Definition of length

The length of a river is actually very hard to calculate. It depends on the identification of the source, the identification of the mouth, and the precise measurement of the river length between source and mouth. As a result, the length measurements of many rivers are only approximations. In particular, there has for long been disagreement as to whether the Amazon or the Nile is the world's longest river.

The source of a river may be hard to determine because a river typically has many tributaries. Among the many sources, the one that is farthest away from the mouth is considered as the source of the river, thus giving a maximal river length. In practice, the tributary with the farthest source is not always the one given the name of the river. For example, the farthest source of the Mississippi River system is the source of the Jefferson River, a tributary of the Missouri River which in turn is a tributary of the Mississippi. However, a different (and shorter) tributary is identified as the Mississippi. When the river is measured from mouth to farthest source, it is called the Mississippi-Missouri-Jefferson. Also, it is hard to state exactly where a river begins as very often rivers are formed by seasonal streams, swamps, or changing lakes. In this article, length means the length of the river system, including all tributaries.

The mouth of a river is hard to determine in cases where the river has a large estuary that gradually widens and opens into the ocean; examples are the River Plate and the Saint Lawrence River. Some rivers like the Okavango do not have a mouth; instead they dwindle to very low water volume and eventually evaporate, or sink into an aquifer, or get diverted for agriculture. The exact point where these rivers end will vary seasonally.

The length of a river between source and mouth may be hard to determine because of a lack of precise maps. In these cases, the measured length of a river will depend on the scale of the map on which the measurement is based; in general, due to the fractal quality of a river, the finer the scale, the longer the resulting length measurement. This issue was discovered by Lewis Fry Richardson and also applies when measuring borders between countries and coastlines. Ideally, length measurements should be based on maps that are of a large enough scale to show the width of the river, and the path measured is the path a small boat would take down the middle of the river.

Even when precise maps are available, the length measurement is not always clear. A river may have multiple arms. It may depend on whether the center or the edge of the river is taken as reference point. It may not be clear how to measure the length through a lake: this may also vary by season. These points make it difficult, if not impossible, to get a precise (or comparable ) measurement of the length of a river or stream.