Gear Design Solver is a free online engineering calculator for the basic geometry of standard 20° full-depth spur gears. It uses the fundamental gear relationship D = m × N to calculate the Module (m), Number of Teeth (N), or Pitch Diameter (D) when the other two values are known.

The calculator also provides important derived gear dimensions, including addendum, dedendum, outside diameter, root diameter, circular pitch, and whole depth. An optional mating-gear calculation gives the mating pitch diameter, center distance, and gear ratio when the second gear’s tooth count is entered.

It is useful for mechanical design, gear selection, machine design, manufacturing, CAD work, and engineering students who need quick preliminary spur-gear calculations.

How to Use the Gear Design Solver

1. Select what you want to calculate

Under “I want to find”, select one of the following:

• Module (m)
• Number of Teeth (N)
• Pitch Diameter (D)

2. Enter the known values

The calculator automatically displays the other two parameters that are required for the selected calculation.

For example:

• To calculate Module (m) → enter N and D
• To calculate Number of Teeth (N) → enter m and D
• To calculate Pitch Diameter (D) → enter m and N

All input values must be positive.

3. Select the appropriate unit

For dimensional values, you can select:

• mm
• cm
• m
• in
• ft

The number of teeth is entered as a count.

4. View the calculated result

The main result is displayed at the top of the results panel. The calculator also automatically calculates the corresponding gear geometry.

5. Check the derived gear geometry

The calculator provides:

Parameter	Description
Addendum	Radial height from pitch circle to outside circle
Dedendum	Radial depth from pitch circle toward the root
Outside Diameter (Do)	Diameter over the gear teeth
Root Diameter (Dr)	Diameter at the tooth root
Circular Pitch	Distance between corresponding points of adjacent teeth
Whole Depth	Total tooth depth

These are calculated using the standard proportions implemented in the calculator.

6. Calculate a mating gear

Enable “Calculate mating gear & center distance” and enter the mating gear’s Number of Teeth (N₂).

The calculator then displays:

• Mating Pitch Diameter (D₂)
• Center Distance (C)
• Gear Ratio (N₂ : N)

The mating gear calculation assumes that both gears use the same module, which is required for proper meshing in this calculation.

---

Formula Used

The primary gear relationship is:

D = m × N

Where:

• D = Pitch Diameter
• m = Module
• N = Number of Teeth

Therefore:

Module:
m = D / N

Number of Teeth:
N = D / m

Pitch Diameter:
D = m × N

Standard Gear Proportions

For the standard 20° full-depth spur gear used by this calculator:

• Addendum = m
• Dedendum = 1.25m
• Whole depth = 2.25m
• Outside Diameter = m(N + 2)
• Root Diameter = m(N − 2.5)
• Circular Pitch = πm

Note: The calculator assumes external spur gears with no profile shift and uses standard AGMA full-depth 20° proportions.