Free Gear Pitch Converter & Spur Gear Sizing Tool

Convert instantly between Diametral Pitch (DP), Metric Module ($m$), and Circular Pitch. Calculate pitch diameter, addendum, dedendum, blank outside diameter, and base circle.

⚙️ Pitch Definition & Tooth Count

Primary Input System

Module (m)

Number of Teeth (N)

Pressure Angle (α)

Tooth Profile Standard

Quick Select Standard Pitch:

📐 Gear Dimensions & Pitch Conversions

Metric Module

2.000 mm

Diametral Pitch

12.70 DP

Circular Pitch

6.283 mm

Primary Diameters Metric (mm) / Imperial (in)

Pitch Diameter (D = m × N): 48.00 mm / 1.890"

Outside Blank OD (D_o = D + 2a): 52.00 mm / 2.047"

Root Diameter (D_r = D - 2b): 43.00 mm / 1.693"

Base Circle Diameter (D_b = D × cos α): 45.10 mm / 1.776"

Tooth Geometry & Cutting Depths

Addendum (a):

2.00 mm (0.0787")

Dedendum (b):

2.50 mm (0.0984")

Whole Depth (h_t):

4.50 mm (0.1772")

Tooth Thickness (t):

3.14 mm (0.1237")

Standard full-depth involute gear geometry verified.

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Spur Gear Pitch Systems & Involute Geometry

Gear manufacturing relies on three standard methods of defining tooth size: Metric Module ($m$) (standard in Europe, Japan, and ISO countries), Diametral Pitch ($P_d$) (standard in ANSI/AGMA imperial engineering), and Circular Pitch ($p$) (common in clockmaking and rack drives).

Fundamental Conversion Formulas

$m = \frac{25.4}{P_d} = \frac{p_{mm}}{\pi}$
$P_d = \frac{25.4}{m} = \frac{\pi}{p_{in}}$
$p = \pi \cdot m = \frac{\pi}{P_d}$
$\text{Pitch Diameter } D = m \cdot N = \frac{N}{P_d}$
$\text{Blank Outside Diameter } D_o = D + 2a = m(N + 2) = \frac{N + 2}{P_d}$
$\text{Root Diameter } D_r = D - 2b = m(N - 2.5) = \frac{N - 2.5}{P_d}$
$\text{Base Circle } D_b = D \cdot \cos(\alpha)$

Standard Metric Modules vs. Common Diametral Pitches

Metric Module (m)	Equivalent DP	Nearest AGMA DP	Circular Pitch (mm)
0.5 mm	50.80	48 DP	1.571 mm
1.0 mm	25.40	24 DP	3.142 mm
1.5 mm	16.93	16 DP	4.712 mm
2.0 mm	12.70	12 DP	6.283 mm
2.5 mm	10.16	10 DP	7.854 mm
3.0 mm	8.47	8 DP	9.425 mm

Frequently Asked Questions

Can a metric module gear mesh with an imperial DP gear?

No. Even if 1.5 Module (16.93 DP) looks close to 16 DP (1.5875 Module), the pitch discrepancy causes rapid tooth interference, binding, severe vibration, and tooth fracture within revolutions.

What is the minimum tooth count to prevent undercutting in spur gears?

For standard full-depth gears with a 20-degree pressure angle, the theoretical minimum tooth count without undercutting is N = 17 (or N = 14 with slight profile shift). For 14.5-degree pressure angles, undercutting begins below N = 32.

How do I calculate the blank outside diameter for turning on a lathe before hobbing?

For standard full-depth gears, the turning blank outside diameter is simply Do = m * (N + 2) in millimeters, or Do = (N + 2) / DP in inches. Always maintain tight concentricity on the blank before cutting teeth.