Use our 3D Section Formula Calculator to effortlessly find the coordinates of a point dividing a line segment in three-dimensional space. Input two 3D points and the ratio (m:n) for internal or external division. Perfect for geometry students and professionals.
Formula:
The 3D Section Formula determines the coordinates P(x, y, z) of a point that divides the line segment joining two points A(x1, y1, z1) and B(x2, y2, z2) in the ratio m:n.
Internal Division:
x = (mx2 + nx1) / (m + n)
y = (my2 + ny1) / (m + n)
z = (mz2 + nz1) / (m + n)
External Division:
x = (mx2 - nx1) / (m - n)
y = (my2 - ny1) / (m - n)
z = (mz2 - nz1) / (m - n)
Where:
A(x1, y1, z1) and B(x2, y2, z2) are the coordinates of the two endpoints.
m:n is the ratio in which the point P divides the line segment AB.