If you cut a gear blank to the wrong diameter, you’re often throwing away expensive stock or dealing with teeth that won’t fully form when you hob—neither is worth the hassle. This Gear Blank Diameter Calculator lets you work out outside diameter, pitch diameter, root diameter, and tooth depth by plugging in module (or diametral pitch) and number of teeth. The method here is what you’d use for gearbox work, power transmission, or automated machinery where you want to get the blank right and avoid wasting money or making a bad gear. On this page you’ll find the actual formulas, a straight example, technical details, and FAQ.
What is Gear Blank Diameter?
Gear blank diameter is just the outside diameter of the round stock you need before tooth cutting. It comes from the gear’s module (or diametral pitch) and the tooth count. Get this wrong, and the finished gear either won’t have complete teeth or you’ll waste time and material fixing simple mistakes.
Simple Explanation
A gear blank is as basic as it sounds: it’s like a coin before you stamp an image on it. It needs to be just big enough to cover the whole distance from tooth tip to tooth tip once machined, but not so big that you’re machining away extra material for no reason. The only numbers you need to pay attention to are tooth count and module (tooth size).
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Gear Blank Dimensions Diagram
Gear Blank OD Calculator
Gear Blank Diameter Interactive Visualizer
See in real time how module and teeth directly set the outside diameter of your blank. Change the numbers and you'll get OD, pitch diameter, and tooth depth updated instantly, along with a dimensioned sketch.
Outside Ø
44.0mm
Pitch Ø
40.0mm
Root Ø
35.0mm
Tooth Depth
4.5mm
FIRGELLI Automations — Interactive Engineering Calculators
How to Use This Calculator
- Pick your system: Metric (Module) or Imperial (Diametral Pitch).
- Type in the module (mm) or diametral pitch (teeth/inch) for your job.
- Add the number of teeth on your gear.
- Click Calculate and check the output numbers.
This calculator is intended for education, concept evaluation, and preliminary design. Results are based on the equations and assumptions described on this page, but cannot account for every real-world load case, tolerance, material property, environmental condition, installation detail, safety factor, code, or regulatory requirement. Verify all inputs, assumptions, units, and results independently before selecting components or using the result in a real application. Safety-critical, structural, medical, lifting, transportation, or regulated applications must be reviewed by a qualified engineer.
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Mathematical Equations for Gear Blank Dimensions
Primary Formulas:
Here’s how you work out gear blank outside diameter and the main dimensions.
OD = m(N + 2)
Where: m = module, N = number of teeth
PD = mN
This is the diameter where two gears actually run together
Root Ø = m(N - 2.5)
Diameter measured at the bottom of the tooth gullet after cutting
h = 2.25m
That’s the full distance from tip to root, per tooth
Imperial System Conversion:
For diametral pitch (DP) gears: m = 25.4 / DP
Simple Example
For a gear with 20 teeth, module 2.0mm:
- Outside Diameter: OD = 2.0 × (20 + 2) = 44.0mm
- Pitch Diameter: PD = 2.0 × 20 = 40.0mm
- Root Diameter: 2.0 × (20 − 2.5) = 35.0mm
- Tooth Depth: 2.25 × 2.0 = 4.5mm
Complete Guide to Gear Blank Diameter Calculations
Understanding Gear Blank Fundamentals
Picking the proper blank diameter is the first real step for anyone making gears, before any cutting—too small and you cut off the tips, too large and you waste time and stock. You want enough meat on the blank for the teeth, but not more than needed.
The outside diameter (OD) is the max diameter of your round stock before teeth are cut. The standard formula, OD = m(N + 2), is simple but effective—it covers the base pitch diameter plus material for an addendum (tooth tip) on each side.
Module vs. Diametral Pitch Systems
Gears are sized by either metric module or imperial diametral pitch, and most shops need to be fluent in both. Using module (m) means every tooth adds m mm to the pitch diameter. For example, module 2.0 adds 2mm of pitch for every tooth—pretty straightforward.
