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Gear Cutting And Gear Calculations


After the completing of this article the students should be able to

  • Define gear technology
  • Calculate hear blank size
  • Calculate gear module
  • Calculate number of teeth
  • Calculate full depth and clearance
  • Know about the plain indexing method and its calculation
  • Know about the differential calculation methods and its calculation
  • To developed skill and apply it in gear cutting


This article will supply the beginner with sufficient information to enable him to understand gear, gear terms, types of gears and the rules used in making spur gears. It will give him the application of the rules necessary to turn a gear blank in a table and to tromp the teeth on a milling machine.


The term gear may be used in engineering practice for almost many kind of mechanism. But it refers specially to toothed wheel, in other words a gear is a wheel on which teeth hake been formed.


The gears most commonly used in industry are

  • Spur gears
  • Bevel and miter gears
  • Internal gear
  • Helical gear
  • Herringbone gear
  • Worm gears
  • Rack and pinion


This type of gear is a cylinder, wheel, or disk on the surface of which are cut parallel teeth. The larger gear is called the Gear and the smaller, the Pinion. Usually when two gears are in mesh and one is larger than the other, the names gear and pinion are applied. Spur gears are used to transmit power from one shift to another in cases where those shifts hake their axes parallel.


Bevel gears are used when it is necessary to transmit power from one shaft to another where the communication shaft are located at an angle, with their axial lines intersecting. Bevel gears are not restricted to shafts at right angles. There are right angle bevel gears and angular bevel gears. In cases where the ration of a pair of bevel gears is 1:1, both gears being the same size and having the same number of teeth, they are known as MITER GEARS. These gears permit the driving of one shaft at right angles to the other. In a bevel gear the teeth are cut on a conical cone. A pair of gears is used to transmit power from one shaft to another, and share the two shafts have their extended axial lines intersecting at some angle other than 90deg. the gears are called angular bevel gears.


This type of gear has parallel teeth similar to the spur gear but cut on the inside of a cylinder of a ring. The mating gear may be a spur gear. However there are internal helical gears and internal bevel gears. The use such a combination of gears gives a much more compact mechanism, because the centers on which the two gears revolve are so much closer together than they can be efficiently made with two external spur gears operating as a pair.


This type of gear the teeth are cut spiraled around the body. Spiraling the teeth gives a smoother operation, such gears can be used to connect parallel shafts, and they operate far more smoothly than ordinary spur gears, because action of the teeth is progressive as they roll upon one another. Helical gears may be used not only to connect parallel shafts but also to connect shafts at angles with one and other, provided that their axial lines do not intersect.


The herring bones gears resembles two helical gears with half right-hand and half left band teeth, placed side by side, so that the teeth come together to from a chevron pattern. Herringbone gears are always used with parallel shafts.


A worm is an integral part of the worm gear mechanism is made of a blank, which has teeth cut into it in the form of a helix, or screw. It resembles a screw and its teeth are referred to as threads. The function of worm gearing is that of speed reduction. Worms may be made with single, double, triple, etc, threads. A double thread worm will revolve the worm gear twice as fast as a single thread a triple thread worm will revolve it three times as fast.


The functions of rack and pinions are to transform circular motion to rectilinear motion. Many types of racks are used in industry. Some have their teeth cut as spur, while other have helical teeth. The larger are called helical racks. Many such racks are used for adjusting the position of parts of machine tools.


Gear teethes are cut in the following ways:
On a milling machine using from a cutter, on a gear shaper using special cutters having the shape of tooth in them, and on a gear hobbler using cutters called Hobs.
Since most polytechnics institutes and colleges of technology of this country do not have gear shapers or gears hobblers as standard equipment. The method of cutting spur gears and simple helical gears on a milling machine will be explained in detail.


The student should know the meaning of the commonly used gear terms; he should be able to make the necessary calculations for spur gears. It is not necessary to learn all the rules, but it is well worthwhile to know where to find them when needed and how to use them.


The radial or perpendicular distance between the pitch circle and the top of the tooth.

