# Which way of calculating VAT is the correct one and why

I kept searching for the logic of the vat calculations, but i still can't understand a few things,maybe you can help me out.

If i want to extract the price without tva,i'll be using this formula:

1. PriceWithoutTva = PriceWithTva / 1.19(for a tva rate of 19%),which i can't understand because for something like this: 100/1.19 = 84.02521008403361 , and that makes the TVA value to be almost 16 , but 19% of 100 is clearly 19.

If i want to extract the TVA from a price with tva,some say to use the above formula and simply decrease it from the PriceWithTva,which makes sense. Other says to multiply with the VAT percentage like this:

1. PriceWithTva * 0.19(for a tva rate of 19%) ,which makes sense because if i have 100 *0.19 it will give 19 which it's logical.

But then,i came across a formula which is widely used if i want to extract the TVA from a PriceWithTva:

1. PriceWithoutTVA = 100/(100+19) * PriceWithTVA , and the result is 84.02521008403361 which makes the TVA value almost 16 again for a PriceWithTVA of 100

Another formula which i can't understand is:

4.TVA = PriceWithoutTVA * 0.19(tva rate) , which again gives almost 16 for the PriceWithoutTVA of 84.02521008403361

Thanks for help.

Your (4) is the theory of how this tax is applied, implying your (1) and (3), while your (2) is wrong. The tax rate is applied to the before-tax price

You have the underlying application of value added tax (I will call this VAT rather than TVA) $$\text{ VAT amount }= \text{ Price before VAT }\times \frac{19}{100}$$

$$\text{ Price after VAT }= \text{ Price before VAT }\times \frac{119}{100}$$

and multiplying both sides by $\frac{100}{119}$

$$\text{ Price before VAT } = \text{ Price after VAT }\times \frac{100}{119}$$

and with substitution

$$\text{ VAT amount }\times \frac{100}{19} = \text{ Price after VAT }\times \frac{100}{119}$$

which, by multiplying both sides by $\frac{19}{100}$, simplifies to

$$\text{ VAT amount } = \text{ Price after VAT }\times \frac{19}{119}$$