Sales tax and VAT

The calculator is a two-direction mathematical net/gross model. Its German title describes the context, but the tool has no country profile, stored legal rate, tax classification or automatic rate choice.

The only paths are `Net → Gross` and `Gross → Net`. Both use one non-negative rate supplied by the user; the result shows net amount, tax amount, gross amount and the proportional composition of gross.

For net to gross, the rate is applied to net. For gross to net, the tax is already contained in gross, so `gross × rate ÷ 100` would be wrong; the service first divides gross by one plus the rate and then takes the difference. The equivalent contained-tax form is gross × rate ÷ (100 + rate).

The service accepts finite amounts and finite rates of zero or more, including decimal rates and rates above 100%. Invalid, empty, negative or non-finite values are rejected. At 0%, net equals gross and tax is zero; amount 0 stays stable in the proportional display.

The same 100/20% case in both directions demonstrates why adding a percentage and extracting it are not the same multiplication. The 19.99/19% case distinguishes the raw service values from the two-decimal monetary display.

Net 100 at 20% gives tax 20 and gross 120; gross 120 at 20% gives net 100 and contained tax 20. Net 19.99 at 19% gives raw tax 3.7981 and gross 23.7881.

All amounts are numbers in one implicit currency. There is no currency selector or FX calculation. The service does not round early; the page displays non-integer money amounts with two decimals and a rate with up to four decimals.

The model contains no input-tax credit, liability, reverse charge, exemption, multiple taxes, invoice-line logic, invoice rounding or legal invoice requirements. It does not tell the user which rate applies and is not tax advice.