River Gradient

The fall of a river from the source and mouth elevations and the gradient in m/km (‰), with a solution.

What to find:

the fall and gradient from the source and mouth heights

the gradient from the fall

the fall from the gradient

Elevations above sea level; a mouth below sea level (like the Volga, −28 m) with a minus sign. A river flowing into the ocean has mouth elevation 0.

Test yourself

The river fall and gradient calculator finds the fall of a river from the source and mouth elevations, the gradient from the fall and length, and the fall from the gradient.

Formulas

Δh = h_source − h_mouth, i = ^Δh/_L

The fall is in meters, the length in kilometers, the gradient in meters per kilometer. Meters per kilometer are numerically equal to per mille (‰); sometimes the gradient is given in centimeters per kilometer (multiply by 100).

A river flowing into the ocean has its mouth at 0 m; the Volga flows into the Caspian Sea, below ocean level (−28 m). Lowland rivers have gradients below 1 m/km, mountain rivers from several to tens of meters per kilometer.

Example. The Volga: source 229 m, mouth −28 m, length 3530 km. Δh = 229 − (−28) = 257 m, i = 257 / 3530 ≈ 0.073 m/km.