The image above represents horizontal strain.

To compute for horizontal strain, five essential parameters are needed and these parameters are **Principal Horizontal Stress Component 1 (σ _{H1}), Principal Horizontal Stress Component 2 (σ_{H2}), Poisson’s Ratio (v), **

**Vertical Stress (σ**and

_{v})**Young’s Modulus (E).**

The formula for calculating the horizontal strain:

ε_{H} = ^{(σH1 – vσH2 – vσv)} / _{E}

Where:

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the horizontal strain when the principal horizontal stress component 1 is 7, the principal horizontal component 2 is 9, the Poisson’s ratio is 11, the vertical stress is 21 and young’s modulus is 27.

This implies that;

σ_{H1} = Principal Horizontal Stress Component 1 = 7

σ_{H2} = Principal Horizontal Stress Component 2 = 9

v = Poisson’s Ratio = 11

σ_{v} = Vertical Stress = 21

E = Young’s Modulus = 27

ε_{H} = ^{(σH1 – vσH2 – vσv)} / _{E}

ε_{H} = ^{(7 – 11(9) – 11(21))} / _{27}

ε_{H} = ^{(7 – 99 – 231)} / _{27}

ε_{H} = ^{-323} / _{27}

ε_{H} = -11.96

Therefore, the **horizontal strain **is **-11.96.**

**Calculating the Principal Horizontal Stress Component 1 when the Horizontal Stress, Principal Horizontal Stress Component 2, Poisson’s Ratio, Vertical Stress and Young’s Modulus is Given.**

σ_{H1} = (ε_{H} x E) + vσ_{H2} + vσ_{v}

Where;

σ_{H1} = Principal Horizontal Stress Component 1

ε_{H} = Horizontal Strain

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 1 when the horizontal strain is 22, the principal horizontal component 2 is 10, the Poisson’s ratio is 7, the vertical stress is 12 and young’s modulus is 3.

This implies that;

ε_{H} = Horizontal Strain = 22

σ_{H2} = Principal Horizontal Stress Component 2 = 10

v = Poisson’s Ratio = 7

σ_{v} = Vertical Stress = 12

E = Young’s Modulus = 3

σ_{H1} = (ε_{H} x E) + vσ_{H2} + vσ_{v}

σ_{H1} = (22 x 3) + 7(10) + 7(12)

σ_{H1} = 66 + 70 + 84

σ_{H1} = 220

Therefore, the **principal horizontal stress component 1 **is **220.**

**Calculating the Principal Horizontal Stress Component 2 when the Horizontal Stress, Principal Horizontal Stress Component 1, Poisson’s Ratio, Vertical Stress and Young’s Modulus is Given.**

σ_{H2} = -(^{(εH x E) – σH1 + vσv} / _{v})

Where;

σ_{H2} = Principal Horizontal Stress Component 2

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

v = Poisson’s Ratio

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the principal horizontal stress component 2 when the horizontal strain is 28, the principal horizontal component 1 is 14, the Poisson’s ratio is 5, the vertical stress is 17 and young’s modulus is 7.

This implies that;

ε_{H} = Horizontal Strain =28

σ_{H1} = Principal Horizontal Stress Component 1 = 14

v = Poisson’s Ratio = 5

σ_{v} = Vertical Stress = 17

E = Young’s Modulus = 7

σ_{H2} = -(^{(εH x E) – σH1 + vσv} / _{v})

σ_{H2} = -(^{(28 x 7) – 14 + 5(17)} / _{5})

σ_{H2} = -(^{196 – 14 + 85} / _{5})

σ_{H2} = -(^{182 + 85} / _{5})

σ_{H2} = -(^{267} / _{5})

σ_{H2} = -(53.4)

σ_{H2} = -53.4

Therefore, the** principal horizontal stress component 2 **is **-53.4.**

**Calculating the Poisson’s Ratio when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Vertical Stress and Young’s Modulus is Given.**

v = ^{σH1 – (εH x E)} / _{σH1 + σH2}

Where:

v = Poisson’s Ratio

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

σ_{v} = Vertical Stress

E = Young’s Modulus

Let’s solve an example;

Find the Poisson’s ratio when the principal horizontal stress component 1 is 2, the principal horizontal component 2 is 4, the horizontal strain is 19, the vertical stress is 26 and young’s modulus is 12.

