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Let's say we have a bolt with a basic major diameter (d) of 10 mm and a thread pitch (P) of 1.5 mm. To find its pitch diameter:

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As a rule of thumb, an internal thread of a given specified size should have the same basic diameters as an external thread of the same specified size. This means that d1=D1d_1 = D_1d1​=D1​, and d2=D2d_2 = D_2d2​=D2​ where D1D_1D1​ and D2D_2D2​ are the internal thread's basic minor diameter and basic pitch diameter, respectively.

An M6 thread has a basic major diameter of 6 mm. Typically, metric thread callouts also come with the thread pitch, such that an M6 × 1 threaded bolt has a basic major diameter of 6 mm and a thread pitch of 1 mm. When purchasing a threaded fastener, make sure you have both the diameter and the thread pitch. Without one of those measurements, you could buy the wrong-sized hardware.

Thread pitch, or simply pitch is the distance between a point on one thread to the corresponding point on the thread adjacent to it (for example, the measurement from crest to crest or from root to root). Learn more about thread pitch by checking out our thread pitch calculator.

On the other hand, here are the different general equations that we use to determine the tolerances based on the tolerance grade of the thread:

In between these two diameters is the pitch diameter. The pitch diameter is the thread's diameter in which the thickness of the thread and the space between two threads are equal. We can approximate the pitch diameter's value by taking the average of the minor and major diameters of the thread. Visit our pitch diameter calculator to learn more about it.

Here are the equations we use to find the fundamental deviations depending on what tolerance position the threads need to be:

For threads with specified thread class details, we can add their codes at the end of the thread callout. For example, an external thread labeled as M30 × 2 × 40 - 5g6g\text{M30 × 2 × 40 - 5g6g}M30 × 2 × 40 - 5g6g means that it has a pitch diameter tolerance grade of 555 and a major diameter tolerance grade of 666, both of which follow a g\text{g}g tolerance position.

The major diameter is the largest diameter of an external or internal thread. We also call this diameter the gross diameter or nominal diameter of the thread. On the other hand, the minor diameter is the smallest diameter of an external or internal thread. We also call it the root or core diameter of the thread.

From what we have already discussed, the basic diameters of a pair of external and internal threads precisely match each other. However, most of the time we provide some allowances to our threads to have some leeway when fitting them together. This is where metric thread classes come into play.

Once you've done the steps above, you'll immediately see not just the basic diameters but also the maximum and minimum diameters of your thread.

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As a result, a screw thread offers a locking feature that would require a good amount of shear stress to break, making it great for fastening objects together. This kind of thread can be an external thread (like on a screw or bolt) or an internal thread (like what we see inside a nut). We call these threaded materials threaded fasteners.

By analyzing the same diagram above, we can then formulate the following equations to find the other basic diameters of an external thread:

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Though we can also see threads in other applications, like bottle caps, bulbs, pipes and connectors, and even worm gears, this thread calculator focuses specifically on metric threads. Metric threads have symmetrical V-shaped threads that form 60º-angle grooves and have basic dimensions shown below:

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The nominal diameter of a thread is the diameter for which a thread is known. We use the nominal diameter for the general identification of threads. For example, a thread with a callout of M10 × 1.5 has a nominal diameter of 10 mm. Generally, the nominal diameter of a thread is the same as the basic major diameter of the thread.

Threads can mean a lot of things. In this thread calculator, we'll discuss the screw thread made out of grooves and ridges wrapped around a cylindrical or conical metal shaft in a helix pattern. The thread's helix spiral pattern acts like an inclined plane that translates rotational movement to axial movement while gaining some mechanical advantage.

In these equations, the value for kkk depends on which tolerance grade the threads use, indicated by nnn. A bolt with a tolerance grade of n=6n = 6n=6 for its major diameter should use k=1.0k = 1.0k=1.0 when solving for TD1T_\text{D1}TD1​. Here are the other values of k in the table below:

For the minor diameter, you can also see that we've got there two other adjustment variables, yyy and zzz, incorporated in the equation. Below are the equations we use for that:

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This thread calculator will help you find the different nut and bolt thread dimensions under ISO metric standards. In this metric thread calculator, you will learn:

You can also click on the Advanced mode button below our metric thread calculator if you wish to explore the different preliminary measurements used in the calculations, such as the height of the fundamental triangle, deviations, tolerance values, and adjustments.

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💡 As you may have noticed, we use the lowercase letter ddd to designate diameters for external threads. For convenience, we use the uppercase letter DDD for metric internal thread dimensions. That is, ddd for external thread major diameter, and DDD for internal thread major diameter. Coincidentally, the measurement for these basic major diameters is equal, such that: d=Dd = Dd=D.

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However, there are limitations as to how much we could deviate from the basic thread dimensions. Therefore, it's good to know our thread's allowable maximum and minimum diameters.

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Metric thread classes indicate a metric thread's tolerance grade and tolerance position. Each tolerance grade and position have corresponding equations that will tell us how much deeper we should cut or cold-roll the threads to achieve those allowances we want.

From the illustration above, we can see that we can use fractions of H to determine the different metric thread dimensions given the basic major diameter (d\small{d}d). But what is H? H\small{H}H is the height of the thread's fundamental triangle. The fundamental triangle is the projected equilateral triangle we can form from the thread's cross-section. We can get its height measurement using this formula:

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Understanding your metric threads starts with knowing how to read metric thread callouts. A thread callout is the same as a threaded fastener's label when you see them in a hardware store. Any thread standard has its own thread callout, and here is an example of a metric thread callout:

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Usually, we only perform manual calculations to find a thread's basic diameters. As you may have found out, it would take many extra steps to determine the diameter limits. And that is where our metric thread dimensions calculator comes in very handy! Here are steps to follow in using our tool:

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Now that we can read metric thread callouts, we can start calculating our threads' different dimensions. Knowing how to determine metric thread sizes gives us another way to distinguish one threaded fastener from another. As a guide, we are going to use this illustration:

Let's say we have a bolt with a basic major diameter (d) of 20 mm and a thread pitch (P) of 2 mm. To find its minor diameter: