How to back out tax formula
How To: Back out Sales Tax from a Cash Sale.
The familiar scenario: You have sold something for a cash amount, but need to report the correct sales tax. You want to use an ordinary calculator, but you also want to understand the process.
1. Express the sales tax as a decimal. Thus, if your sales tax is 6%, the decimal equivalent is .06 and if your sales tax is 6.5%, the decimal equivalent is .065. It is important that you get this conversion correctly.
2. The formula is:
Tax Amount = [Sale Price * Tax Rate] / (1+Tax Rate)
Here is an example of something that sold for $100.00 and the sales tax was 6%:
Tax Amount = [$100.00 * .06] / (1.06)
Tax Amount = $5.66
3. Confirm the value of the sale to record in your accounts.
Value of the Sale = Sale Price - Tax Amount
Value of the Sale = $94.34
In the above example, it would be wrong to simply back $6 out of the sale. You'd think the tax collector would not mind getting $6.00 instead of $5.66, but that is not how the system works. Backing out the $6 would mean the Value of the Sale was only $94.00, meaning the sales tax should be $5.64 instead of $5.66, and yes, the state does take a dim view of those missing few pennies.
Here is another $100.00 example using a 6.5% tax rate:
Tax Amount = [$100.00 * .065] / (1.065)
Tax Amount = $6.10
Value of Sale = $100.00 - $6.10 = $93.90
Confirmation: $93.90 x .065 = $6.10
For the more mathematically inclined, you are calculating a simple ratio. Thus, you can probably see that all the decimal points aren't needed. For clarity. 06 / 1.06 is the same number as 6/106. Try it. You can use this type of mental shorthand for states that have integer sales tax. For states with 5% use 5/105, and for states with 12% use 12/112. However, make sure you have this right in your head before proceeding.
Thus, the above 6% example is reduced to $100.00 x 6/106 = Sales Tax.
The cerebral acrobats get a little tougher with fractional sales taxes, for example, 7.5% means 7.5/107.5, but it still can be done. However, double-check everything.
All above calculations done on a simple dollar-store calculator without any special tax keys:
Hint, if you are using a spreadsheet, use a special cell to calculate the ratio just once or each time the sales tax rate changes, and use that cell as a fixed reference in all your sales tax calculations. I won't give the spreadsheet formula as there are many ways to accomplish the same thing. For example, I use a formula that recalculates the ratio every time, just to be on the safe side.
Many states that publish tax tables often make it a rule that you MUST use said tables by default, so if you are in such a jurisdiction, the above formula is only a guideline.
Disclaimer: veryatlantic™ is a non-technical source for advice and entertainment and is not responsible for any damages under any theory. All posts sacrifice technical accuracy for user-friendliness. If unsure, get help. Please feedback errors for correction.
This article written May 14, 2010.Source: firehow.com