# VAT: Recalculate Gross Amount (With Tax Included), 19.12, From 19% Original VAT Rate to the New Rate of 14%. Calculate the Net Amount (Without Tax), the New Price (Gross Amount) and the Value of the VAT Tax

## Calculate the Gross Amount 19.12 with a different VAT Rate

### Gross Amount = The amount with VAT included (including VAT)

### Net Amount = The amount without VAT (excluding VAT)

### 1. Rewrite the Gross Amount.

#### Formula:

#### Original VAT Amount = Original VAT Rate × Net Amount

#### Gross Amount = Net Amount + Original VAT Amount

#### ⇒ Substitute for the Original VAT Amount in the Gross Amount formula

#### Gross Amount =

#### Net Amount + Original VAT Amount =

#### Net Amount + (Original VAT Rate × Net Amount) =

#### Net Amount × (1 + Original VAT Rate)

### 2. Calculate the Net Amount:

#### Formula:

#### Gross Amount = Net Amount × (1 + Original VAT Rate)

#### ⇒ Net Amount = Gross Amount ÷ (1 + Original VAT Rate)

#### Calculation:

#### Net Amount =

#### 19.12 ÷ (1 + 19%) =

#### 19.12 ÷ (1 + ^{19}/_{100}) =

#### 19.12 ÷ (1 + 19 ÷ 100) =

#### 19.12 ÷ (1 + 0.19) =

#### 19.12 ÷ 1.19 ≈

#### 16.067226890756 ≈

#### 16.07

(Rounded off to a maximum of 2 decimals)

### 3. Calculate the VAT Amount due to the Original VAT Rate:

#### Formula:

#### Original VAT Amount =

#### Gross Amount - Net Amount

#### Calculation:

#### Original VAT Amount =

#### 19.12 - 16.067226890756 =

#### 3.052773109244 ≈

#### 3.05

(Rounded off to a maximum of 2 decimals)

### 4. Calculate the VAT Amount due to the New VAT Rate:

#### Formula:

#### New VAT Amount =

#### New VAT Rate × Net Amount

#### Calculation:

#### New VAT Amount =

#### 14% × 16.067226890756 =

^{14}/_{100} × 16.067226890756 =

#### 14 ÷ 100 × 16.067226890756 =

#### 14 × 16.067226890756 ÷ 100 =

#### 224.941176470584 ÷ 100 ≈

#### 2.249411764706 ≈

#### 2.25

(Rounded off to a maximum of 2 decimals)

### 5. Calculate the New Gross Amount.

#### Formula:

#### New Gross Amount =

#### Net Amount + New VAT Amount

#### Calculation:

#### New Gross Amount =

#### 16.067226890756 + 2.249411764706 =

#### 18.316638655462 ≈

#### 18.32

(Rounded off to a maximum of 2 decimals)

## Net Amount = 16.07

Original VAT Amount (19%) = 3.05

New VAT Amount (14%) = 2.25

New Gross Amount = 18.32 (- 0.8 vs. initial)

#### Used symbols: % percent, ÷ divide, × multiply, = equal, / fraction bar, ≈ approximately equal;

#### Writing numbers: comma ',' as thousands separator; point '.' as a decimal mark.

### More operations, calculate prices with new VAT Rates:

## Recalculate Gross Amount (Tax Included) with a New VAT Rate

#### Gross Amount = Net Value × (1 + Tax%)

#### Net Amount = Gross Amount ÷ (1 + Tax%)

## The Latest Gross Amounts Recalculated With New VAT Rates

## Calculate the Gross Amount (With Tax Included) With Different, New, VAT Rates

### Step 1: Calculate the Net Amount (Without Tax)

- Initial Gross Amount = Net Amount + Initial Tax Amount
- Initial Tax Amount = Initial Tax% × Net Amount
- Initial Gross Amount = Net Amount + Initial Tax% × Net Amount = (1 + Initial Tax%) × Net Amount
#### Initial Gross Amount = (1 + Initial Tax%) × Net Amount

In conclusion: #### Net Amount = Initial Gross Amount ÷ (1 + Initial Tax%) =

### Step 2: Add the New Tax Amount to the Net Amount

- New Gross Amount = Net Amount + New Tax Amount
- New Tax Amount = New Tax% × Net Amount
- New Gross Amount = Net Amount + New Tax% × Net Amount = (1 + New Tax%) × Net Amount
- In conclusion, New Gross Amount = (1 + New Tax%) × Net Amount = (1 + New Tax%) × Initial Gross Amount ÷ (1 + Initial Tax%) =
^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount #### New Gross Amount = ^{(1 + New Tax%)}/_{(1 + Initial Tax%)} × Initial Gross Amount

### Examples of calculations:

**Case 1: Initial Tax Rate = 20%, New Tax Rate = 19% **

Step 1, Calculate Net Amount:

(1 + Initial Tax%) = 1 + 20% = ^{100}/_{100 + 20/100 = 120/100 = 1.2 => Initial Gross Amount = 1.2 × Net Amount, and Net Amount = Initial Gross Amount ÷ 1.2 Step 2, Add the New Tax Amount: New Gross Amount = (1 + New Tax%) × Net Amount = (1 + 19%) × Net Amount = (100/100 + 19/100) × Net Amount = 119/100 × Net Amount = 1.19 × Net Amount = 1.19 × Initial Gross Amount ÷ 1.2 = 1.19/1.2 × Initial Gross Amount Answer: New Gross Amount = (1.19 ÷ 1.2) × Initial Gross Amount}**Case 2: Initial Tax Rate = 20%, New Tax Rate = 5% **

Step 1, Calculate Net Amount:

(1 + Initial Tax%) = 1 + 20% = ^{100}/_{100} + ^{20}/_{100} = ^{120}/_{100} = 1.2 => **Initial Gross Amount** = 1.2 × Net Amount, and **Net Amount** = Initial Gross Amount ÷ 1.2

Step 2, Add the New Tax Amount:

**New Gross Amount** = (1 + New Tax%) × Net Amount = (1 + 5%) × Net Amount = (^{100}/_{100} + ^{5}/_{100}) × Net Amount = ^{105}/_{100} × Net Amount = 1.05 × Net Amount = 1.05 × Initial Gross Amount ÷ 1.2 = ^{1.05}/_{1.2} × Initial Gross Amount

Answer: **New Gross Amount** = (1.05 ÷ 1.2) × Initial Gross Amount.