How many calories are in alcohol-free beer?

Generally fewer than the alcoholic version, often meaningfully so - but it varies a lot by brand, so treat any number here as a rule of thumb rather than gospel and check the actual label.

The main reason alcohol-free beer tends to be lower calorie is simple: alcohol itself is calorie-dense (about 7 kcal per gram) with nothing else to show for it, and removing most of that alcohol removes those calories along with it. A standard 5% ABV pint gets a large chunk of its calories from the alcohol content alone.

What is left comes from the same source as any beer: malt sugars and carbohydrate. Some brands add sugar back in during production to make up for flavour lost when the alcohol is stripped out, which can partly offset the calorie saving. So "alcohol-free" is a reasonable rule of thumb for lower calorie, but it is not automatic - two 0.0% beers from different brewers can have noticeably different numbers.