# How do I reverse sales tax?

Works back from a total that includes sales tax to the price before tax and the tax paid, or finds the tax rate from the total and the price.

- Page: https://www.acalculator.org/finance/reverse-sales-tax-calculator
- JSON spec: https://www.acalculator.org/finance/reverse-sales-tax-calculator.json
- Version: 5632de2cb6fa

## Default answer

Example with the default inputs (Total with tax $108.25, Sales tax rate 8.25%): A total of $108.25 with 8.25% sales tax is a price of $100.00 before tax, plus $8.25 of tax.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| total | Total with tax | What you paid, including the sales tax. |
| rate | Sales tax rate | The sales tax rate: state and local rates added together. |
| price | Price before tax | The price without sales tax: total × 100 ÷ (100 + rate). |
| tax | Sales tax | The sales tax inside the total: total − price before tax. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| total | Total with tax | What you paid, including the sales tax. |
| rate | Sales tax rate | The sales tax rate: state and local rates added together. |
| price | Price before tax | The price without sales tax: total × 100 ÷ (100 + rate). |
| tax | Sales tax | The sales tax inside the total: total − price before tax. |

## Method

price before tax = total × 100 ÷ (100 + rate); tax = total − price before tax; rate = tax ÷ price before tax × 100.

## Assumptions

- One sales tax rate applies to the whole total. Items taxed at different rates, and fees that are not taxed, are not included.
- Arithmetic is exact on the typed decimals; money shows to the cent, halves up.
- Stores round the tax on a receipt to the cent, so a price worked back from a total can be a fraction of a cent off the shelf price.

## Worked examples

1. total = $417.48, rate = 6.5% gives price = $392.00, tax = $25.48. Source: OpenStax, Prealgebra 2e, section 6.3 "Solve Sales Tax, Commission, and Discount Applications" (https://openstax.org/books/prealgebra-2e/pages/6-3-solve-sales-tax-commission-and-discount-applications), Example 6.25 worked back: 417.48 ÷ 1.065 = 392.
2. price = $499.00, tax = $42.42 gives rate = 8.501002%, total = $541.42. Source: OpenStax, Prealgebra 2e, section 6.3 "Solve Sales Tax, Commission, and Discount Applications" (https://openstax.org/books/prealgebra-2e/pages/6-3-solve-sales-tax-commission-and-discount-applications), Example 6.26: 42.42 ÷ 499 = 8.5% (rounded there; exactly 8.501002…%).
3. total = $100.00, rate = 8.25% gives price = $92.38, tax = $7.62.
4. total = $108.25, price = $100.00 gives rate = 8.25%, tax = $8.25.

## FAQ

### How do I take sales tax out of a total?

Divide the total by 1 plus the tax rate as a decimal. A total of $108.25 at 8.25% is 108.25 ÷ 1.0825 = $100 before tax, and $8.25 of tax.

### Why can I not just take the tax percent off the total?

Because the tax was a percent of the lower price, not of the total. 8.25% of $108.25 is $8.93, which is more than the $8.25 of tax that was added. Dividing by 1.0825 gives the right price.

### How do I find the sales tax rate from a receipt?

Divide the tax by the price before tax and multiply by 100. $42.42 of tax on a $499 purchase is 42.42 ÷ 499 × 100 = 8.501%, which a receipt rounds to 8.5%.

### Why is the price a fraction of a cent off?

Stores round the tax on each receipt to the cent. Working back from a rounded total can give a price like $92.3788, which shows as $92.38. The exact price on the shelf is the nearest amount that gives your total.

### What rate should I use?

Use the full rate you paid: the state rate plus any county and city rates. The rate is printed on most receipts, or your state revenue department lists the local rates.

### Does this work for VAT or GST?

Yes. VAT and GST included in a price work the same way: divide the price by 1 plus the rate. Enter the VAT or GST rate as the tax rate.

## Sources

- OpenStax, Prealgebra 2e, section 6.3 "Solve Sales Tax, Commission, and Discount Applications", Examples 6.25 and 6.26. https://openstax.org/books/prealgebra-2e/pages/6-3-solve-sales-tax-commission-and-discount-applications