Diametral pitch (DP), on the other hand, means “teeth per inch of pitch diameter.” So a 12DP gear fits 12 teeth in every inch diameter at the pitch circle. If you need to swap from imperial to metric, use m = 25.4/DP.
Critical Dimensions in Gear Design
Everything about blank sizing is connected—get one wrong and things downstream go off. Pitch diameter (mN) is the main reference and drives all other measurements. You need this for spacing, meshing, and gear ratio.
OD = m(N + 2) just gives you space for a standard addendum (1.0m) on both sides of the pitch circle, ensuring every tooth gets its full tip and strength regardless of tooth count.
The root diameter formula (m(N - 2.5)) knocks off 2.5 module lengths below the pitch circle—this leaves clearance at the bottom of the gullet so the mating teeth don’t bottom out.
Practical Manufacturing Applications
On the shop floor, a blank that’s too big is wasted money and machining time. Too small and you’ll end up with undercut or missing tips and a scrap part. Most gear-cutting systems (robotic, manual, CNC) depend on a consistent blank size for repeatable tooth profiles—especially if you’re working with FIRGELLI linear actuators or automated positioners. If blanks vary, tool setup goes off and you risk poor-quality teeth.
Worked Example: Calculating Gear Blank Dimensions
Suppose you’re building a 24-tooth gear with module 3.0mm for a machine transmission.
Given data:
- Number of teeth (N) = 24
- Module (m) = 3.0mm
Step-by-step calculations:
Outside Diameter:
OD = m(N + 2) = 3.0(24 + 2) = 3.0 × 26 = 78.0mm
Pitch Diameter:
PD = mN = 3.0 × 24 = 72.0mm
Root Diameter:
Root Ø = m(N - 2.5) = 3.0(24 - 2.5) = 3.0 × 21.5 = 64.5mm
Tooth Depth:
h = 2.25m = 2.25 × 3.0 = 6.75mm
So, your blank should be at least 78.0mm in diameter. If you want to allow for chucking or later finishing, add a bit more—but not much.
Design Considerations and Best Practices
There’s more to getting a blank right than just the math. Material makes a difference—harder steels need some extra margin in the blank to allow for potential size changes during heat treating. Softer metals hold their size better, so you can make blanks closer to net size.
The machining process matters too. Hobbing cuts close to final OD, so you don’t need much extra. Gear shaping or manual work might require another millimeter or two for trimming and work holding. CNC and automation demand sticking closely to the actual blanks for results and tool life.
If your gears end up as part of a servo or feedback system—especially with FIRGELLI linear actuators—tight tolerances hold profile accuracy. That means OD, concentricity, and finish all matter more than on a basic power transmission gear.
Quality Control and Inspection
Before you ever cut a tooth, check the blank. Measure OD at several spots. Check roundness and that the bore is centered. Look at surface finish if that matters for your process. If you inspect the blank and it matches the spec, you save headaches during machining and avoid producing junk parts.
If you’re running automated lines, inline or pre-machining diameter checks are a lifesaver for spotting problems early, especially with varying material or lot sources.
Integration with Modern Manufacturing
Today’s shop often pulls blank dimensions from CAD or CAM directly, but it pays to know the math so you can troubleshoot or catch issues before material gets wasted. Also, if you’re handed an unknown gear and need to reverse engineer, simple OD measurement plus tooth count gives you back to the original module.
This calculator is just for the basics. For complex drives—planetary, differentials, or where load and deflection matter—shift over to specialty calculators in our engineering calculators library.
Frequently Asked Questions
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About the Author
Robbie Dickson
Chief Engineer & Founder, FIRGELLI Automations
Robbie Dickson brings over two decades of engineering expertise to FIRGELLI Automations. With a distinguished career at Rolls-Royce, BMW, and Ford, he has deep expertise in mechanical systems, actuator technology, and precision engineering.
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