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Polar Modulus Formula

GoPolar Modulus of Hollow Shaft Formula

GoPolar Modulus of Solid Shaft Formula

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The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp. Check FAQs

Z p = \frac{J}{R}

Z_p - Polar Modulus?J - Polar Moment of Inertia?R - Radius of Shaft?

Polar Modulus Example

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Here is how the Polar Modulus equation looks like with Values.

Here is how the Polar Modulus equation looks like with Units.

Here is how the Polar Modulus equation looks like.

0.0373 = \frac{0.0041}{110}

0.0373m³ = \frac{0.0041m⁴}{110mm}

0.0373 = \frac{0.0041}{110}

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Polar Modulus Solution

Follow our step by step solution on how to calculate Polar Modulus?

FIRST Step Consider the formula

Z p = \frac{J}{R}

Next Step Substitute values of Variables

∴

Z p = \frac{0.0041m⁴}{110mm}

Next Step Convert Units

∴

Z p = \frac{0.0041m⁴}{0.11m}

Next Step Prepare to Evaluate

∴

Z p = \frac{0.0041}{0.11}

Next Step Evaluate

∴

Z p = 0.0372727272727273m³

LAST Step Rounding Answer

∴

Z p = 0.0373m³

Polar Modulus Formula Elements

Variables

Polar Modulus

The Polar Modulus of the shaft section is equal to the ratio of the polar moment of inertia to the radius of the shaft. It is denoted by Zp.

Symbol: Z_p

Measurement: VolumeUnit: m³

Note: Value should be greater than 0.

Formulas to find Polar Modulus

Polar Moment of Inertia

Polar Moment of Inertia is the moment of inertia of a cross-section with respect to its polar axis, which is an axis at right angles to the plane of the cross-section.

Symbol: J

Measurement: Second Moment of AreaUnit: m⁴

Note: Value should be greater than 0.

Formulas to find Polar Moment of Inertia

Radius of Shaft

The Radius of Shaft is the line segment extending from the center of a circle or sphere to the circumference or bounding surface.

Symbol: R

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Radius of Shaft

Other Formulas to find Polar Modulus

Go Polar Modulus of Hollow Shaft

Z p = \frac{π \cdot (({d o}^{4}) - ({d i}^{4}))}{16 \cdot d o}

Go Polar Modulus of Solid Shaft

Z p = \frac{π \cdot d^{3}}{16}

Go Polar Modulus using Maximum Twisting Moment

Z p = (\frac{T}{τ max})

Other formulas in Polar Modulus category

Go Diameter of Solid Shaft with known Polar Modulus

d = {(\frac{16 \cdot Z p}{π})}^{\frac{1}{3}}

Go Inner diameter of Hollow Shaft using Polar Modulus

d i = {(({d o}^{4}) - (\frac{Z p \cdot 16 \cdot d o}{π}))}^{\frac{1}{4}}

Go Polar Moment of Inertia using Polar Modulus

J = R \cdot Z p

Go Polar Moment of Inertia of Solid Shaft

J = \frac{π \cdot d^{4}}{32}

How to Evaluate Polar Modulus?

Polar Modulus evaluator uses Polar Modulus = Polar Moment of Inertia/Radius of Shaft to evaluate the Polar Modulus, The Polar Modulus formula is defined as the ratio of the polar moment of inertia to the radius of the shaft. It is also called a torsional section modulus. It is denoted by Z p. Polar Modulus is denoted by Z_p symbol.

How to evaluate Polar Modulus using this online evaluator? To use this online evaluator for Polar Modulus, enter Polar Moment of Inertia (J) & Radius of Shaft (R) and hit the calculate button.

FAQs on Polar Modulus

What is the formula to find Polar Modulus?

The formula of Polar Modulus is expressed as Polar Modulus = Polar Moment of Inertia/Radius of Shaft. Here is an example- 0.037273 = 0.0041/0.11.

How to calculate Polar Modulus?

With Polar Moment of Inertia (J) & Radius of Shaft (R) we can find Polar Modulus using the formula - Polar Modulus = Polar Moment of Inertia/Radius of Shaft.

What are the other ways to Calculate Polar Modulus?

Here are the different ways to Calculate Polar Modulus-

Polar Modulus=(pi*((Outer Diameter of Shaft^4)-(Inner Dia of Shaft^4)))/(16*Outer Diameter of Shaft)
Polar Modulus=(pi*Dia of Shaft^3)/16
Polar Modulus=(Torque/Maximum Shear Stress)

Can the Polar Modulus be negative?

No, the Polar Modulus, measured in Volume cannot be negative.

Which unit is used to measure Polar Modulus?

Polar Modulus is usually measured using the Cubic Meter[m³] for Volume. Cubic Centimeter[m³], Cubic Millimeter[m³], Liter[m³] are the few other units in which Polar Modulus can be measured.

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Polar Modulus Formula

​GoPolar Modulus of Hollow Shaft Formula

​GoPolar Modulus of Solid Shaft Formula

Polar Modulus Example

Polar Modulus Solution

Polar Modulus Formula Elements

Other Formulas to find Polar Modulus

Other formulas in Polar Modulus category

How to Evaluate Polar Modulus?

FAQs on Polar Modulus

Variable Name

GoPolar Modulus of Hollow Shaft Formula

GoPolar Modulus of Solid Shaft Formula