Pitch Diameter Calculator

This pitch diameter calculator will help you find one of the essential dimensions of threaded fasteners — the pitch diameter. In this calculator, you will learn:

• What pitch diameter is;
• How to use the metric thread pitch diameter calculator;
• The different pitch diameter formulas; and
• How to calculate thread pitch diameter.

Ready to learn about pitch diameters? Then keep on reading 🙂.

Threads on threaded fasteners have three different diameters essential in determining the proper fit of bolts in nuts or bolts in threaded holes. These three diameters are the major diameter, minor diameter, and pitch diameter, as shown in the diagram below:

We can also see in the diagram above that the thickness of the thread and the space between two threads are equal along the pitch diameter. At the same time, the sum of these distances also equates to the thread's pitch, hence the name pitch diameter. Learn more about the pitch of screw threads by checking out our thread pitch calculator.

Before we learn how to find a pitch diameter's value, let us first discuss how to use this pitch diameter calculator in the next section of this text.

Let's say we want to calculate the pitch diameter of an $\text{M25 × 1.5 - 6g}$ bolt. Since this is a callout for a metric bolt thread, our first step is to:

1. Pick external thread dimensions as the option for what we want to calculate.
2. Next, we select $\small{1.5\ \text{mm}}$ for the thread pitch and enter $\small{25\ \text{mm}}$ for the Basic major diameter.
3. We then select $\small{6}$ and $\small{\text{g}}$ for the tolerance grade and tolerance position, respectively.

Upon completing these steps, we should already get the values for the basic pitch diameter of $\small{24.026\ \text{mm}}$, the maximum pitch diameter of $\small{23.994\ \text{mm}}$, and the minimum pitch diameter of $\small{23.850\ \text{mm}}$.

We also show the preliminary values used to obtain these pitch diameter values in the Other measurements section of the calculator. The section displays the values for the fundamental deviation and tolerances, upper deviation ($\rm\small{es}$) and pitch diameter tolerance ($\small{T_\text{d2}}$), and the fundamental triangle height ($\small{H}$) of the thread.

In the next section of this text, we'll discuss the different formulas we use in our pitch diameter calculator.

From our discussion of how to use the pitch diameter calculator, we know that we need the values of the basic major diameter and the pitch of the thread we are investigating. Knowing those values, we can easily find the basic pitch diameter using this formula:

where:

• $d_2$ — Basic pitch diameter;
• $d$ — Basic major diameter; and
• $P$ — Thread pitch.

We derive this formula by substituting the value of the thread's fundamental triangle height, $H$, which is equal to $\small{(\sqrt{3}) \times \frac{P}{2}}$ into this equation $\small{d_2 = d - (2 \times \frac{3}{8}}) \times H$, where it means that $\small{\frac{3}{8}\ \text{of}\ H}$ gets deducted from both sides of the basic major diameter, as illustrated below:

Now that we know how to find the pitch diameter's base value, let us now figure out the maximum and minimum limits of the pitch diameter. Here are the equations that we use to find those values:

For external thread (bolt or screw) pitch diameter (d₂):

• $d_\text{2max} = d_2 + \rm es$
• $d_\text{2min} = d_2 + {\rm es} - T_\text{d2}$

For internal thread (nut or threaded hole) pitch diameter (D₂):

• $D_\text{2max} = D_{2} + {\rm EI} + T_\text{D2}$
• $D_\text{2min} = D_{2} + {\rm EI}$

where:

• $\rm es$ and $\rm EI$ – fundamental deviations, upper and lower deviations, respectively; and
• $T_\text{d2}$ and $T_\text{D2}$ – thread pitch diameter tolerance for external and internal threads, respectively.

The fundamental deviations and tolerances are the minute allowances that we apply on the threads to give the threaded fasteners some wiggle room when they are threaded together. We can either have them fit very tightly or have more wiggle room, but we cannot file down threads such that they become very loose even at their recommended bolt torques. Explore the physics behind how much torque a bolt needs for sufficient tightness with our bolt torque calculator.

We can calculate the fundamental deviations, $\rm es$ and $\rm EI$, depending on the thread's tolerance position:

For external threads:

• For e position: $\small{{\rm es} = -(50 + 11 \times P) / 1000}$;
• For f position: $\small{{\rm es} = -(30 + 11 \times P) / 1000}$ ;
• For g position: $\small{{\rm es} = -(15 + 11 \times P) / 1000}$; and
• For h position: $\small{{\rm es} = 0}$.

For internal threads:

• For G position: $\small{{\rm EI} = (15 + 11 \times P) / 1000}$; and
• For H position: $\small{{\rm EI} = 0}$.

On the other hand, we determine the tolerance values using these equations for external and internal threads, respectively:

• $\small{T_\text{d2}(n) = k \times (90 \times P^{0.4} \times d^{0.1} / 1000)}$
• $\small{T_\text{D2}(n) = k \times (90 \times P^{0.4} \times d^{0.1} / 1000)}$

They are rather the same, but their multipliers, $\small{k}$, depend on the tolerance grade of the thread indicated by the value of $\small{n}$. For a tolerance grade of 6 for an external thread, we should use $\small{1.0}$ for the value of $\small{k}$. We can see the other values of $\small{k}$ in the table below:

Let's say we have an M30×2-6h bolt, and we want to determine its screw pitch diameter. We know that our bolt has a 30-mm basic major diameter and a 2-mm thread pitch given the thread callout. From there, we can already calculate our bolt's basic pitch diameter, as shown below:

Since our bolt has a tolerance class of 6h, we can use the table in the previous section to find the multiplier $\small{k}$ to be equal to 1, and from the list of fundamental deviation formulas, we know that $\small{{\rm es} = 0\ \text{mm}}$. We can then obtain the tolerance, $\small{T_{d2}}$ with this equation:

Finally, we can solve for the maximum pitch diameter, as follows:

And the minimum pitch diameter:

If you found this calculator useful, perhaps you'll also find our bolt circle calculator informational. That tool will help you estimate the location of holes in a circular pattern, especially when drilling bolt holes on a flange.