The image above represents shaft length.

To compute for shaft length, four essential parameters are needed and these parameters are **Applied Torque (T), Length of Shaft (L), Modulus of Rigidity (G)** and **Diameter of Shaft (D).**

The formula for calculating shaft length:

θ = ^{T x L x 32}/_{G x π x D4}

Where:

θ = Shaft Length

T = Applied Torque

L = Length of Shaft

G = Modulus of Rigidity

D = Diameter of Shaft

Let’s solve an example;

Find the shaft length when the applied torque is 8, the length of shaft is 12, the modulus of rigidity is 4 and the diameter of shaft is 10.

This implies that;

T = Applied Torque = 8

L = Length of Shaft = 12

G = Modulus of Rigidity = 4

D = Diameter of Shaft = 10

θ = ^{T x L x 32}/_{G x π x D4}

θ = ^{(8) x (12) x 32}/_{(4) x π x (10)4}

θ = ^{3072}/_{(4) x π x (10000)}

θ = ^{3072}/_{125663.7}

θ = 0.024

Therefore, the **shaft length **is **0.024 m.**

**Calculating the Applied Torque when the Shaft Length, the Length of Shaft, the Modulus of Rigidity and the Diameter of Shaft is Given.**

T = ^{θ x G x π x D4} / _{L x 32}

Where;

T = Applied Torque

θ = Shaft Length

L = Length of Shaft

G = Modulus of Rigidity

D = Diameter of Shaft

Let’s solve an example;

Find the applied torque when the shaft length is 10, the length of shaft is 5, the modulus of rigidity is 4 and the diameter of shaft is 2.

This implies that;

θ = Shaft Length = 10

L = Length of Shaft = 5

G = Modulus of Rigidity = 4

D = Diameter of Shaft = 2

T = ^{θ x G x π x D4} / _{L x 32}

T = ^{10 x 4 x π x 24} / _{5 x 32}

T = ^{40 x π x 16} / _{160}

T = ^{2010.6} / _{160}

T = 12.56

Therefore, the **applied torque **is **12.56 m.**

**Calculating the Length of Shaft when the Shaft Length, the Applied Torque, the Modulus of Rigidity and the Diameter of Shaft is Given.**

L = ^{θ x G x π x D4} / _{T x 32}

Where;

L = Length of Shaft

θ = Shaft Length

T = Applied Torque

G = Modulus of Rigidity

D = Diameter of Shaft

Let’s solve an example;

Find the length of shaft when the shaft length is 10, the applied torque is 4, the modulus of rigidity is 6 and the diameter of shaft is 2.

This implies that;

θ = Shaft Length = 10

T = Applied Torque = 4

G = Modulus of Rigidity = 6

D = Diameter of Shaft = 2

L = ^{θ x G x π x D4} / _{T x 32}

L = ^{10 x 6 x π x 24} / _{4 x 32}

L = ^{10 x 6 x π x 16} / _{4 x 32}

L = ^{3015.9} / _{128}

L = 23.56

Therefore, the **length of shaft **is **23.56 m.**

**Calculating the Modulus of Rigidity when the Shaft Length, the Applied Torque, the Length of Shaft and the Diameter of Shaft is Given.**

G = ^{T x L x 32} / _{θ x π x D4}

Where;

G = Modulus of Rigidity

θ = Shaft Length

T = Applied Torque

L = Length of Shaft

D = Diameter of Shaft

Let’s solve an example;

Find the modulus of rigidity when the shaft length is 2, the applied torque is 10, the length of shaft is 6 and the diameter of shaft is 3.

This implies that;

θ = Shaft Length = 2

T = Applied Torque = 10

L = Length of Shaft = 6

D = Diameter of Shaft = 3

G = ^{T x L x 32} / _{θ x π x D4}

G = ^{10 x 6 x 32} / _{2 x π x 34}

G = ^{1920} / _{2 x π x 81}

G = ^{1920} / _{508.9}

G = 3.77

Therefore, the **modulus of rigidity **is **3.77 m.**

**Calculating the Diameter of Shaft when the Shaft Length, the Applied Torque, the Length of Shaft and the Modulus of Rigidity is Given.**

D = ^{4}√(^{T x L x 32} / _{θ x π x G})

Where;

D = Diameter of Shaft

θ = Shaft Length

T = Applied Torque

L = Length of Shaft

G = Modulus of Rigidity

Let’s solve an example;

Find the diameter of shaft when the shaft length is 14, the applied torque is 8, the length of shaft is 4 and the modulus of rigidity is 6.

This implies that;

θ = Shaft Length = 14

T = Applied Torque = 8

L = Length of Shaft = 4

G = Modulus of Rigidity = 6

D = ^{4}√(^{T x L x 32} / _{θ x π x G})

D = ^{4}√(^{8 x 4 x 32} / _{14 x π x 6})

D = ^{4}√(^{1024} / _{263.8})

D = ^{4}√(3.88)

D = 7.88

Therefore, the **diameter of shaft **is **7.88 m.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the shaft length.

To get the answer and workings of the shaft length using the **Nickzom Calculator – The Calculator Encyclopedia. **First, you need to obtain the app.

You can get this app via any of these means:

**Web** – https://www.nickzom.org/calculator-plus

To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 2,000 **per** annum** to have utter access to all functionalities.

You can also try the **demo **version via https://www.nickzom.org/calculator

**Android (Paid)** – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator

**Android (Free)** – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator

**Apple (Paid)** – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8

Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Materials and Metallurgical **under **Engineering****.**

Now, Click on **Ball Mill Sizing**** **under **Materials and Metallurgical**

Now, Click on **Shaft Length**** **under **Ball Mill Sizing**

The screenshot below displays the page or activity to enter your values, to get the answer for the shaft length according to the respective parameters which is the **Applied Torque (T), Length of Shaft (L), Modulus of Rigidity (G)** and **Diameter of S****haft (D).**

Now, enter the value appropriately and accordingly for the parameter as required by the **Applied Torque (T)** is **8**,** Length of Shaft (L)** is **12**,** Modulus of Rigidity (G)** is **4 **and **Diam****eter of Shaft (D)** is **14**.

Finally, Click on Calculate

As you can see from the screenshot above, **Nickzom Calculator**– The Calculator Encyclopedia solves for the shaft length and presents the formula, workings and steps too.