Taking a look at something as simple as a screw actually shows a high level of complexity. You can notice how precise and refined it must be for how it is used. Screws need to be manufactured for their exact purposes, large or small. Thread count gives you one way of measuring this.

## Converting TPI to Metric

Scientists and engineers use the **threads per inch (TPI)** unit to measure how fine and precise the threads, the grooves that spiral, of a screw or bolt are. This gives you an idea of what screw will fit what bolt and how secure and fastened that specific screw may be.

The manufacturing plants of screws and bolts use these refined measurements to ensure they have the appropriate grade and quality for their uses. You can understand more of the TPI units to figure out how to convert between them and inches or millimeters.

If you know what TPI means in thread purposes, you can determine the size of a screw. Place a screw down on a flat surface with the head of the screw off of the edge so that the threads themselves lay flat next to one another. Use a ruler next to the first thread, and count the number of threads gaps in the first inch of the screw. Keep in mind that you count the first thread as zero.

After you've counted, divide one inch by the count of grooves in the thread. This simple thread pitch formula means that if you had four thread gaps in one inch, the thread pitch would be 0.25 inch. The TPI is, then, four because it measures "threads per inch." To convert the pitch to millimeters, use the conversion that 1 inch equals 25.4 millimeters.

You can convert 26 TPI to inches per thread by dividing 1 by 26 to get 0.038, and then multiplying this by 25.4 to get a pitch of 0.98 millimeters. If this TPI measurement is common among the screws you have, then it may be the standard unit at which they were produced. Use it to keep track of damage to the screw's design like worn out threads or grooves of screws.

## Measuring TPI

You can calculate that a fastener with a TPI of 32 has a pitch in inches of 0.031 by dividing 1 by 32. Then, you can convert this to millimeters by multiplying it by 25.4 millimeters and end up with millimeter pitch as 0.793 mm. will give 0.793 mm (0.8) and one with a TPI of 56 will give 0.45 mm. These measurements depend on how the screws themselves were manufactured and what purpose they're meant to be used for.

Other factors are important when describing the quality of screws and bolts. The head style and shape of screws have certain radii at which they're built. Measuring the diameter of the head and the shape using curvature or flatness can tell you more about the quality and purpose of a screw. The geometry of screws themselves give many ways of calculating how secure or fastened a screw can be.

Comparing the rotation of a screw to a wave, you can imagine how the paths along the spiral of a screw would look if you stripped it of its paths. The exact shape of the spiral would have a wave shape with the crests, the highest peaks of the wave, giving you a way to measure the spiral peak to peak. The frequency of this wave would tell you how many full lengths of the wave pass over a given point during one second.

When you observe a screw closely, you may notice the thickness the spiral of the screw takes as it wraps around the shaft of the screw. The angle that the helix shape of the screw takes when it forms a patch itself is the flank angle. You use this when counting the crests, the edge of the path itself, to determine the pitch of a screw. You can describe more of the specific angles and distances within a screw using the lead distance, too.

## Lead Distance of a Screw

When a screw wraps around with a single rotation along its grooves, it moves up in height by a certain amount. **Lead** measures this height and serves as another example of measuring the quality of screws. The lead is the distance along the screw's axis a single pitch rotation uses.

You could imagine, if the grooves of a screw were a spiral staircase, the lead would be the distance between floors when you climb a single revolution of stair steps, or, with the analogy of a screw as a wave, the lead would correspond to the "wavelength" of the screw.

For each rotation (measured as 360°), lead measures the width of the groove or ridge itself. If the screw is single-start, the "ridge" of the screw is a single rotation around the circular path. For double-start screws, the groove wraps around twice with one direction on either side of the circle just like the double-stranded nature of DNA. Triple-start screws use three grooves that are equally partitioned around the circular spiral.

This means that a double-start screw will have twice the lead of a single-start screw of the same pitch, and a triple-start one will have triple the lead. The **lead angle** measures this angle of the helix that the screw takes according to lead distance and pitch. The more starts a screw has, the higher its lead angle. You can use a formula to describe the lead as it relates to pitch.

## Calculating Lead Angle

You can calculate the **lead angle** "lambda"

for the the **lead distance** *I* and **major diameter** *D*, both in millimeters. Major diameter is the diameter of the entire shaft of the screw, including the height of the helix as the groove loops around. If you place a screw on its side and looked at its head, measure the diameter of its head to get the major diameter. The lead distance *I* can be calculated as the number of threads times the pitch with appropriate units.

The **minor diameter,** on the other hand, measures the smallest diameter that the screw takes when the groove spirals around the axis of the screw. This is the innermost part of the screw, also called the root, that a manufacturer measures precisely to ensure the the grooves wrap around to produce the desired effective diameter.

## Gauge Number

Engineers use **gauge number** to account for the diameter of the screw. They're usually only used with screws less than 1/4 of an inch. For lengths higher than that, the diameter is measured in fractions of an inch. Online tables such as the one from Zytrax offer ways of converting between gauge numbers and length of the screw.

The metric version of gauge number uses the term "Maa x bb" for aa, the diameter in millimeters, and bb, the pitch with distance between threads in millimeters. This means that, for 3.5 mm diameter and .6 millimeter pitch, the gauge number would read as "M3.5 x .6" for the screw. Make sure to use the right units when using these terms.

## Online TPI Thread Chart

There are online thread pitch charts such as the one by Newman Tools. These charts give you a straightforward way of converting between metric and US customary units. A TPI thread chart makes the conversion easier.

Other online resources like calculators may prove helpful, too. Mitsubishi Materials offers a method of calculating lead angle for different leads of screw threading.

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About the Author

S. Hussain Ather is a Master's student in Science Communications the University of California, Santa Cruz. After studying physics and philosophy as an undergraduate at Indiana University-Bloomington, he worked as a scientist at the National Institutes of Health for two years. He primarily performs research in and write about neuroscience and philosophy, however, his interests span ethics, policy, and other areas relevant to science.