My receipt shows 13.04 of tax on a total of 100; is that wrong if the rate is 15%?
It is not wrong. If the receipt states a 15% rate, that rate is charged on the net amount, not the total. In a total of 100 the net is 86.96 and the tax 13.04, which is 15% of 86.96 but only about 13.04% of 100. Extracting 100 at the rate printed on the receipt reproduces the same figures.
Where 13.04 comes from
Imagine a net price of 86.96. Add 15% and the tax is 13.04, making the total 100. Now read the receipt from the bottom up: you see 100 and 13.04, divide one by the other and get 13.04% instead of 15%. Nothing went missing; you simply measured the tax against the wrong number.
The general rule: the tax share of the total = rate ÷ (100 + rate). At 15 that is 15 ÷ 115, about 13.04%. That is why the same share turns up on every receipt at that rate, whatever the amount.
Check the receipt yourself
- Open the VAT calculator and choose Extract tax from a gross amount.
- Enter the receipt total of 100 and the rate printed on the receipt itself, here 15.
- You get net 86.96 and tax 13.04. If that matches the receipt, its maths is sound.
To check the other direction, choose add and enter 86.96 at the same rate: tax 13.04, gross 100.
When a receipt really is wrong
- If it shows tax of 15 on a total of 100, someone took 15% off the total, leaving a net of 85, which is too low.
- If the net plus the tax does not equal the printed total, there is an adding or rounding error.
- If your result differs from the receipt by more than a cent, check the stated rate; it may not be the one you assumed.
If you are the one issuing the receipt
The Receipt generator records the amount received only; it neither calculates nor splits tax. If you want your customer to see the split, work it out in the calculator first and write it in the optional notes field, with the rate stated, which shows at a glance that 13.04 is 15% of the net amount. A receipt confirms a payment; it is not a certified tax invoice.
Common questions
Is this specific to a 15 rate?
No. At any rate you enter, the tax share of the total is smaller than the rate itself, because it is divided by (100 + rate).
Why does 86.96 × 1.15 not give exactly 100?
Because 86.96 is rounded. The exact result is 100.004, shown as 100 after rounding.
