Terminology of Spur Gear and Their Formulas

Hello friends, Today's topic is related to gear terminology in which we will know about the terminology of spur gear.

Along with spur gear terminology, we will also know about the spur gear formula which is related to the terminology of spur gear.

Gears are often used to transmit power or motion from one shaft to another shaft when the shafts are located close to each other. 

There are so many types of gears are used in machines or equipment to transmit power which I have already discussed in our previous post.

So without wasting time let's know spur gear terminology and their formula.

What is Spur Gears?

These are the gears on which the teeth are cut parallel to their own axis. 

As the teeth are parallel to the axis, they are used on drives whose shafts are parallel to each other.

 Spur gearing is mostly used.

Terminology of Spur Gear

There are following the terminology of spur gear with their formulas:

  • Top Land
  • Bottom Land
  • Pitch Circle
  • Pitch Circle Diameter
  • Module
  • Circular Pitch
  • Addendum
  • Addendum Circle
  • Clearance
  • Dedendum
  • Dedendum Circle
  • Tooth Thickness
  • Diametral Pitch 
  • Total Depth
  • Face of Tooth
  • Face Width
  • Working Depth
  •  Pitch Point
  • Pressure angle
  • Flank
  • Fillet
  • Tooth Space
  • Backlash
  • Gear Ratios

See in figure terminology of spur gears which is described below.

terminology of spur gear
Terminology of Spur Gear

Top Land

The top most surface of the gear tooth is called top land. 

Bottom Land

The bottom most surface of the gear tooth is called bottom land.

Pitch Circle

When two gears have meshed together, then the point on which one gear tooth is in contact with the tooth of the other gear is called the contact point.

And the imaginary circle that passes through this contact point is called the pitch circle.

The perpendicular drawn at the point of contact in a pair of teeth must pass through the point of pitch.  This is called the law of gearing.

Pitch Circle Diameter (PCD)

As the name indicate it is the diameter of the pitch circle. 

It can be denoted by the PCD.


A module is defined as the ratio of pitch circle diameter in mm to the total no of teeth.

It can be denoted by m.

The formula of the module

m = PCD/N


PCD = Pitch circle diameter

N = No of teeth

Circular Pitch

The distance between a point of the tooth, measured at the same point in the adjacent teeth, is known as the circular pitch along the circumference of the pitch circle.

Circular pitch can be denoted by Cp.

Cp = PCD×π/N

Cp = m×π (since, m = PCD/N)


PCD = Pitch circle diameter

N = No of teeth

π = 3.14

m = Module


When the radial distance between the pitch circle and the addendum circle is measured, it is called the addendum.

Addendum can be denoted by the capital letter A.

Since we know that, Addendum is equal to the module.


A = m = PCD/N

Addendum Circle

The circle that passes from the top of the tooth is called the addendum circle.

It is also called the outside circle which surrounds the outer ends of the teeth.

In external gears, the addendum circle is on the outer cylinder while in the internal gears the addendum circle is on the inner cylinder.

The diameter of the addendum circle can be calculated by this formula.



ACD = Addendum circle diameter

PCD = Pitch circle diameter

A = Addendum


When two gears meshed together, then the gap between the addendum circle of the top tooth and the dedendum circle of the other tooth is called the clearance.

Clearance can be denoted by the capital letter C.

It can be calculated by.

C = Cp/20


Cp = Circular Pitch


When the radial distance between the pitch circle and the dedendum circle is measured, it is called the dedendum.

It can be denoted by the capital letter D.

D = A + Clearance


A = Addendum

Dedendum circle 

The circle that passes from the bottom of the tooth is called the dedendum circle.

It is also called the root circle which surrounds the bottom of teeth.

The diameter of the dedendum circle can be calculated by.

DCD = PCD -2× D


DCD = Dedendum circle diameter

PCD = Pitch circle diameter

D = Dedendum

Tooth Thickness

Tooth thickness is the distance that is measured along the pitch circle of two attached teeth.

Tooth thickness is also called circular thickness.

It is denoted by the capital letter T.

The formula of tooth thickness is,

T = Cp/2


Cp = Circular Pitch

Diametral Pitch  

Diametric pitch is the number of gear teeth divided by the pitch circle diameter. 

It can be denoted by DP.



DP = 1/m (since, m = PCD/N)


PCD = Pitch circle diameter

N = No of teeth

m = Module

Total Depth

Total depth is the sum of addendum and Dedendum.

TD = A+D


TD = Total Depth

A = Addendum

D = Dedendum

Face of Tooth

Above the pitch circle, the surface of the tooth is called the face of the tooth.

Face Width

Face width is the width of the tooth. 

Working Depth 

This is the distance of the arrangement of two teeth which is expressed as '2A'.


A = Addendum 

Pitch Point

When two gears are in contact, the common point of both pitch circles of the meshing gear is called the pitch point.


Pressure angle

The tangent line drawn at the pitch point and the normal line drawn from the same pitch point, the angle it makes from that tangent line is called the pressure angle.

Generally, pressure angle is used up to 20°.


The face of the tooth of a gear that comes in contact with the teeth of another gear is called the flank.

The flank is always below the pitch circle.


Fillet is a region of maximum bending stress concentration in a gear tooth.

However, its outline in the gear profile is usually less specified.

Tooth Space

Tooth space is the distance that is measured along with the pitch circles of the two adjacent teeth.


Backlash is the difference between the tooth space of one gear to the tooth width of another gear.

The backlash in pairs of gears is the amount of clearance between the meshed gear teeth.

It is the maximum distance a part can be moved without moving its connected part.

It is the amount of motion destroyed due to clearance. 

The minimum backlash is always provided in between two meshed gear such that the gear can transmit motion or power without any restriction.

Gear Ratios

A gear ratio of spur gears is defined as it is the ratio of the number of teeth on the driven gear to the number of teeth on the drive gear.

Different gear ratios can be obtained by connecting gears with the same pitch, but different numbers of teeth.

Gear ratios are used to increase mechanical torque or to increase rotational speed or velocity. 


It is denoted by the capital letter G.

G = N2/N1


G = Gear ratio

N2 = No of teeth in the driven gear

N1 = No of teeth in driver gear

Care and Maintenance of Spur Gear

There are following should be kept in mind when using a spur gear.
  • Proper Support
  • Proper Alignment to Connected Equipment
  • Correct Lubrication

Proper Support

Most small and medium-sized gear drives provide correct tooth contact and bearing alignment if they maintain their normal shape.

Proper Alignment to Connected Equipment

In most cases, the gear drive is attached to the prime mover on the input side and the driven machine on the output side.

Good alignment means that the shafts are parallel to each other, there is no angular misalignment, and their midlines are not divergent. 

Good alignment reduces the load on the bearings.

Correct Lubrication

Inadequate lubrication is the single biggest reason for gear drives malfunction.

Mineral oil with a slight corrosion inhibitor and oxidation inhibitor is the most commonly used gear lubricant.

Although some synthetic oils are useful for some low and high temperature applications, they are expensive. 

When choosing a lubricant, it is important to pay attention to its viscosity because heat loss is caused by lubricants with very high viscosity.

In general, the higher the viscosity lubricant, the higher the temperature. 

High oil temperatures are not harmful to the metal, bearings, and housings of the gears, but the oil can be hazardous to seals and the oil itself. 

The quantity of oil should be used as per the recommendation of the gear producers because very little oil can often result in a lack of oil circulation in the bearings and the effect of too much oil is often that there is more heat loss and higher temperatures. 

So, here, we discussed the terminology of spur gear as well as spur gear formula which is related to spur gear terminology.

I hope you all like this post.

Thank You

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