Reverse Sales Tax Formula — How It Works

The Forward Tax Relationship

A standard sales tax works like this:

Total = Pre-tax × (1 + rate)

Example: $100 item + 8% tax:

Total = $100 × 1.08 = $108

Reversing the Formula

To solve for pre-tax when you know the total:

Pre-tax = Total / (1 + rate)

This is algebraically identical — just divide both sides by (1 + rate).

Example: $108 total at 8%:

Pre-tax = $108 / 1.08 = $100.00
Tax     = $108 - $100 = $8.00

The Common Mistake

Many people instinctively calculate: $108 × 8% = $8.64 — wrong.

This is wrong because 8% applies to the pre-tax price ($100), not the total price ($108). The tax is embedded inside the total at a compressed rate: tax fraction = rate / (1 + rate) = 0.08 / 1.08 = 7.407%.

Correct tax amount = $108 × 7.407% = $8.00 ✓ Or equivalently: $108 - ($108 / 1.08) = $8.00 ✓

Works for Any Flat-Rate Tax

The formula is identical for:

• US Sales Tax: added at point of sale, varies by state/locality
• VAT (UK, EU): included in the displayed price (tax-inclusive pricing)
• GST (Australia, Canada): same structure as VAT
• HST (Canadian provinces): harmonized GST + provincial tax, same formula

The only input that changes is the rate. UK VAT 20%: pre-tax = total / 1.20. Australian GST 10%: pre-tax = total / 1.10.

Finding the Tax Rate from Pre-Tax and Total

If you know both the pre-tax and total prices:

Rate = (Total - Pre-tax) / Pre-tax

Example: receipt shows $100 subtotal and $108 total:

Rate = ($108 - $100) / $100 = 0.08 = 8%

Compound Tax Rates (State + Local)

When a US purchase includes both a state tax rate and a local rate, they combine additively:

Combined rate = State rate + Local rate
Pre-tax = Total / (1 + combined rate)

Example: Texas (6.25% state + 2% local = 8.25%):

$108.25 total → Pre-tax = $108.25 / 1.0825 = $100.00

Always use the combined effective rate that appeared on your receipt, not just the state base rate.