Spur Gear Teeth Geometry Calculators And Explanations

Because of the complex teeth geometries of spur gears, diameter calculations, teeth geometry calculations are a bit complex. Here, we explain all the calculations related to the gear-teeth relations.

Explanation Of Addendum, Dedendum, And Clearance Of Spur Gears

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Designing the construction of machinery, all the geometrical features must be calculated. Contacting of pinion and gears must be calculated in detail to obtain the required construction. There are a bunch of terms related to these calculations;

• Addendum(a) Of Spur Gears: The distance between the pitch circle and the outermost section of the gear tooth.
• Dedendum(b) Of Spur Gears: The distance between the pitch circle and the bottom of the tooth space.
• Clearance(c) Between Spur Gears: At assembled gears, clearance defines the space between the outermost section of the first spur gear and the bottom of tooth space of the second spur gear.

You can use the calculator below to calculate Addendum, Dedendum, and Clearance of a spur gear if you know diametric pitch or metric module;

Pitch Or Metric Module? Metric Module System Diametral Pitch System
– Select the formula Coarse Pitch Fine Pitch

Enter m :

Addendum_(a) =


Dedendum_(b) =


Clearance_(c) =

Enter P_d :

Addendum_(a) =


Dedendum_(b) =


Clearance_(c) =

Enter P_d :

Addendum_(a) =


Dedendum_(b) =


Clearance_(c) =

The use of the calculator above to calculate addendum, dedendum, and clearance values for spur gear mates is very easy. Select the required information from the list which you know; diametral pitch or metric module. Do not forget that the unit of diametral pitch is inches and the metric module is millimeters.

Enter the required value then click on the ‘Calculate!’ button. To make another calculation, click on the ‘Reset’ button then re-enter the values.

Calculation Of Outside Diameter Of A Spur Gear

The outside diameter of spur gear is a very important constructional value. It is generally referred to as ‘Da’. If you know the metric module or diametric pitch and number of teeth of your spur gear, you can use the calculator below to calculate the outside diameter.

Just like the calculator before this, you need to select the information you have about your spur gear mates; metric module, or diametral pitch…

Outside diameter calculated via diametral pitch formula is like below. Check your calculations with this formula;

Metric module outside diamater formula;

The diameter of spur gear is calculated as the extraction of two dedendum values from the calculated outside diameter. This value is called ‘D’.

Calculation Of Other Constructional Values Of Spur Gear Tooth

• Working Depth Calculation: Working depth is calculated as multiplying addendum with 2.
• Tooth Thickness Calculation: You can calculate the tooth thickness value of mating spur gears by using this equation; pi/(2*Pa). Pa is the diametral pitch of spur gear.
• Root Diameter Calculation: If you extract two dedendums from the diameter of spur gear, you will find out the root diameter value.
• Whole Depth Value: Whole depth is the summation of addendum and dedendum of a spur gear.

Center Distance Calculation Of Mating Spur Gears With Calculators

Maybe center distance calculation is the most important aspect of spur gear mates. The exact calculation of center distance is very important in terms of the construction of other elements inside machinery such as shafts etc.

If you know the number of teeth of pinion and gear mates, and diametral pitch or metric module, you can easily calculate the center distance value between mating gears.

Center distance formula via diametral pitch;

Center distance formula via metric module;

Conclusion For Spur Gear Geometrical Calculators

These calculators can be very useful when you are making spur gear construction design.

All the responsibilities of calculations made in Mechanical Base calculators are about the users of calculators. Calculators are prepared based on very reliable sources.

You can take a look at other engineering calculators available in Mechanical Base!

You can also use the MB-Unit Converter tool to convert your unit sets to another set of units.

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