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## Credits

Osmania University (OU), Hyderabad
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## Number of Teeth on the Sprocket When Pitch Circle Diameter is Given Solution

STEP 0: Pre-Calculation Summary
Formula Used
number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch)
z = 180*(pi/180)*asin(D/P)
This formula uses 1 Constants, 2 Functions, 2 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sin - Trigonometric sine function, sin(Angle)
asin - Inverse trigonometric sine function, asin(Number)
Variables Used
Pitch Circle Diameter - Pitch Circle Diameter is the diameter of the pitch circle. (Measured in Millimeter)
Pitch - Pitch is the distance between screw threads and is commonly used with inch sized products and specified as threads per inch. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Pitch Circle Diameter: 0.001 Millimeter --> 1E-06 Meter (Check conversion here)
Pitch: 0.01 Meter --> 0.01 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
z = 180*(pi/180)*asin(D/P) --> 180*(pi/180)*asin(1E-06/0.01)
Evaluating ... ...
z = 0.000314159265882578
STEP 3: Convert Result to Output's Unit
0.000314159265882578 --> No Conversion Required
FINAL ANSWER
0.000314159265882578 <-- Number of teeth
(Calculation completed in 00.018 seconds)

## < 10+ Design of Chain Drives Calculators

Number of Teeth on the Sprocket When Pitch Circle Diameter is Given
number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch) Go
Velocity Ratio of the Chain Drives
velocity_ratio = Angular speed of the driving member in rpm/Angular speed of the driven member in rpm Go
Number of Teeth on the Driven Sprocket When Velocity of the Chain Drives is Given
number_of_teeth_on_driven_sprocket = Number of Teeth on Driving Sprocket*Velocity ratio Go
Number of Teeth on Driving Sprocket When Velocity of the Chain Drives is Given
number_of_teeth_on_driving_sprocket = Number of Teeth on Driven Sprocket/Velocity ratio Go
Speed of Rotation of the Driving Shaft When Velocity Ratio of the Chain Drives is Given
angular_speed_driving_rpm = Velocity ratio*Angular speed of the driven member in rpm Go
Speed of Rotation of the Driven Shaft When Velocity Ratio of the Chain Drives is Given
angular_speed_driven_rpm = Angular speed of the driving member in rpm/Velocity ratio Go
Length of the Pitch When Pitch Circle Diameter is Given
pitch = Pitch Circle Diameter*sin(180/Number of teeth) Go
Pitch Circle Diameter in terms of Pitch
pitch_circle_diameter = Pitch/sin(180/Number of teeth) Go
Pitch Angle of the Sprocket
pitch_angle = 2*3.14/Number of teeth Go
Number of Teeth on the Sprocket When Pitch Angle of the Sprocket is Given
number_of_teeth = 360/Pitch Angle Go

### Number of Teeth on the Sprocket When Pitch Circle Diameter is Given Formula

number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch)
z = 180*(pi/180)*asin(D/P)

## 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 the Sprocket When Pitch Circle Diameter is Given?

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

How to calculate Number of Teeth on the Sprocket When Pitch Circle Diameter is Given using this online calculator? To use this online calculator for Number of Teeth on the Sprocket When Pitch Circle Diameter is Given, enter Pitch Circle Diameter (D) and Pitch (P) and hit the calculate button. Here is how the Number of Teeth on the Sprocket When Pitch Circle Diameter is Given calculation can be explained with given input values -> 0.000314 = 180*(pi/180)*asin(1E-06/0.01).

### FAQ

What is Number of Teeth on the Sprocket When Pitch Circle Diameter is Given?
The Number of Teeth on the Sprocket When Pitch Circle Diameter is Given formula is defined as the number of indentations present on the sprocket wheel and is represented as z = 180*(pi/180)*asin(D/P) or number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch). Pitch Circle Diameter is the diameter of the pitch circle and Pitch is the distance between screw threads and is commonly used with inch sized products and specified as threads per inch.
How to calculate Number of Teeth on the Sprocket When Pitch Circle Diameter is Given?
The Number of Teeth on the Sprocket When Pitch Circle Diameter is Given formula is defined as the number of indentations present on the sprocket wheel is calculated using number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch). To calculate Number of Teeth on the Sprocket When Pitch Circle Diameter is Given, you need Pitch Circle Diameter (D) and Pitch (P). With our tool, you need to enter the respective value for Pitch Circle Diameter and Pitch 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?
In this formula, Number of teeth uses Pitch Circle Diameter and Pitch. We can use 10 other way(s) to calculate the same, which is/are as follows -
• pitch_angle = 2*3.14/Number of teeth
• number_of_teeth = 360/Pitch Angle
• pitch_circle_diameter = Pitch/sin(180/Number of teeth)
• pitch = Pitch Circle Diameter*sin(180/Number of teeth)
• number_of_teeth = 180*(pi/180)*asin(Pitch Circle Diameter/Pitch)
• velocity_ratio = Angular speed of the driving member in rpm/Angular speed of the driven member in rpm
• angular_speed_driving_rpm = Velocity ratio*Angular speed of the driven member in rpm
• angular_speed_driven_rpm = Angular speed of the driving member in rpm/Velocity ratio
• number_of_teeth_on_driving_sprocket = Number of Teeth on Driven Sprocket/Velocity ratio
• number_of_teeth_on_driven_sprocket = Number of Teeth on Driving Sprocket*Velocity ratio
Where is the Number of Teeth on the Sprocket When Pitch Circle Diameter is Given calculator used?
Among many, Number of Teeth on the Sprocket When Pitch Circle Diameter is Given calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
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