a Flange?
Fig: PCD Calculation of a Flange

Sometimes it’s hard to measure the PCD of a butterfly valve or a flange that’s installed in pipework. Realising your requirement at crutial time, we brought some handy tips to find the PCD calculation of flange having different numbers of holes. 

As accurately as you can, measure two adjacent holes using a varniar scale and calculate the PCD; then calculate for-

4 holes: multiply by 1.414

8 holes: multiply by 2.613

12 holes: multiply by 3.864

16 holes: multiply by 5.126


This 150mm flange has 8 holes and measures 90mm.

PCD = 90 x 2.613 = 235mm

How Calculate Pitch Circle Diameter of a Bolt Thread?

Another difficulty to measure the PCD- Pitch Circle Diameter of bolt or wire thread. Here we brought you some easy and simple way to calculate the bolt thread PCD.

Major Diameter: Given On Print (if it is a machine screw #0-14 SEE NOTE 1A).
Pitch: 1/number of threads per inch.
Flat: pitch/8.
Compound Movement: .75(pitch).
Single Thread Height: .75(pitch) (cosine 30 degree’s).
Pitch Diameter: major diameter - single thread height.
Minor Diameter: major diameter - 2 (single thread height).
Vertex Diameter: major diameter - 1.75(pitch) (cosine 30 degree’s).
Best Wire Size (BWS): pitch (tangent 30 degree’s).
Measurement Over Wires (MOW): vertex diameter + 3 (best wire size).
Lead: equals pitch if thread is a single lead.
Pitch Circumference: Pi (pitch diameter).
Lead Angle (Also Called Helix Angle): arc tangent of lead/pitch circumference.
NOTE 1A: Machine Screw Major Diameter: [machine screw# (0.013”)] +0.060”.
Major Diameter of a #10 Screw = [10 (0.013”)] + 0.060” or 0.1900”
Major Dia = 0.750”
Pitch = 1/10” OR 0.1000”
Flat = 0.0100/8 OR 0.0125”
Compound Movement = .75(0.01000”) or 0.0750”
Single Thread Height = .75(0.1000”)(cos 30 deg) or 0.06495”
Pitch Diameter = 0.7500”- 0.06495”or 0.6850”
Minor Diameter = 0.7500”- 2(0.06495”) or 0.6201”
Vertex Diameter = 0.7500”- 1.75(0.1000”)(cos 30 deg) or 0.5985”
BWS= 0.1000” (tan 30 deg) or 0.0577”
MOW= vertex dia + 3(0.0577”) or 0.7716”
Lead is a single lead or 0.1000”
Pitch Circumference = Pi(0.6850”) or 2.1520”
Helix Angle = arc tan 0.1000”/2.1520” or 2.66053 deg [2 deg, 39 min, 38 sec)
NOTE: Helix Angle has to be calculated if you are going to grind threads. The reason is that if the grinding
wheel head is not rotated to the same as the lead angle the thread will have either a drunken lead or a
zero lead, both of which are unacceptable.

Must Remember When Cutting Threads on a Lathe.

Even Pitch Threads 2, 4, 6....Etc: use any line on the threading dial.
Odd Pitch Threads 3, 5, 7….Etc: use any numbered line on the chasing dial.
½ Pitch Threads 11½: use #1 or #3.

  • Compound rest is always swung to idle side of tool.
  • The tool must have the correct thread angle.
  • The tool must be sharp.
  • The tool must be square to surface being threaded.
  • The tool must be on center.
  • The compound rest is used to cut thread to correct depth.
  • The crosslide is used to maintain a zero point on the “x” axis.


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