Segment Addition Postulate Calculator
If point B lies between points A and C on a line, then AB + BC = AC. Enter any two of the three lengths and this calculator finds the missing one.
Find
Length of the missing segment (AB + BC = AC)
- 1
Known segments
AB = 5, BC = 3 - 2
AC = AB + BC
5 + 3 = 8
How does this calculator work?
The segment addition postulate states AB + BC = AC when B is between A and C. Rearranging: AB = AC − BC or BC = AC − AB. Enter any two lengths to find the third. A negative result means the inputs are inconsistent.
Formula
How this is calculated
The segment addition postulate is a foundational rule in Euclidean geometry: if point B is between points A and C on a line segment, then the two shorter segments AB and BC together equal the total segment AC. This seems obvious but forms the rigorous basis for many geometric proofs and constructions.
To find AC: add AB and BC together. To find AB: subtract BC from AC. To find BC: subtract AB from AC. In each case the result must be a non-negative number — a negative length is geometrically impossible and indicates that B is not actually between A and C (or the inputs are inconsistent).
The postulate applies only to collinear points (points on the same line). For points not on the same line, the distance between them follows the triangle inequality rather than simple addition.
Frequently asked questions
If B is between A and C, then AB + BC = AC. In other words, the whole equals the sum of its parts: the total segment length equals the sum of the two sub-segment lengths.
A negative result means the given lengths are inconsistent — B cannot be between A and C with those measurements. Check that AC is longer than both AB and BC individually.
Yes — it is commonly used in geometry proofs to justify equalities between segment lengths, to prove congruence, or to set up equations when coordinates or algebraic expressions are involved.
Also known as
TG we-Calculate Editorial Team. (2026). Segment Addition Postulate Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/segment-addition-postulate-calculator
TG we-Calculate Editorial Team. "Segment Addition Postulate Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/segment-addition-postulate-calculator.
TG we-Calculate Editorial Team, "Segment Addition Postulate Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/segment-addition-postulate-calculator
@misc{wecalculate_segment_addition_postulate_calculator, title = {Segment Addition Postulate Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/segment-addition-postulate-calculator}}, year = {2026}, note = {TG we-Calculate} }
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