Collinear Points Calculator

Work out collinear points instantly with clear inputs, formula shown and shareable results.

About Collinear Points Calculator

Points are collinear when the vectors between them are parallel, which makes their cross product the zero vector. Half that cross product's magnitude is the area of the triangle they form.

Formulas

Collinearity test

AB × AC = 0 ⇔ A, B and C lie on one line

Triangle area

Area = ½|AB × AC|

Worked example

With the default values below, Collinear Points Calculator returns Result of The three points are collinear. Change any input above and every figure here is recalculated in your browser.

Inputs used

Point A (x, y, z): 1, 2, 3
Point B (x, y, z): 3, 5, 7
Point C (x, y, z): 7, 11, 15

Results

Result: The three points are collinear
|AB × AC|: 0.00000000
Area of triangle ABC: 0.00000000
Length of AB: 5.38516481

Step by step

1Values used
2Collinearity test
3Triangle area
4Result= The three points are collinear
5|AB × AC|= 0.00000000
6Area of triangle ABC= 0.00000000
7Length of AB= 5.38516481

Assumptions and limits

The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Are (1,2,3), (3,5,7) and (7,11,15) collinear?

Yes. AC = (6, 9, 12) is exactly three times AB = (2, 3, 4), so the cross product vanishes.

Why use the cross product rather than gradients?

Gradients break down for vertical lines and do not extend cleanly to three dimensions; the cross product handles every case.