Free Spur Gear Module & Pitch Calculator
Calculate pitch diameter, tip diameter, tooth thickness, circular pitch, and operating center-to-center distance for Metric Module and Imperial DP gears.
⚙️ Gear Sizing Standard & Tooth Count
📊 Gear Geometry & Center Distance
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Spur Gear Geometry & Sizing Principles
Spur gears are the simplest and most common type of cylindrical gears, featuring straight teeth parallel to the axis of rotation. They transmit motion and torque between parallel rotating shafts.
1. Metric Module (m) vs Diametral Pitch (DP)
- Metric Module ($m$): Defined as the pitch diameter in millimeters divided by the number of teeth: $m = d / N$. Direct conversion: $m = 25.4 / DP$.
- Diametral Pitch ($DP$): The American AGMA standard, defined as the number of teeth per inch of pitch diameter: $DP = N / d_{inches}$.
2. Core Gear Dimensions
- Pitch Diameter ($d$): The theoretical rolling diameter where two gears contact: $d = m imes N$.
- Outside Diameter ($d_a$): The blank diameter to turn on the lathe before cutting teeth: $d_a = m imes (N + 2)$.
- Root Diameter ($d_f$): The bottom diameter of the tooth gullets: $d_f = m imes (N - 2.5)$.
- Addendum ($h_a$): Height above pitch circle = $1.0 imes m$.
- Dedendum ($h_f$): Depth below pitch circle = $1.25 imes m$.
- Operating Center Distance ($a$): $a = (d_1 + d_2) / 2 = m imes (N_1 + N_2) / 2$.
Frequently Asked Questions
Why did the industry transition from 14.5-degree to 20-degree pressure angles?
A 20° pressure angle thickens the tooth root, substantially increasing beam bending strength and load capacity while reducing the minimum tooth count to avoid undercutting from 32 teeth down to 17 teeth.
How much backlash clearance is necessary between spur gears?
Standard industrial spur gears require a small amount of backlash (typically 0.03 to 0.05 times the module, e.g. 0.003" to 0.008") to allow lubricant film formation and accommodate thermal expansion without tooth binding.
Can a metric Module gear mesh with an imperial Diametral Pitch gear?
No! Even if pitch diameters seem close, a 2.0 Module gear (DP 12.7) will not properly mesh with a 12 or 13 DP gear. Tooth profiles, circular pitches, and pressure lines will mismatch, causing severe vibration and rapid tooth destruction.
What is the "hunting tooth" frequency?
When the number of teeth on the pinion and gear share no common factors (coprime, such as 19 and 60), each tooth on the pinion contacts every tooth on the gear before repeating. This distributes manufacturing wear evenly across all teeth.