Swiss MWST at 8.1%, 2.6% and 3.8%

What this works out

Swiss VAT — Mehrwertsteuer, taxe sur la valeur ajoutée, imposta sul valore aggiunto — in both directions. Type a net amount and it adds the tax; type a gross amount and it works the tax back out, which is a division rather than a subtraction.

The table underneath applies the same amount in every Swiss rate at once, with the VAT fraction for each.

Three rates, all raised at the same moment

Normalsatz, 8.1%. The default, and among the lowest standard VAT rates in Europe.

Beherbergungssatz, 3.8%. Overnight accommodation, including the breakfast that comes with it. It is a rate for a supply, not a status a hotel holds: dinner in the same building, a spa treatment or a meeting room is at 8.1%.

Reduziert, 2.6%. Food and non-alcoholic drinks, medicines, books, newspapers and magazines, seeds, bulbs and cut flowers.

All three rose on 1 January 2024, funding the AHV 21 old-age insurance reform approved by referendum in September 2022. The old set — 7.7%, 3.7% and 2.5% — applies to supplies made before that date whatever the invoice says, which is why the typed-rate field on this tool starts on 7.7 rather than on nothing.

Not one usable fraction

British guidance makes the VAT fraction sound like a dependable shortcut, because 20% happens to give exactly one sixth. Switzerland is the clearest proof that this is a coincidence of one rate rather than a property of VAT:

Rate	Fraction	Reduces to
8.1%	81/1081	nothing — 1081 is 23 × 47
3.8%	19/519	nothing — 519 is 3 × 173
2.6%	13/513	nothing — 513 is 27 × 19
7.7%	77/1077	nothing

Every Swiss rate has a decimal place, and a fractional rate almost never produces a fraction anybody would use. The tool prints them anyway, because a fraction that does not reduce is still the exact answer to “what share of this price is tax” — it just is not one you can do in your head.

Before you read on

A Swiss price includes VAT at the 8.1% standard rate. What share of it is tax?

• A8.1% of the price.

  That applies the rate to the wrong number — the 8.1% was charged on the figure before tax.

• B81/1081, which does not reduce.

  Yes, and 1081 is 23 x 47, so there is nothing to cancel.

• COne thirteenth.

  Close in value and wrong: 1/13 is 7.69%, and the real share is 7.49%.

81/1081, or about 7.49% — and unlike the British sixth, it does not reduce to anything, because 1081 factors as 23 x 47. Every Swiss rate has a decimal place and not one of the three produces a fraction a person would use. That is the useful lesson: the VAT fraction is an exact answer everywhere, and a mental shortcut only in the one country whose rate happens to give a sixth.

The method

Adding is a multiplication. Removing is a division: a gross of CHF 108.10 including 8.1% is 108.1% of the net, so the net is CHF 108.10 divided by 1.081.

Only the VAT is rounded, and the third figure follows from the other two, so the net and the tax always add back to the price actually charged.

Rounding is half up to the centime, with no option — as on every country tool here except UK VAT, whose round-down choice exists because HMRC grants invoice traders a concession. There is nothing Swiss to point at, and the five-centime rounding on a till receipt is a cash convention applied to the total after the tax is settled.

The arithmetic is decimal rather than binary floating point. 8.1% of CHF 25.00 is exactly CHF 2.025 and rounds to CHF 2.03, but the nearest double sits fractionally below it, so a naive implementation reports CHF 2.02.

A worked example

Adding. CHF 100.00 net at the Normalsatz:

VAT	CHF 8.10
Net	CHF 100.00
Gross	CHF 108.10
VAT fraction	81/1081

Getting back to CHF 100.00 from CHF 108.10 is a division by 1.081, not an 8.1% subtraction: taking 8.1% off CHF 108.10 gives CHF 99.34, which is CHF 0.66 short. The error is the rate squared — 0.66% of the net.

Removing, at the Beherbergungssatz. A hotel bill of CHF 207.60 including 3.8%:

vat = 207.60 x 3.8 / 103.8
    = 7.60

net = 207.60 - 7.60
    = 200.00

The centime case. CHF 25.00 plus 8.1% is CHF 2.03 of tax — not the CHF 2.02 a floating-point calculation reports.

These are the same figures asserted in this tool’s test file, so the page and the formula cannot drift apart without the build going red.

What it does not do

It does not decide which rate a supply falls in; the ESTV publishes guidance on the awkward cases, and the split between an overnight stay and everything else a hotel sells is the usual one. It holds no pre-2024 rates as bands, so an older invoice needs the rate typing in. It does not apply the five-centime cash rounding, which belongs to the payment rather than to the tax. And it does not handle the acquisition tax on services bought from abroad, the net-tax-rate method for small businesses, import VAT, or the Liechtenstein administration that applies the same percentages under its own authority.

For a country with no tool of its own, a VAT calculator with no rate table is the right page. The neighbours covered so far are German VAT and Austrian VAT.

Adding VAT to a net amount:
  vat   = round(net x rate / 100)
  gross = net + vat

Removing VAT from a gross amount:
  vat = round(gross x rate / (100 + rate))
  net = gross - vat

Swiss rates and their VAT fractions:
  Normalsatz      8.1%   81/1081
  Beherbergung    3.8%    19/519
  Reduziert       2.6%    13/513
  Normalsatz to 2023   7.7%   77/1077

Not one of them reduces to anything you could
use on paper. That is normal; 20% giving one
sixth is the exception.

round = to the nearest centime, half up.

Only the VAT is rounded. The third figure is derived
from the other two, so net + vat = gross to the centime.