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Spur Gear Calculator

Pitch diameter, gear ratio, tooth geometry, and center distance

Gear Ratio

2:1

Center

60 mm

Output

500 RPM

Gear Ratio

2:1

Center Dist

60 mm

Output RPM

500

Contact Ratio

1.64

Pinion (Z1=20)

Pitch Dia40 mm
Outside Dia44 mm
Root Dia35 mm
Torque9.55 Nm

Gear (Z2=40)

Pitch Dia80 mm
Outside Dia84 mm
Root Dia75 mm
Torque19.1 Nm

Tooth Geometry

Circular Pitch6.28 mm
Addendum2 mm
Dedendum2.5 mm
Tooth Thickness3.14 mm
Tangential Force477.5 N

What You'll Need

Arduino Uno R4 Minima Microcontroller Board

Arduino Uno R4 Minima Microcontroller Board

$20-$284.6
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Raspberry Pi 4 Model B 4GB RAM Starter Kit

Raspberry Pi 4 Model B 4GB RAM Starter Kit

$75-$1004.6
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STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

$10-$154.5
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BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

$49.004.4
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Stanley FatMax 25 ft. L x 1.25 in. W Magnetic Tape Measure Yellow 1 pk

Stanley FatMax 25 ft. L x 1.25 in. W Magnetic Tape Measure Yellow 1 pk

$23.404.7
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Arduino Uno R4 Minima Microcontroller Board

Arduino Uno R4 Minima Microcontroller Board

$20-$284.6
View on Amazon
Raspberry Pi 4 Model B 4GB RAM Starter Kit

Raspberry Pi 4 Model B 4GB RAM Starter Kit

$75-$1004.6
View on Amazon
STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

STEPPERONLINE Nema 17 Stepper Motor 84oz.in 1.5A

$10-$154.5
View on Amazon
BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

BOSCH GLM100-23 100 Ft BLAZE Laser Distance Measure, Includes 2 AA Batteries

$49.004.4
View on Amazon
Stanley FatMax 25 ft. L x 1.25 in. W Magnetic Tape Measure Yellow 1 pk

Stanley FatMax 25 ft. L x 1.25 in. W Magnetic Tape Measure Yellow 1 pk

$23.404.7
View on Amazon

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Example Calculations

120T pinion meshing with 40T gear, module 2

Inputs

Z120 teeth
Z240 teeth
Module2 mm

Result

Gear Ratio2:1
Center Distance60 mm

Ratio = 40/20 = 2:1. d1=40mm, d2=80mm. Center = (40+80)/2 = 60mm.

215T pinion meshing with 60T gear, module 3

Inputs

Z115 teeth
Z260 teeth
Module3 mm

Result

Gear Ratio4:1
Center Distance112.5 mm

Ratio = 60/15 = 4:1. d1=45mm, d2=180mm. Center = (45+180)/2 = 112.5mm.

Frequently Asked Questions

Q

How do I calculate spur gear pitch diameter?

Pitch diameter = module × number of teeth. A 20-tooth gear with module 2mm has a pitch diameter of 40mm. Module is the metric standard; diametral pitch (DP) is the imperial equivalent.

  • d = m × Z (metric)
  • DP = Z / d for imperial (teeth per inch)
  • Module 2, 20 teeth = 40mm pitch dia
  • Module 2, 40 teeth = 80mm pitch dia
Module (mm)DP Equivalent20T Pitch Dia40T Pitch Dia
125.4 DP20 mm40 mm
212.7 DP40 mm80 mm
38.5 DP60 mm120 mm
Q

What is a good contact ratio for spur gears?

Contact ratio should be at least 1.2 for smooth operation. Values above 1.4 are preferred. Contact ratio below 1.0 means teeth lose contact during rotation, causing impact and noise.

  • Minimum: 1.2 for quiet operation
  • Ideal: 1.4–1.8
  • Below 1.0: teeth lose contact (bad)
  • Higher tooth count increases contact ratio
Q

What pressure angle should I use?

20° is the modern standard for most applications. 14.5° is legacy (smoother but weaker). 25° is for heavy-duty power transmission with higher tooth strength.

  • 14.5°: legacy, smooth, lower strength
  • 20°: standard, good balance
  • 25°: heavy duty, strongest teeth
  • 20° gears cannot mesh with 14.5° gears
Q

How do I find center distance between two gears?

Center distance = (d1 + d2) / 2 = m × (Z1 + Z2) / 2. For a 20T and 40T pair at module 2: (40 + 80) / 2 = 60mm center distance.

  • C = m(Z1+Z2)/2
  • Module 2, 20T+40T: C = 60mm
  • Must be exact for proper meshing
  • Adjustable via profile shift correction

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Last Updated: Jun 18, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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