Base diameter:

The diameter of the circle from which the involutes are generated.

Bore diameter:

The diameter of the hole in the gear


The surface between the flanks of adjacent teeth

Centro distance:

The shortest distance between the axes and the minting gears.

Circular path:

The distance on the circumference of the pitch circle between corresponding points of adjacent teeth.

Circular thickness:

The thickness of the tooth on pitch circle


The radial distance between the top of a tooth and the bottom of the mating tooth space.


The radial or perpendicular distance between the pitch circle and the bottom of the tooth space.

Diametric pitch:

The ratio of the number of teeth to the number of inches in the pitch diameter. It indicates the number of teeth in the gear for each inch of pitch diameter

Face width (face of gear) :

The width of the pitch surface

Face of tooth :

The surface between the pitch-line element and the bottom. It includes the fillet, which is the curved surface that adjoins the bottomland of the space.

Module (in English measure):

The module (meaning measure) is the same proportional part of the pitch diameter as the circular pitch is of the pitch circumference that is if the pitch diameter of a gear is divided into as many equal parts as there are circular pitches (teeth) in the gear, for example 3-in pitch diameter, 30 teeth, the module is 1/10 in, and in a gear 2-in pitch diameter, 24 teeth, the module is 1/12 in. Note in each case, the module is fractional part of an inch and equals one divided by the pitch1/DP. In other words, module is the reciprocal of the diametric pitch. The term module is seldom used in this country; the expression 1/DP is used instead.

Module (in SI. System) :

In S.I system module is the ratio of the pitch circle diameter to the number of teeth. It is denoted by (m) the module is the index of tooth size.
Module, m=(PD)/N=(pitch circle diameter)/(No of teeth)
The recommended series of modules are:
1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40 and 50.
The module of second choice are:
1.25, 1.375, 1.75, 2.25, 2.75, 3.5, 4.5, 5.5, 7, 9, 11, 14, 18, 22, 28,36, and 45.

Outside diameter :

The diameter of the circle that contains the top of the teeth.

Pitch circle:

The circle through the pitch point having its center at the axis of the great

Pitch circumference :

Circumference of the pitch circle

Pitch diameter :

The diameter of the pitch circle, equals number of teeth divided by the diametric pitch PD=N/(DP)

Root circle:

The circle containing the bottom of the tooth spaces

Root diameter:

The diameter of the pitch circle equal pitch diameter minus two addendum.

Tooth space:

It is width of space between the two adjacent teeth measured along the pitch circle

Tooth thickness:

It is width of the tooth measured along the pitch circle


It is the difference between the tooth space and the tooth thickness as measured o the pitch circle.

Whole depth:

The radial distance between the outside circle and the root circle; equals addendum plus addendum.

Working depth:

The greatest depth to which a tooth of one gear extends into the tooth space of a mating gear; equals addendum of pinion plus addendum of gears or (usually) twice the addendum of either.


The following formulas are for 14 1/2 deg. Composite system; 14 1/2 deg. involutes (generated) system, and 20-geg, full depth stub in volute system
DP= diametric pitch
PD= pitch diameter of the gear
Pd= pitch diameter of the pinion
CP= circular path
N= number of teeth on gear
n= number of teeth in opinion
OD= out side diameter or diameter of the gear blank
a= addendum
b= addendum
CD= center distance between gear and pinion
WD= whole depth
C= clearance
T= tooth thickness
m= module


nanaji Bhamare on April 14, 2019:

no of teeth 64 ..plz tell the gear train for fauter Hobbing machine

rajan on November 16, 2018:

how to find A/D for helical gear formulae

Rashpaul Rana on August 22, 2017:

sir' tell me formulas of gear and chainwheel cutting in inches

rashpaul rana on August 22, 2017:

Please send me gear and chaineheel cutting formulas thanks.

Dnyanesh Jadhav on May 04, 2017:

can anybody tell, how to select hob number of start based on number of teeth on compoent?

is there any relation for number of start with component number of teeth.

amit dhiman on February 18, 2016:

Scroll to Continue

send me table of gear used for cutting for less than 20 teeth and more than 100 teeth

Rashid Mughal on August 17, 2015:

Can any one told me the complete formula of worm and worm gear cutting and crown gears cutting formula also......

