How this calculator works
The segment addition postulate says that if point B lies on the line segment between A and C, then the two shorter lengths add to the whole: AB + BC = AC. It is one of the basic tools for setting up equations in geometry. This calculator applies it in either direction. When you know the two parts it adds them; when you know the whole and one part it subtracts the known part. A part cannot be as long as or longer than the whole segment, because B must sit strictly between A and C.
Formula
AB + BC = AC. Therefore AC = AB + BC, AB = AC - BC, and BC = AC - AB, with each part shorter than the whole.
Worked example
If AB = 3 m and BC = 5 m, then AC = 8 m. If AC = 8 m and BC = 5 m, then AB = 3 m. If AC = 8 m and AB = 3 m, then BC = 5 m.
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Frequently asked questions
Does B have to be between A and C?
Yes. The postulate applies to a point on the segment between the endpoints. If B lies outside the segment, the lengths obey a different relationship and this tool does not apply.
Can a segment have zero length?
In this calculator every entered length must be greater than zero. A zero-length part would put B on top of A or C rather than strictly between them.
Why is my subtraction rejected?
Subtracting a part from the whole must leave a positive remainder. If the part is longer than the whole, the three lengths cannot describe B between A and C.
Is this the same as adding distances?
It is the one-dimensional case. For points along a straight line, distances along the line add. In two or three dimensions you would use the distance formula instead.