# How To Calculate Sales Tax Backwards From Total?

A lot of the below answers are incorrect! In short, to calculate the sales tax from the total you need to first calculate the price of the item without the sales tax. This is done by dividing the original price by (1 + tax as a percentage). In your example we divide 2086.80 by 1.063 to get the original price as 1963.12. Then the tax can be easily calculated as 2086.80-1963.12=123.68 tax. The only confusing bit here is probably the 1.063, which comes from the 1 + tax in percentage bit. To understand this, remember that a 10% tax is the same as multiplying by 0.1. Therefore a 6.8% tax is equivalent to 0.068 as a decimal. Then 1 + 0.068 = 1.068 which is the number you divide the original amount by. To make this clearer, I'll use another example. Imagine you've paid £120 on an item which had 20% tax. It should be obvious that the original item was £100 (so the tax is £20), but let's follow the method through so we can see how it works. Take 120 and divide it by (1 + tax in %). So that's 120 / (1+0.2) = £100. This tells us the original item was £100 before tax. Now to find the tax we take the cost before tax away from the cost with tax. £120 - £100 = £20. Therefore the tax is £20.
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Lets call the original cost C and the sales tax T.

Then C x (1+T) = The final cost

This can be rearranged to

(final cost / C) - 1 = T

input the infor you have and you should be able to calculate the sales tax
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Total amount of sale:  \$18.45
Sales tax:  8.25%
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^ This would be if 2086.80 was the total purchase before tax... He had the tax included.
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Hmm! I am not sure that one would do it - a negative tax? I'm moving to there. So, let's start again:  To determine tax, per-se, simply subtract price (the product sticker or shelf tag, or invoice, amount) from Cost (the total amount you paid). In other words, your cost, C, is the price, P, plus the sale tax, T. So, therefore, the tax would be calculated as: T = C - P.  But, perhaps you meant to ask how to deduce a tax Rate, R, from cost (from total amount paid for an item) when you know what the object's Price was. In that case (as attempted to be suggested previously), you will derive the solution from the formula by which tax was computed and added on originally. Your cost was the sum of price and tax, where tax is price multiplied by tax rate:  C = P + (R)(P) From there we want to solve for R, the tax rate. (R)(P) = C - P, so R = (C - P) / P. (For general use, a verbalized restatement of this formula appears after the examples.)  Example Given: C = 1.05; P = 1.00 Find R. 1.05 = 1.00 + (R)(1.00) . . . R = (1.05 - 1.00)/(1.00) R = 0.05 which equates to a 5% taxation rate. Example Given: C = 304.48; P = 279.98 R = (C - P) / P = (304.48 - 279.98) / 279.98 = 24.50 / 279.98 = 0.0875 (times 100) yields 8.75% taxation rate.  Generally speaking, the the derived Taxation Rate is the Percentage difference between Cost and Price, divided by Price. t = 24.49825
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1564.46 at 7%
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331.24 is the sale tax amount before the total bill.
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