Enter two points in 3D and instantly get the distance between them and the section formula point for any ratio.
3D Distance & Section Formula Calculator
How It’s Calculated
Distance extends the 2D formula into three dimensions: PQ = √((x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²). The section formula finds the point dividing PQ internally in ratio m:n — each coordinate is the weighted average (m·x₂ + n·x₁)/(m+n). Setting m = n = 1 gives the midpoint, which is why this tool shows both together.
Worked Example
For P(1,2,3) and Q(4,6,9): PQ = √(3²+4²+6²) = √(9+16+36) = √61 ≈ 7.81. The midpoint is ((1+4)/2, (2+6)/2, (3+9)/2) = (2.5, 4, 6).
Frequently Asked Questions
Q: What’s the difference between internal and external division?
Internal division (what this tool computes) finds a point between P and Q. External division finds a point outside the segment, on the extended line — that uses (m·x₂ − n·x₁)/(m−n) instead, a different formula covered separately.
Q: Does the order of P and Q matter for the section formula?
Yes — the ratio m:n is measured from P to Q in that order. Swapping P and Q with the same ratio gives a different point (unless m = n).
3D coordinate geometry extends the 2D straight-line ideas from 1st PUC into three dimensions. See how Daniel Classes teaches 1st and 2nd PUC Mathematics →