Measuring a spur gear starts with three things you can capture using basic tools: the number of teeth, the outside diameter, and the tooth thickness. From those, you can calculate every other dimension you need to identify or replace the gear. Whether you’re reverse-engineering an unknown gear or verifying a new one against specs, the process follows a logical sequence that builds each measurement on the last.
Count the Teeth First
The number of teeth (N) is the one measurement you can’t get wrong, and everything else depends on it. Count them by marking one tooth with a marker or piece of tape, then counting all the way around. On larger gears, count in groups of five to avoid losing your place. This number, combined with the outside diameter, lets you calculate the module or diametral pitch, which defines the entire tooth geometry.
Measure the Outside Diameter
The outside diameter (OD) is the distance across the gear measured at the tips of the teeth. Use calipers for this. On gears with an even number of teeth, you can measure straight across from one tooth tip to the opposite tooth tip. On gears with an odd number of teeth, no two tips sit directly opposite each other, so you’ll need to measure from a tooth tip to the root on the opposite side and compensate, or use a V-block and height gauge for better accuracy.
Place the gear on a flat surface and take several measurements at different positions around the circumference. If the readings vary by more than a few thousandths of an inch, the gear may be worn or damaged, and you should use the largest consistent reading as your baseline.
Calculate Module or Diametral Pitch
These two values describe the size of the teeth. Diametral pitch (DP) is the standard in the United States and counts how many teeth fit per inch of pitch diameter. Module (m) is the metric equivalent and is simply the pitch diameter divided by the number of teeth, expressed in millimeters. The two convert cleanly: module equals 25.4 divided by diametral pitch.
For a standard full-depth tooth profile, the outside diameter relates to the tooth count and diametral pitch through this formula:
OD = (N + 2) / DP
Rearranging that gives you the diametral pitch directly from your two measurements:
DP = (N + 2) / OD
If you’re working in metric, the module is:
m = OD / (N + 2)
So a gear with 40 teeth and an outside diameter of 42 mm has a module of 42 / 42 = 1.0 mm. A gear with 30 teeth and an OD of 2 inches has a diametral pitch of 32 / 2 = 16 DP. The result should land very close to a standard size. Common diametral pitches include 8, 10, 12, 16, 20, 24, 32, 48, and 64. Common modules include 0.5, 1.0, 1.5, 2.0, 2.5, and 3.0 mm. If your calculation gives you 15.9 DP, it’s a 16 DP gear, and the small discrepancy is measurement tolerance or light wear.
One caveat: the formula above assumes full-depth teeth, which covers the vast majority of spur gears. American Standard stub teeth use a slightly different formula where OD = (N + 1.6) / DP, resulting in shorter teeth. If your calculated pitch doesn’t land near a standard value using the full-depth formula, try the stub tooth version.
Determine the Pressure Angle
Spur gears use either a 14.5-degree or 20-degree pressure angle. This defines the shape of the tooth profile, and gears with different pressure angles cannot mesh properly. The 20-degree standard is more common today because it produces a thicker, stronger tooth root. Gears made to diametral pitch standards (primarily U.S. manufacture) are more likely to use 14.5 degrees, while metric module gears almost universally use 20 degrees.
Visually, 14.5-degree teeth look slightly more slender and have a more curved profile, while 20-degree teeth appear broader at the base with straighter flanks. The most reliable way to check is with a gear tooth comparator or a set of gear gauges that match known profiles. You press the gauge against the tooth flank; the correct pressure angle will make flush contact along the entire surface. If you don’t have gauges, a printed profile template scaled to your gear’s module or DP can work in a pinch.
Measure Tooth Thickness
Tooth thickness at the pitch circle is the critical dimension for determining how well a gear will mesh with its mate. The simplest tool for this is a gear tooth caliper (sometimes called a gear tooth vernier), which has two scales: one sets the depth from the tooth tip to the pitch line, and the other reads the width of the tooth at that depth.
For a full-depth gear, the theoretical tooth thickness at the pitch circle is half the circular pitch. In practice, teeth are cut slightly thinner to create backlash, the small gap between mating teeth that prevents binding. Comparing your measured tooth thickness to the theoretical value tells you how much material has been removed for backlash allowance or lost to wear.
Span Measurement
A more precise method is span measurement (also called base tangent length). Instead of measuring a single tooth, you use a special tooth thickness micrometer to measure across several teeth at once. The micrometer jaws contact the tooth flanks on the outside of the gear, and the reading captures the combined normal tooth thickness plus the normal pitch across the span. This method is less sensitive to positioning errors than a single-tooth measurement because the micrometer naturally seats itself against the involute profile. You’ll need to know the correct number of teeth to span for your gear size, which is typically calculated from the tooth count and pressure angle.
Calculate the Remaining Dimensions
Once you have the module (or diametral pitch), tooth count, and pressure angle, every other standard dimension follows from simple formulas.
The pitch diameter (d) is the fundamental reference circle where the teeth of two meshing gears effectively make contact. For metric gears: d = m × N. For imperial gears: d = N / DP. This is not a physical feature you can touch on the gear, but it’s the dimension used for calculating center distance between two meshing gears. The center distance between a mating pair is simply half the sum of their two pitch diameters.
The root diameter is measured at the bottom of the tooth spaces, the lowest point of the gap between teeth. For a standard full-depth metric gear, the root diameter equals the pitch diameter minus 2.5 times the module. You can measure this directly with calipers placed in the tooth spaces, using the same even/odd tooth considerations as the outside diameter. The root diameter matters for checking clearance with the mating gear’s tooth tips.
The addendum is the height of the tooth above the pitch circle (equal to one module, or 1/DP). The dedendum is the depth below the pitch circle (equal to 1.25 times the module, or 1.25/DP). The total tooth height is the sum of these two: 2.25 times the module.
Check for Wear
If you’re measuring a used gear, compare your tooth thickness readings to the theoretical values for a new gear of that specification. Wear shows up as a reduction in tooth thickness, particularly near the pitch line where the sliding contact is highest. Take measurements at multiple teeth around the gear, since wear is rarely perfectly uniform.
Look at the tooth profiles as well. Healthy involute teeth have a smooth, consistent curve from root to tip. Pitting (small craters on the tooth surface), scoring (fine lines running in the direction of sliding), or a polished, concave wear pattern at the pitch line all indicate a gear that’s been absorbing significant loads. If the tooth thickness has decreased noticeably from spec, the backlash between mating gears will have increased, leading to noise, impact loading, and accelerated wear on both gears in the pair.
Tools You’ll Need
- Digital calipers: For outside diameter, root diameter, and general tooth dimensions. Resolution of 0.01 mm or 0.001 inches is sufficient for most gears.
- Gear tooth caliper: A specialized vernier that measures tooth thickness at a set depth from the tooth tip. Essential for checking individual tooth thickness at the pitch circle.
- Tooth thickness micrometer: Used for span measurement across multiple teeth. More accurate than a gear tooth caliper for quality verification.
- Pressure angle gauges or templates: Thin profile gauges that match against the tooth flank to confirm 14.5-degree or 20-degree profiles.
- Pin or ball set: Used for measurement over pins, an alternative precision method where calibrated pins are placed in opposing tooth spaces and the overall dimension is measured with a micrometer.
For a quick identification of an unknown gear, calipers and a tooth count get you 90% of the way there. The specialized tools become important when you’re verifying tolerances, assessing wear, or confirming that a replacement gear will mesh correctly with an existing one.