To add VAT, multiply the net price by (1 + rate). To remove VAT from a price that already includes it, divide by (1 + rate) - do not just subtract the rate, because the rate applies to the net price, not the total.
Example at 20%: £100 net becomes £120 gross (£20 VAT). Removing 20% from £120 gives £100, but subtracting 20% of £120 would wrongly give £96.
Divide the gross price by 1 plus the rate to get the net price; the difference is the VAT. For 20% VAT this is the same as dividing by 1.2, or taking one sixth of the gross price.
Standard rates differ by country and change over time - for example around 20% in the UK and France, 19% in Germany, 21% in Spain and the Netherlands, 23% in Ireland and 25% in Sweden. Check your tax authority for the current rate and any reduced rates; this calculator works with whatever rate you enter.
Similar idea, different mechanics: VAT is included in shelf prices and charged at each stage of the supply chain, while US sales tax is added at the till. For sales tax use the sales tax calculator.
See also: Sales Tax Calculator · Discount Calculator · Percentage Calculator