There's no official, universally accepted definition of when a hill becomes a mountain. It's more of a matter of cultural perception and local convention.

Here are some factors that are generally considered:

* Elevation: While there's no specific height threshold, mountains are generally considered to be taller than hills. However, this can vary significantly depending on the region.

* Prominence: Prominence refers to the vertical height of a peak above the surrounding terrain. Mountains tend to have greater prominence than hills.

* Shape: Mountains often have a more pointed or jagged shape, while hills tend to be more rounded or gradual slopes.

* Geological formation: Mountains are often formed by tectonic plate movements or volcanic activity, while hills can be formed by erosion or glacial activity.

In practice, it's often up to local communities and authorities to decide what they classify as a hill or a mountain.

Here are some examples:

* The UK: The Ordnance Survey (OS) doesn't have a definitive height threshold for hills and mountains. They use the term "mountain" for peaks over 2,000ft (610m) high, but other peaks can be classified as mountains as well.

* The US: There is no official definition for hills and mountains in the US. The US Geological Survey (USGS) uses the term "mountain" for peaks over 1,000ft (300m) high, but this is not a hard and fast rule.

Ultimately, whether a hill is a mountain or not depends on your perspective, the local context, and the specific features of the landform.