How to Reverse Calculate the Sales Tax Amount and the Selling Price out of the Final Price With Tax (After Tax)

The Sales Tax is a consumption tax imposed by states, counties or/and cities and municipalities in the United States on the sale of goods and services.
The sales tax is paid by the final consumer to the retailer at the point of sale as a percentage of the selling price of the sold good or service.
This percentage, called the Sales Tax Rate, varies from state to state, in Texas for example there is a general sales tax rate of around 6.25%.
To continue our example above, cities and/or municipalities of Texas are also allowed to collect their own sales tax with rates ranging up to 2%. So a combined sales tax rate could build up to 8.25% or even more if we also add the county sales tax rate...
6.25% is the lowest possible sales tax rate in Texas, 6.3%, 6.5%, 6.75%, 7%, 7.25%, 7.5%, 7.75%, 8%, 8.125% or 8.25% are other possible sales tax rates.

Let's say that a farmer sells apples to a company that produces cider.
To avoid paying the sales tax, the cider maker must obtain a resale certificate from the government saying that it is not the end user.
The cider maker then sells its product on to a retail store, which will charge the final customer the sales tax along with the price of cider.

Let's say that a person who lives in an area where the sales tax rate is 5% bought some cider and had to pay a total of a $525 dollar bill that already had the sales tax included.
"Sales tax amount" = "Sales tax rate%" × "Price without sales tax".
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = "Price without sales tax" + "Sales tax rate%" × "Price without sales tax"
- = "Price without sales tax" × (1 + "Sales tax rate%").
"Price without sales tax"
- = "Sales tax charged price" ÷ (1 + "Sales tax rate%")
- = $525 ÷ (1 + 5%)
- = $525 ÷ (1 + _5/₁₀₀)
- = $525 ÷ (1 + 0.05)
- = $525 ÷ 1.05
- = $500 dollars.
That person had to pay a "Sales tax amount"
- = "Sales tax charged price" - "Price without sales tax"
- = $525 - $500
- = $25 dollars.

"Sales tax amount" = "Sales tax rate%" × "Price without sales tax"
"Sales tax charged price"
- = "Price without sales tax" + "Sales tax amount"
- = "Price without sales tax" + "Sales tax rate%" × "Price without sales tax"
- = "Price without sales tax" × (1 + "Sales tax rate%")
In conclusion:
"Price without sales tax"
- = "Sales tax charged price" ÷ (1 + "Sales tax rate%")

Example 1. If "Sales tax rate" is 5% and we paid a final total "Sales tax charged price" of $525 dollars:
"Price without sales tax"
- ="Sales tax charged price" ÷ (1 + "Sales tax rate%")
- = $525 ÷ (1 + 5%)
- = $525 ÷ (1 + ⁵/₁₀₀)
- = $525 ÷ (1 + 0.05)
- = $525 ÷ 1.05
- = $500 dollars;
"Sales tax amount"
- = "Sales tax charged price" - "Price without sales tax"
- = $525 - $500
- = $25 dollars;

Example 2. If "Sales tax rate" is 6.5% and we paid a final total "Sales tax charged price" of $745.5 dollars:
"Price without sales tax"
- = "Sales tax charged price" ÷ (1 + "Sales tax rate%")
- = $745.5 ÷ (1 + 6.5%)
- = $745.5 ÷ (1 + ^6.5/₁₀₀)
- = $745.5 ÷ (1 + 0.065)
- = $745.5 ÷ 1.065
- = $700 dollars;
"Sales tax amount"
- = "Sales tax charged price" - "Price without sales tax"
- = $745.5 - $700
- = $45.5 dollars;

Example 3. If "Sales tax rate" is 10.5% and we paid a final total "Sales tax charged price" of $1,878.5 dollars:
"Price without sales tax"
- = "Sales tax charged price" ÷ (1 + "Sales tax rate%")
- = $1,878.5 ÷ (1 + 10.5%)
- = $1,878.5 ÷ (1 + ^10.5/₁₀₀)
- = $1,878.5 ÷ (1 + 0.105)
- = $1,878.5 ÷ 1.105 = $1,700 dollars;
"Sales tax amount"
- = "Sales tax charged price" - "Price without sales tax"
- = $1,878.5 - $1,700
- = $178.5 dollars;