Technical Reference
Spur Gear Terminology, Formulas & Reverse Engineering
Everything engineers need to specify, calculate and identify spur gears, plus the manufacturing capability to match any spec you find.
Step-by-Step Guide
How to Reverse Engineer a Spur Gear
Have a worn or legacy gear with no drawing or part number? This guide walks you through identifying the key parameters with basic shop tools. Then Grob can manufacture the replacement.
What We Need to Identify
- Tooth count (number of teeth)
- Diametral pitch (DP)
- Pressure angle (14.5° or 20°)
This guide works for standard gears. If your gear has modified tooth geometry, non-standard backlash or an unusual profile, basic measurement won’t be enough. Grob’s CMM inspection service is the right path.
Tools You’ll Need
- Micrometer (recommended)
- Calipers (acceptable)
- Pi tape (optional)
- Calculator
- Gear pitch gauge (optional but ideal)
- Reference gear for pressure angle comparison
Steps
How to Calculate
Step 1
Count the Number of Teeth
This is the most fundamental parameter. Count every tooth carefully all the way around the gear, and mark your starting tooth so you don’t lose count. Never estimate.
Mark the starting tooth with a paint marker or tape. Count in one direction, then do a full verification pass in the opposite direction.
The tooth count feeds every later calculation, so an error here carries through everything.
Step 2
Measure the Outside Diameter (OD)
With a micrometer or calipers, measure across the outermost tooth tips. Take several measurements at different orientations and average them for accuracy.
Even number of teeth: measure directly tip to tip across the gear center.
Odd number of teeth: you can’t measure straight across. Rock the calipers across adjacent teeth and approximate, or use a pi tape for a circumference-based OD.
Step 3
Calculate the Diametral Pitch
With the tooth count and OD in hand, rearrange the outside diameter formula to solve for diametral pitch. The result will rarely be a clean whole number because of manufacturing tolerances, so round to the nearest standard DP.
Formula: diametral pitch from OD
DP = (Number of Teeth + 2) / Outside Diameter
Round to the nearest standard DP. Common values: 6, 8, 10, 12, 16, 18, 20, 24, 32, 48.
Worked example
Tooth count = 16 Outside diameter = 1.005″
DP = (16 + 2) / 1.005 = 17.91 ≈ 18 DP
17.91 is very close to 18, so this gear is almost certainly 18 DP. Verify before ordering.
If the result doesn’t land near a standard value, the gear may be a combination-pitch gear, where the OD doesn’t follow the standard DP formula. That case needs CMM inspection.
Step 4
Identify the Pressure Angle
The hardest step without specialized tooling. Grob manufactures both standard angles, 14.5° and 20°. Comparing visually against a known reference gear is the practical approach; a gear pitch gauge gives a definitive answer.
14.5°
Pressure Angle
- Tooth flanks rise nearly straight up at the base
- Wider tooth at root, narrower at tip
- Older, legacy standard (pre-1960s designs)
- Common in replacements for older machinery
- Quieter operation in some applications
20°
Pressure Angle
- Thinner tooth at tip, visibly wider at base
- Modern industry standard (most common)
- Higher load capacity per tooth
- Better resistance to undercutting on small tooth counts
- Higher separating force on bearings
When in doubt between 14.5° and 20°, send us your sample. Grob’s CMM and gear-checking software will determine the pressure angle definitively, with no guesswork.
Reverse Engineering Service
Let Grob Reverse Engineer It for You
When basic measurement isn’t enough (modified profiles, combination-pitch gears or non-standard tolerances), Grob uses a coordinate measuring machine (CMM) with specialized gear inspection software to determine the exact parameters of any spur gear sample. Just send us the part.
Grob manufactures cold-formed spur gears from 6 to 48 DP in either 14.5° or 20° pressure angles. If your gear falls within that range, we can build it.
Ready to Source Your Spur Gears?
Whether you need stock bar today, a fully custom gear, or help identifying an existing part, our team responds within one business day.