Joseph banda on May 11, 2015:

Please help me with the basics on how to use the hobbing machine thank you.

Gouthami,Muddasani on August 04, 2014:

Sir, I have a project to design a helical gear. On the variable rack there are small teeth and large teeth. length of the rack is 16 inch. I neeed to design helical gear of small teeth and large teeth o it. First there is large and at the middle small teeth and again large teeth. My task is to find out the tooth pitch of that small teeth and large teeth. Tooth pitch of small teeth is one third of the large tooth pitch, length covered by the small teeth is 20% of the length of big teeth.

Atsinafe james on July 15, 2014:

Pls I need one calculation for each type of gear formula thanks in advance. Gmail Jamesuto70@rocketmail. com.

denis on July 05, 2014:

send me a video on how to cut helical gear on milling machine and gear hobber machine. at email

denis on July 05, 2014:

how to cut helical gear and culculation

salman mohammad on June 10, 2014:

as salam o alikum sir

i want to make ring of following dimension




how to claculate no of teeth&module

umar on April 12, 2014:

Hi i am in millat tractor ltd

As a technician how we calculate helical gear feed gears plz tell us

Raaju on March 17, 2014:

I wanted In milling machine changing gear calculation formula for helical gear & worm , Please send it to my email add :

sajith on February 21, 2014:

can you send me helical gear cutting calculation , how can select driven&driver gear??? email;

gulab on January 12, 2014:

Aal gear cating hoobbing calculasn

omprakash on December 04, 2013:

plz help ,me

how to find four differential gear if u have any new technic plz tell me

if given hob start single=1 ,helix angle=20 .m/c contnt=15

sapose ratio=0.6530872056

then find technic four gear A B C D mb n-07304077896

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deepak on November 08, 2013:

Dear sir plese send my email adress how. To cut helical gear in hoobbing machine

wiqas on September 23, 2013:

i m wqias any side problem in any gear cutting in milling machine plz contact me (

derek on September 17, 2013:

hi, im drawing a module 1, 12 tooth, 20 degree pressure angle gear can you send any info for drawing these gears....

email -



santosh on September 05, 2013:

In a gear cutting with milling machine,The gear ratio is ? please send me the ans.

Fahad on July 20, 2013:

Please send me the gear tooth cutting formulas. and how to find hob cutter diameter.

alfadil on June 01, 2013:

i need all the roll of milling gear and all cutting calculation by my email is

Natraj on May 13, 2013:

Please send me the gear cutting formulas to cut spur and helical gears. I need it urgently. Send it to

Thanks in advance.

hashem111 on May 08, 2013:

please send me all gear cutting calculation by my mail is

Fahad on April 15, 2013:

Please send me the gear cutting formula and which hob cutter is suitable for different size of gear. my id is

krishnananth on February 23, 2013:

Please send me the gear cutting formula to this email id

Mark on February 19, 2013:

hey guys i need to draw a bevel pinion gear for collage and have no idea how to do it even after doing research for a week. can someone please help me find a website or what not that shows me how to calculate all the different dimensions

sukesh on December 16, 2012:

pls send me formula for teeth cutting & how to calculate span?

pradip thapa on December 08, 2012:

plase provide me calculation and formula of gear cutting with example

Gurpreet singh on November 26, 2012:

hello sir i have design a gear for spur and pls tell me how to callculate of module given data center distance 2 shaft & ratio of gear 1:1.54, my email id

manojkumar on November 17, 2012:

sir sent me the total gear cutting calculations

kamal kishore on October 15, 2012:

lead formula of this hobbing machine

steve on October 10, 2012:

what was the point of this information? a simple drawing explaining pitch circle etc would be far more usefull. This all just serves to add confusion to an already confusing subject.

vjd on October 05, 2012:

i wants to cut helical gear on gear hobing machine but idont have diffrential constant pl tel me how to cut the gear.

