Number of Teeth on Sprocket given Pitch Circle Diameter Calculator

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Design of Chain Drives

Design of Brakes

Design of Flywheel

Design of Friction Clutches

Design of Shafts

Design of Splines

Design of Springs

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Geometric Relationships for Chain

Polygonal Effect

Power Rating of Roller Chains

Proportions of the Sprocket Wheel

✖Pitch of Chain is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link.ⓘ Pitch of Chain [P]			+10% -10%
✖Pitch Circle Diameter of Sprocket is the diameter of the pitch circle (passing through rollers centre) of the sprocket.ⓘ Pitch Circle Diameter of Sprocket [D]			+10% -10%

✖Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).ⓘ Number of Teeth on Sprocket given Pitch Circle Diameter [z]

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Formula

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Number of Teeth on Sprocket given Pitch Circle Diameter

Formula

`"z" = 180*asin("P"/"D")`

Example

`"36.24443"=180*asin("22mm"/"110mm")`

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Number of Teeth on Sprocket given Pitch Circle Diameter Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)
z = 180*asin(P/D)
This formula uses 2 Functions, 3 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
asin - The inverse sine function, is a trigonometric function that takes a ratio of two sides of a right triangle and outputs the angle opposite the side with the given ratio., asin(Number)

Variables Used

Number of teeth on sprocket - Number of teeth on sprocket is defined as the number of teeth (which mesh with another compatible toothed part to the chain or convert torque and speed).
Pitch of Chain - (Measured in Meter) - Pitch of Chain is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link.
Pitch Circle Diameter of Sprocket - (Measured in Meter) - Pitch Circle Diameter of Sprocket is the diameter of the pitch circle (passing through rollers centre) of the sprocket.

STEP 1: Convert Input(s) to Base Unit

Pitch of Chain: 22 Millimeter --> 0.022 Meter (Check conversion here)
Pitch Circle Diameter of Sprocket: 110 Millimeter --> 0.11 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

z = 180*asin(P/D) --> 180*asin(0.022/0.11)

Evaluating ... ...

z = 36.2444257422595

STEP 3: Convert Result to Output's Unit

36.2444257422595 --> No Conversion Required

FINAL ANSWER

36.2444257422595 ≈ 36.24443 <-- Number of teeth on sprocket

(Calculation completed in 00.006 seconds)

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Osmania University (OU), Hyderabad

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< 23 Geometric Relationships for Chain Calculators

Number of Links in Chain

Go Number of links in chain = 2*(Centre Distance between Chain Pulleys/Pitch of Chain)+(Number of Teeth on Driving Sprocket+Number of Teeth on Driven Sprocket)/2+(Pitch of Chain/Centre Distance between Chain Pulleys)*((Number of Teeth on Driven Sprocket-Number of Teeth on Driving Sprocket)/2*pi)^2

Roller Radius given Top Diameter of Sprocket Wheel

Go Roller Radius of Chain = (Pitch Circle Diameter of Sprocket+(Pitch of Chain*(1-(1.6/Number of teeth on sprocket)))-Top Diameter of Sprocket Wheel)/2

Roller Radius given Maximum Tooth Height above Pitch Polygon

Go Roller Radius of Chain = 0.625*Pitch of Chain-Maximum Sprocket Tooth Height+0.8*Pitch of Chain/Number of teeth on sprocket

Number of Teeth on Driving and Driven Sprockets given Average Chain Velocity

Go Number of teeth on sprocket = Average Chain Velocity*60/(Pitch of Chain*Speed of chain drive shaft in rpm)

Pitch of chain given Average Chain Velocity

Go Pitch of Chain = Average Chain Velocity*60/(Number of teeth on sprocket*Speed of chain drive shaft in rpm)

Average Chain Velocity given Number of Teeth on Sprocket

Go Average Chain Velocity = Number of teeth on sprocket*Pitch of Chain*Speed of chain drive shaft in rpm/60

Speed of Rotations of Driving and Driven Shafts given Average Chain Velocity

Go Speed of chain drive shaft in rpm = Average Chain Velocity*60/(pi*Pitch Circle Diameter of Sprocket)

Average Velocity of Chain

Go Average Chain Velocity = pi*Pitch Circle Diameter of Sprocket*Speed of chain drive shaft in rpm/60

Pitch of chain given Pitch Circle Diameter

Go Pitch of Chain = Pitch Circle Diameter of Sprocket*sin(3.035/Number of teeth on sprocket)

Number of Teeth on Sprocket given Pitch Circle Diameter

Go Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)

