Segment Addition Postulate Calculator

The segment addition postulate describes how lengths combine when three points lie on the same straight line. If point B lies between points A and C, the two smaller segments AB and BC join without a gap or overlap to form the whole segment AC. Their lengths therefore satisfy AB + BC = AC. This calculator rearranges that relationship to solve for whichever of the three segment lengths is unknown. To find the whole segment AC, add AB and BC. To find the first part AB, subtract BC from AC. To find the second part BC, subtract AB from AC. These are not separate rules; they are equivalent forms of one geometric statement. Choosing the missing segment tells the calculator which arrangement to use and which two labels to show for the known values. All segment lengths must be nonnegative. When solving for a part, the known part cannot be longer than the whole segment. For example, if AC is 12 units and BC is 5 units, AB is 7 units. Entering AC as 5 and BC as 12 would imply a negative AB, which cannot represent an ordinary geometric length. The calculator reports this inconsistency rather than displaying a negative segment. The postulate is often introduced early in geometry because it connects a visual diagram with algebra. A diagram might label AB as x + 2, BC as 6, and AC as 15. First use segment addition to write x + 2 + 6 = 15, then solve the resulting equation to get x = 7. This calculator handles numeric segment lengths directly; if your labels contain variables, simplify or solve those expressions before entering their values. Segment addition is useful in coordinate geometry, construction layouts, map distances, measurement chains, and proofs involving betweenness. The order of the letters names each endpoint, so AB and BA have the same length even though the notation is reversed. What matters is that the middle point truly lies between the outer endpoints. If the points are not collinear or B is not between A and C, AB + BC does not necessarily equal AC. Use the displayed formula to confirm how the answer was obtained and keep all inputs in the same unit. If AB and BC are entered in centimeters, AC is also in centimeters. Decimal values are supported, and results are rounded only for display while the underlying arithmetic retains full numeric precision.