Ummar Mughal on October 02, 2012:

i need to know the formula of gear hobbing machine and

lead formula of this machine

vipul rajkot on September 20, 2012:

please send to me all gear calculation formala

vipul m patel on September 20, 2012:

pls send the caculation methord for mikron gear hobing machin hilical gear cod and my cell no is 09099377877


Jacques on September 08, 2012:

I would like to know the formula to work out the addendum and tooth thickness of corrected gears please.

JassiGurpreet on September 05, 2012:

helical gear cutting

1999 to 2012

ineed exsampel cuting geer on September 04, 2012:

example cutting gee r

Ashok on September 02, 2012:

i want to know gear calculation in DP

please let me know

will be so thankful

my email add is

Akshay on September 01, 2012:

Respected Sir,

I want to know why module less than 1 not included in standard series, still they are in use.

palash on June 11, 2012:

Hi,I'm palash das from kolkata,india.

please anybody send me how to calculate the differential changegears from differential ratio.

my mob no is-09830319249

my email id

Anthony saviour on June 01, 2012:

Please am just confuse on the spur gear calculation. 08057852880

davinder on May 23, 2012:

please tell me formula of a helix angle change gear with a different lead of screw my id

sukhvinder singh on May 02, 2012:

please send me or let me know how to calculate or remove the 4 gears to cut helical gears of different degrees

my email id is

Thanking u

kipkoske on April 30, 2012:

send me gear cutting formular to my e-mail

Farzad on April 29, 2012:


My name is farzad

Im mechanical engineer and now i study about industriall design.

I like to learn more about gear and culc

pleas if u can help to me

with thanks


HASSAN AQEEL on March 30, 2012:


sushil saini on March 25, 2012:

please send to me all gear calculation formala

vassos tapakoudes on March 17, 2012:

i have a diameter of 10 and i want to have approximate 10 teeth. can you tell me what the module should be? also is the module constant in all gears in a power screw? my email is

Yi on March 13, 2012:

pls send me the bevel gear calculation formula


Nagaraj on March 11, 2012:


Jagjit on March 08, 2012:

Please send me the formula to find gear to make worm of various DP for 3DP,4DP,5DP mail me

Prashant on March 08, 2012:

Pls send me the stap of gear desing to Mfg.

B.krishnamoorthy on March 05, 2012:

hi,I need to know about the spur gear calculation on making in gear hobbing machine,please send me.

p.ravi on March 05, 2012:

please send to me all gear calculation formala

VICTOR MWANIGI on March 04, 2012:

AM FROM KENYA WHO WORKS WiTH MILLING BUT STILL I DON`t know how to cut gears can you please send me those calculations

Mogy on February 29, 2012:

plz send to me all the formula thanks

Allan on February 20, 2012:

Kindly give me formula. Mail me on thanks

Allan on February 20, 2012:

Pls give me formula. Thanks

Roman on February 19, 2012:

plz give me the formula ....

sampath kuppan on February 10, 2012:


Naveen kumar sharma on February 09, 2012:

Email:- Dear sir. It good see this site. But i need something more. I need some defnition like what is profile of gear,lead,ranout,pitch variation, accumaleted pitcherror ,

rahul on February 06, 2012:

i want to know why we do not use 2nd and 4th angle in engineering please sent the answer on my e-mail at

TULJARAM on February 02, 2012:


Mahesh on February 01, 2012:

I want how to calculate the dia of gear wheel with the using of gear teeths. My name is mahesh plz sent me the ans to my e-mail

SKG on January 23, 2012:

Any body drive the formula for SAP and EAP for Internal gears in roll lengths

s singh on January 19, 2012:

please help me to know how to calculate the train of gears for differiential on gear hobbing machine

Sunil Weerasinghe on January 03, 2012:

We hope to buy a Gear Planner(Gear cutter) Machine

Therefore please send us the Price

Thanks Sunil

jeet on December 17, 2011:

hi sir,

i know to cut helical gear, warm gear, spur gear, straight bevel gear, warm shaft,

but i want to learn to cut sperial bevel gear, for this i need to know the formula and attachment ofl the sperial beve