Speed of Rotation of Driving Shaft given Velocity Ratio of Chain Drives

Go Angular speed of chain driving shaft = Velocity Ratio of Chain Drive*Angular speed of chain driven shaft

Speed of Rotation of Driven Shaft given Velocity Ratio of Chain Drives

Go Angular speed of chain driven shaft = Angular speed of chain driving shaft/Velocity Ratio of Chain Drive

Velocity Ratio of Chain Drives

Go Velocity Ratio of Chain Drive = Angular speed of chain driving shaft/Angular speed of chain driven shaft

Number of Teeth on Driving Sprocket given Velocity of Chain Drives

Go Number of Teeth on Driving Sprocket = Number of Teeth on Driven Sprocket/Velocity Ratio of Chain Drive

Number of Teeth on Driven Sprocket given Velocity of Chain Drives

Go Number of Teeth on Driven Sprocket = Number of Teeth on Driving Sprocket*Velocity Ratio of Chain Drive

Roller Radius given Tooth Flank Radius

Go Roller Radius of Chain = Sprocket Tooth Flank Radius/(0.016*((Number of teeth on sprocket)^2+180))

Roller Radius given Minimum Tooth Flank Radius

Go Roller Radius of Chain = Minimum Tooth Flank Radius/((Number of teeth on sprocket+2)*0.24)

Chain Pitch given Minimum Tooth Height above Pitch Polygon

Go Pitch of Chain = (Minimum Tooth Height+Roller Radius of Chain)/0.5

Roller Radius given Minimum Tooth Height above Pitch Polygon

Go Roller Radius of Chain = 0.5*Pitch of Chain-Minimum Tooth Height

Number of Links in Chain given Length of Chain

Go Number of links in chain = Length of Chain/Pitch of Chain

Pitch of chain given Length of Chain

Go Pitch of Chain = Length of Chain/Number of links in chain

Length of Chain

Go Length of Chain = Number of links in chain*Pitch of Chain

Roller Radius given Minimum Roller Seating Radius

Go Roller Radius of Chain = Minimum Roller Seating Radius/(2*0.505)

Number of Teeth on Sprocket given Pitch Circle Diameter Formula

Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket)
z = 180*asin(P/D)

Define Sprocket?

A sprocket, sprocket-wheel or chainwheel is a profiled wheel with teeth, or cogs, that mesh with a chain, track or other perforated or indented material. The name 'sprocket' applies generally to any wheel upon which radial projections engage a chain passing over it.

How to Calculate Number of Teeth on Sprocket given Pitch Circle Diameter?

Number of Teeth on Sprocket given Pitch Circle Diameter calculator uses Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket) to calculate the Number of teeth on sprocket, The Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as number of indentations present on sprocket wheel. Number of teeth on sprocket is denoted by z symbol.

How to calculate Number of Teeth on Sprocket given Pitch Circle Diameter using this online calculator? To use this online calculator for Number of Teeth on Sprocket given Pitch Circle Diameter, enter Pitch of Chain (P) & Pitch Circle Diameter of Sprocket (D) and hit the calculate button. Here is how the Number of Teeth on Sprocket given Pitch Circle Diameter calculation can be explained with given input values -> 36.24443 = 180*asin(0.022/0.11).

FAQ

What is Number of Teeth on Sprocket given Pitch Circle Diameter?

The Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as number of indentations present on sprocket wheel and is represented as z = 180*asin(P/D) or Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). Pitch of Chain is usually defined as the distance between links, as measured from the center of the roller pin on one link to the center of the roller pin on the next link & Pitch Circle Diameter of Sprocket is the diameter of the pitch circle (passing through rollers centre) of the sprocket.

How to calculate Number of Teeth on Sprocket given Pitch Circle Diameter?

The Number of Teeth on Sprocket given Pitch Circle Diameter formula is defined as number of indentations present on sprocket wheel is calculated using Number of teeth on sprocket = 180*asin(Pitch of Chain/Pitch Circle Diameter of Sprocket). To calculate Number of Teeth on Sprocket given Pitch Circle Diameter, you need Pitch of Chain (P) & Pitch Circle Diameter of Sprocket (D). With our tool, you need to enter the respective value for Pitch of Chain & Pitch Circle Diameter of Sprocket and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of teeth on sprocket?

In this formula, Number of teeth on sprocket uses Pitch of Chain & Pitch Circle Diameter of Sprocket. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of teeth on sprocket = Average Chain Velocity*60/(Pitch of Chain*Speed of chain drive shaft in rpm)

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