Free Segment Addition Postulate Calculator

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The segment addition postulate is one of the foundational building blocks of formal geometry, stating that if point B lies between points A and C on the same line, then the two smaller pieces add up to the whole: AB+BC=AC. It's typically one of the very first postulates introduced in a geometry course, used to build up proofs about congruent segments, and it's the direct 1D analog of how areas or volumes of adjacent regions add up to a total. Given any two of the three lengths (AB, BC, or AC), the third follows directly by rearranging the equation.

How it works

Choose which length you're solving for and enter the other two. Since AB+BC=AC, solving for AC is a direct addition, while solving for AB or BC instead requires subtracting the other known segment from AC (AB=AC-BC, or BC=AC-AB).

Enter what are you solving for?.
Enter aB.
Enter bC.
Enter aC.
Click Calculate to see your results.

Examples

AB=5, BC=3, solve for AC

AC = 5+3 = 8.

AC=20, AB=7, solve for BC

BC = AC-AB = 20-7 = 13.

Common mistakes to avoid

Assuming B is between A and C without checking — the postulate only applies when that's actually true.
Subtracting in the wrong order when solving for AB or BC (e.g., computing AB-AC instead of AC-AB).
Confusing this with the midpoint formula, which only applies in the special case where B is exactly halfway between A and C.

Frequently asked questions

That means the given lengths are inconsistent with B actually lying between A and C — for example, if you're solving for BC=AC-AB and AB happens to be larger than AC, the postulate's assumption (that B is between A and C) has been violated.

No — the postulate specifically requires B to lie on segment AC, between the two endpoints. If B is somewhere else entirely, AB+BC does not necessarily equal AC.

The segment addition postulate is a general relationship for any point B between A and C, regardless of where exactly it sits; the midpoint formula is the special case where AB and BC happen to be equal (B is exactly halfway).

In classical axiomatic geometry, a postulate is a basic statement accepted as true without proof, used as a starting point to prove other, more complex statements (theorems) — the segment addition postulate is one of these foundational starting assumptions.

Yes — if several points lie in order along the same line, the same additive logic extends naturally: the sum of all the smaller consecutive segments equals the length of the overall segment they make up.

The direct analog for angles is called the angle addition postulate, which states that if a ray lies between two other rays sharing a vertex, the two smaller angles add up to the larger angle — same underlying idea, just applied to angles instead of segment lengths.