Nanditha Vijay Engg Works on December 13, 2011:

Dear Sir,

Staehely German make gear hobbing machines ,teeth calculations formula required to calculate the teeth.

kindly send us the formula if u have . on December 05, 2011:

Dear sir;

i m faruk from Saudi Arabia i ve finished machinist still i m working one workshop. 2 ,3 years i can't work in my felled. so i forget milling calculation and how to use special attachment. so kindly send and reply my answer. thank you. on December 05, 2011:

Dear sir;

i m faruk from Saudi Arabia i ve finished machinist still i m working one workshop. 2 ,3 years i can't work in my felled. so i forget milling calculation and how to use special attachment. so kindly send and reply my answer. thank you.

akhtar.humayon on November 29, 2011:

thanx its nice way to teach about gearing calculation . i appreciat that u teach , on November 24, 2011:

can u send me a cutting gear formula? thanks!

Prasanna on November 02, 2011:

Dear sir

can u pls send me the datas to be required for manufacturing straight bevel gears, wat r the datas we have to show in the drafting..

thanks in advance


sukhvinder singh thethi on November 01, 2011:

I would like to request to send me ,either the formula or the ratio chart ,along with which we can remove the change gears to cut helical gears of different degree

Ivan D'souza on October 17, 2011:

I want to cut a spur gear of 14 teeth on milling machine using indexing head, do help me to calculate the number of turns on the indexing head and to know which type of cutter to be used for cuting this 14 teeth stub gear, u can snd on my Email:


ashok kumar singh on October 08, 2011:

PLG sir sed me I Want to know the helical gear cutting calculations formulas.please send my e thanks

jayaraj on October 06, 2011:

pleseopenevrythgs ok

Rajesh Paul on October 06, 2011:

I want to know the helical gears cutting calculations formulas.please send urgently

Paul Engg.Works.


rakesh chaudhary on September 26, 2011:

I want to know the helical gears cutting calculations formulas.please send urgently

alfred on August 31, 2011:

pls send formula eor cutting spocket

Edem on August 17, 2011:

Am edem from ghana,student pls can u help with books on gears plx.. My address nicolas_edemson@yahoo.Com

manoj on August 13, 2011:

hi,I need to know about the helical gear calculation on making in milling machine,please send me.

julymac on August 09, 2011:

hi,I i need to know the calculations on making spur gear using a gear hobbing machine.thank you.

dheeraj sharma on July 31, 2011:

pls send the caculation methord for cutting worm gear and shafts and my cell no is 09837400008

im from uttrakhand city(kashipur)


gear cutter on May 06, 2011:

TMI specialises in the manufacture of wide range of Milling Cutters,Gear Cutters,Drills, Endmills,Reamers, Toolbits, threading tools and custom tools for the industrial use. more...

markwei jacob on April 23, 2011:

plz i need some of ur book for more learning

my address. sda church po box as 694

ashaiman ghana



Chain Sprocket Hobs on April 19, 2011:

We at Capital Tool Industries welcome all international and domestic inquiries pertaining to our products and services. We reaffirm our commitment to all our valued customers and potential clients that all inquiries will be replied to within 48 hours as we value your business.

Chain Sprocket Hobs on April 15, 2011:

We at Capital Tool Industries welcome all international and domestic inquiries pertaining to our products and services. We reaffirm our commitment to all our valued customers and potential clients that all inquiries will be replied to within 48 hours as we value your business.

sodiqment on March 14, 2011:

how to construct automatic door

simon on March 12, 2011:

please help me to get the lead if the given is outside diameter and helical angle? ..thanks

Gear cutters on February 13, 2011:

Gear cutters have unique stud tooth depth to cut all types of standrad or non strandad involutes splines.

anth on January 26, 2011:

please complete the formulas

Scalping Cutter on January 16, 2011:

scalping cutter used for milling of plain surfaces of ferrous as well as non- ferrous metals

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