Bathymetric Profile Calculator

It's the arctangent of the vertical depth difference divided by the horizontal distance between the two points, converted from radians to degrees -- the same rise-over-run trigonometry used to describe a hillside slope on land. A 3,800 m depth change over 100 km of horizontal distance, for example, works out to an angle of only a couple of degrees, because horizontal distances at ocean scale are enormous compared to depth changes, even across a full continental slope.

Continental shelves genuinely are close to flat in real bathymetry -- typically well under a tenth of a degree of average gradient, since they are shallow, gently sloping extensions of the continental landmass. The transition to the much steeper continental slope, where the seafloor drops off toward the deep ocean basin, is where gradients jump from a small fraction of a degree to several degrees or more, which is why this calculator's classification bands treat that jump as a real category boundary, not just an arbitrary cutoff.

No -- it assumes a single straight, uniform slope connecting your start and end depths, which is a simplification. Real seafloor profiles surveyed with multibeam sonar typically show terraces, ridges, canyons, and local steepening that a straight-line average between two endpoints cannot capture. This calculator is useful for a quick overall-gradient estimate between two known soundings, not as a substitute for an actual bathymetric survey when the detailed shape of the seafloor matters.

The slope angle is the arctangent of depth change divided by horizontal distance, so for the same depth difference, stretching that change over a longer horizontal run always divides by a bigger number and produces a smaller angle. This is why abyssal plains and continental shelves, which span huge horizontal distances relative to their depth change, read as nearly flat, while the same depth change compressed into a short horizontal run -- like a canyon wall -- reads as a steep slope.

It approximates the area of the vertical slice of ocean between your two points, using the average of the start and end depths multiplied by the horizontal distance (a trapezoidal approximation). It's a rough way to compare the relative scale of different profiles -- for example, a wide, deep basin versus a narrow, shallow shelf section -- rather than a precise volumetric or engineering figure, since it inherits the same straight-slope simplification as the rest of this calculator.