# How to back out tax formula

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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.

Step-by-Step Instructions:

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

OTHER INFORMATION:

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.

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