One US teaspoon is 4.92892159375 millilitres, universally rounded to 5 ml. The rounding is so entrenched that measuring spoons sold as teaspoons are manufactured to 5 ml exactly, which means the nominal unit and the physical object differ slightly.
About the units
The US teaspoon is one third of a US tablespoon and 1/48 of a US cup, which puts it at 1/768 of a US gallon. The metric teaspoon, standard across Europe and used in Swedish recipes as the tesked, is exactly 5 ml. The imperial teaspoon in older British recipes is 5.919 ml, twenty per cent larger. Australia uses 5 ml, matching the metric value, even though its tablespoon does not match. The teaspoon's history as a measure is unusual in that it began as an actual object — the spoon used for stirring tea — and only became a defined volume when recipe writing standardised in the nineteenth century.
The exact factor
The exact value is 4.92892159375 ml, and 5 ml is high by 1.4 per cent. Three teaspoons make one US tablespoon exactly, and that relationship holds in the metric system too, where 3 × 5 ml gives the 15 ml tablespoon. It does not hold in Australia, where the tablespoon is four teaspoons. In medicine the 5 ml value is the standard, and dosing spoons and oral syringes are marked in millilitres rather than teaspoons precisely because household teaspoons vary from about 2.5 to 7 ml.
Where you meet this conversion
Spices, extracts, salt, baking powder and yeast are all measured in teaspoons, and these are the ingredients where a proportional error does the most damage. A teaspoon of instant yeast is roughly 3 g, and doubling it by accident changes the rise dramatically. In medicine the teaspoon was abandoned as a dosing unit after repeated overdoses caused by patients using cutlery: studies found that people asked to measure 5 ml with a kitchen spoon delivered anywhere from 3 to 9 ml.