Section Formula Calculator

About this calculator

The section formula is a coordinate-geometry tool for finding the exact point that divides a line segment between two given endpoints in a chosen ratio m:n. For a segment from (x₁,y₁) to (x₂,y₂), the internal division point is ((mx₂+nx₁)/(m+n), (my₂+ny₁)/(m+n)). When m equals n, this collapses to the familiar midpoint formula, which is why the midpoint calculation is really just a special case of the more general section formula.

Students meet it first in analytic geometry to prove properties of triangles and quadrilaterals (like locating a centroid, which divides each median in a 2:1 ratio), but the same math drives practical work elsewhere: computer graphics programmers use it for linear interpolation (lerp) between two points when animating motion or blending colors, and surveyors and civil engineers use it to place stakes or way-points at a specified fractional distance along a boundary line.

Enter your two endpoint coordinates and the ratio m:n, and this calculator returns the coordinates of the dividing point instantly, without you needing to work through the algebra by hand.