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Pitch Circle Diameter of Helical Gear Formula

GoPitch Circle Diameter of Gear given Radius of Curvature at Point Formula

GoPitch Circle Diameter of Gear given Addendum Circle Diameter Formula

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Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle. Check FAQs

d = z \cdot \frac{m n}{\cos (ψ)}

d - Diameter of Pitch Circle of Helical Gear?z - Number of Teeth on Helical Gear?m_n - Normal Module of Helical Gear?ψ - Helix Angle of Helical Gear?

Pitch Circle Diameter of Helical Gear Example

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Here is how the Pitch Circle Diameter of Helical Gear equation looks like with Values.

Here is how the Pitch Circle Diameter of Helical Gear equation looks like with Units.

Here is how the Pitch Circle Diameter of Helical Gear equation looks like.

122.4749 = 37 \cdot \frac{3}{\cos (25)}

122.4749mm = 37 \cdot \frac{3mm}{\cos (25°)}

122.4749 = 37 \cdot \frac{3}{\cos (25)}

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Pitch Circle Diameter of Helical Gear Solution

Follow our step by step solution on how to calculate Pitch Circle Diameter of Helical Gear?

FIRST Step Consider the formula

d = z \cdot \frac{m n}{\cos (ψ)}

Next Step Substitute values of Variables

∴

d = 37 \cdot \frac{3mm}{\cos (25°)}

Next Step Convert Units

∴

d = 37 \cdot \frac{0.003m}{\cos (0.4363rad)}

Next Step Prepare to Evaluate

∴

d = 37 \cdot \frac{0.003}{\cos (0.4363)}

Next Step Evaluate

∴

d = 0.122474949004832m

Next Step Convert to Output's Unit

∴

d = 122.474949004832mm

LAST Step Rounding Answer

∴

d = 122.4749mm

Pitch Circle Diameter of Helical Gear Formula Elements

Variables

Functions

Diameter of Pitch Circle of Helical Gear

Diameter of Pitch Circle of Helical Gear is the diameter of the pitch circle of a gear that touches the meshing gear's pitch circle.

Symbol: d

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Pitch Circle of Helical Gear

Number of Teeth on Helical Gear

Number of Teeth on Helical Gear is defined as the number of teeth (which mesh with another compatible toothed part to transmit or convert torque and speed) on a specimen or part under consideration.

Symbol: z

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Number of Teeth on Helical Gear

Normal Module of Helical Gear

The Normal Module of Helical Gear is defined as the unit of size that indicates how big or small is the helical gear.

Symbol: m_n

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Normal Module of Helical Gear

Helix Angle of Helical Gear

Helix Angle of Helical Gear is the angle between any helical gear and an axial line on its right, circular cylinder, or cone.

Symbol: ψ

Measurement: AngleUnit: °

Note: Value should be greater than 0.

Formulas to find Helix Angle of Helical Gear

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other Formulas to find Diameter of Pitch Circle of Helical Gear

Go Pitch Circle Diameter of Gear given Radius of Curvature at Point

d = 2 \cdot r' \cdot {(\cos (ψ))}^{2}

Go Pitch Circle Diameter of Gear given Addendum Circle Diameter

d = d a - 2 \cdot h a

Go Pitch Circle Diameter of Gear given Dedendum Circle Diameter

d = d f + 2 \cdot d h

Other formulas in Core Design Parameters category

Go Transverse Module of Helical Gear given Transverse Diametrical Pitch

m = \frac{1}{P}

Go Normal Module of Helical Gear

m n = m \cdot \cos (ψ)

Go Transverse Module of Helical Gear given Normal Module

m = \frac{m n}{\cos (ψ)}

Go Number of Teeth on Gear given Pitch Circle Diameter

z = d \cdot \frac{\cos (ψ)}{m n}

How to Evaluate Pitch Circle Diameter of Helical Gear?

Pitch Circle Diameter of Helical Gear evaluator uses Diameter of Pitch Circle of Helical Gear = Number of Teeth on Helical Gear*Normal Module of Helical Gear/cos(Helix Angle of Helical Gear) to evaluate the Diameter of Pitch Circle of Helical Gear, The Pitch Circle Diameter of Helical Gear formula is the diameter of the imaginary circle on the gear about which it may be supposed to roll without slipping with the pitch circle of another gear. The point of contact of the two pitch circles becomes the pitch point. Diameter of Pitch Circle of Helical Gear is denoted by d symbol.

How to evaluate Pitch Circle Diameter of Helical Gear using this online evaluator? To use this online evaluator for Pitch Circle Diameter of Helical Gear, enter Number of Teeth on Helical Gear (z), Normal Module of Helical Gear (m_n) & Helix Angle of Helical Gear (ψ) and hit the calculate button.

FAQs on Pitch Circle Diameter of Helical Gear

What is the formula to find Pitch Circle Diameter of Helical Gear?

The formula of Pitch Circle Diameter of Helical Gear is expressed as Diameter of Pitch Circle of Helical Gear = Number of Teeth on Helical Gear*Normal Module of Helical Gear/cos(Helix Angle of Helical Gear). Here is an example- 122474.9 = 37*0.003/cos(0.4363323129985).

How to calculate Pitch Circle Diameter of Helical Gear?

With Number of Teeth on Helical Gear (z), Normal Module of Helical Gear (m_n) & Helix Angle of Helical Gear (ψ) we can find Pitch Circle Diameter of Helical Gear using the formula - Diameter of Pitch Circle of Helical Gear = Number of Teeth on Helical Gear*Normal Module of Helical Gear/cos(Helix Angle of Helical Gear). This formula also uses Cosine (cos) function(s).

What are the other ways to Calculate Diameter of Pitch Circle of Helical Gear?

Here are the different ways to Calculate Diameter of Pitch Circle of Helical Gear-

Diameter of Pitch Circle of Helical Gear=2*Radius of Curvature of Helical Gear*(cos(Helix Angle of Helical Gear))^2
Diameter of Pitch Circle of Helical Gear=Addendum Circle Diameter of Helical Gear-2*Addendum of Helical Gear
Diameter of Pitch Circle of Helical Gear=Dedendum Circle Diameter of Helical Gear+2*Dedendum of Helical Gear

Can the Pitch Circle Diameter of Helical Gear be negative?

No, the Pitch Circle Diameter of Helical Gear, measured in Length cannot be negative.

Which unit is used to measure Pitch Circle Diameter of Helical Gear?

Pitch Circle Diameter of Helical Gear is usually measured using the Millimeter[mm] for Length. Meter[mm], Kilometer[mm], Decimeter[mm] are the few other units in which Pitch Circle Diameter of Helical Gear can be measured.

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Pitch Circle Diameter of Helical Gear Formula

​GoPitch Circle Diameter of Gear given Radius of Curvature at Point Formula

​GoPitch Circle Diameter of Gear given Addendum Circle Diameter Formula

Pitch Circle Diameter of Helical Gear Example

Pitch Circle Diameter of Helical Gear Solution

Pitch Circle Diameter of Helical Gear Formula Elements

Other Formulas to find Diameter of Pitch Circle of Helical Gear

Other formulas in Core Design Parameters category

How to Evaluate Pitch Circle Diameter of Helical Gear?

FAQs on Pitch Circle Diameter of Helical Gear

Variable Name

GoPitch Circle Diameter of Gear given Radius of Curvature at Point Formula

GoPitch Circle Diameter of Gear given Addendum Circle Diameter Formula