This implies that;

ε_{H} = Horizontal Strain = 19

σ_{H1} = Principal Horizontal Stress Component 1 = 2

σ_{H2} = Principal Horizontal Stress Component 2 = 4

σ_{v} = Vertical Stress = 26

E = Young’s Modulus = 12

v = ^{σH1 – (εH x E)} / _{σH1 + σH2}

v = ^{2 – (19 x 12)} / _{2 + 4}

v = ^{2 – 228} / _{6}

v = ^{-226} / _{6}

v = -37.6

Therefore, the **Poisson’s ratio **is **-37.6.**

**Calculating the Vertical Stress when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Poisson’s Ratio and Young’s Modulus is Given.**

σ_{v} = -(^{(εH x E) – σH1 + vσH2} / _{v})

Where:

σ_{v} = Vertical Stress

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

E = Young’s Modulus

Let’s solve an example;

Find the vertical stress when the horizontal strain is 27, the principal horizontal stress component 1 is 12, the principal horizontal component 2 is 9, the Poisson’s ratio is 24 and young’s modulus is 8.

This implies that;

ε_{H} = Horizontal Strain = 27

σ_{H1} = Principal Horizontal Stress Component 1 = 12

σ_{H2} = Principal Horizontal Stress Component 2 = 9

v = Poisson’s Ratio = 24

E = Young’s Modulus = 8

σ_{v} = -(^{(εH x E) – σH1 + vσH2} / _{v})

σ_{v} = -(^{(27 x 8) – 12 + 8(9)} / _{24})

σ_{v} = -(^{216 – 12 + 72} / _{24})

σ_{v} = -(^{204 + 72} / _{24})

σ_{v} = -(^{276} / _{24})

σ_{v} = -(11.5)

σ_{v} = -11.5

Therefore, the **vertical stress **is **-11.5.**

**Calculating the Young’s Modulus when the Horizontal Stress, Principal Horizontal Stress Component 1, Principal Horizontal Stress Component 2, Poisson’s Ratio and Vertical Stress is Given.**

E = ^{(σH1 – vσH2 – vσv)} / _{εH}

Where:

E = Young’s Modulus

ε_{H} = Horizontal Strain

σ_{H1} = Principal Horizontal Stress Component 1

σ_{H2} = Principal Horizontal Stress Component 2

v = Poisson’s Ratio

σ_{v} = Vertical Stress

Let’s solve an example;

Find the young’s modulus when the horizontal strain is 44, principal horizontal stress component 1 is 28, the principal horizontal component 2 is 5, the Poisson’s ratio is 4 and the vertical stress is 3.

This implies that;

ε_{H} = Horizontal Strain = 44

σ_{H1} = Principal Horizontal Stress Component 1 = 28

σ_{H2} = Principal Horizontal Stress Component 2 = 5

v = Poisson’s Ratio = 4

σ_{v} = Vertical Stress = 3

E = ^{(σH1 – vσH2 – vσv)} / _{εH}

E = ^{(28 – 4(5) – 4(3))} / _{44}

E = ^{(28 – 20 – 12)} / _{44}

E = ^{(8 – 12)} / _{44}

E = ^{(-4)} / _{44}

E = -0.09

Therefore, the **young’s modulus **is **-0.09.**

Nickzom Calculator – **The Calculator Encyclopedia** is capable of calculating the horizontal strain.

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

You can get this app via any of these means:

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To get access to the **professional **version via web, you need to **register** and **subscribe **for** NGN 1,500 **per** annum** to have utter access to all functionalities.

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

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Once, you have obtained the calculator encyclopedia app, proceed to the **Calculator Map, **then click on **Geology**** **under **Add-on.**

Now, Click on **Rock Mechanics**** **under **Geology**

Now, Click on **Horizontal**** ****Strain **under **Rock Mechanics**

The screenshot below displays the page or activity to enter your values, to get the answer for the horizontal strain according to the respective parameters which are the **Principal Horizontal Stress Component 1 (σ _{H1}), Principal Horizontal Stress Component 2 (σ_{H2}), Poisson’s Ratio (v), **

**Vertical Stress (σ**and

_{v})**Young’s Modulus (E).**

Now, enter the values appropriately and accordingly for the parameters as required by the **Principal Horizontal Stress Component 1 (σ _{H1})** is

**7**,

**Principal Horizontal Stress Component 2 (σ**is

_{H2})**9**,

**Poisson’s Ratio (v)**is

**11**,

**Vertical Stress (σ**is

_{v})**21**and

**Young’s Modulus (E)**is

**27**.

Finally, Click on Calculate

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