Segment Addition Postulate - Find the Missing Segment Length

The segment addition postulate is the geometry rule that says, when three points A, B, and C are collinear and B sits between A and C, the length of the whole segment AC equals the sum of the two smaller segments AB and BC, written AB + BC = AC. This calculator lets you type any two of AB, BC, or AC and immediately read back the third, with a live check that the three values actually satisfy AB + BC = AC.

• • High-school geometry homework: Solve the standard 'find the missing segment' problem by entering the two known lengths and reading the third, the most common form of this postulate in textbooks.
• • Number-line and coordinate problems: Convert between three collinear coordinates and the three segment lengths they produce, which is the coordinate-geometry form of the same rule.
• • Verification of segment diagrams: Check a hand-drawn or computer-generated diagram by confirming the three labeled segment lengths on a line satisfy AB + BC = AC, catching typos before they propagate.

The theorem is one of the first results in a geometry course, and almost every measurement you take on a straight line is a sum of smaller pieces. The rule turns 'add up the small distances' into a single equation, AB + BC = AC, that you can check on the page.

When the segment is given by its two endpoints in 2D or 3D, Length of a Line Segment Calculator computes the distance, midpoint, and slope of the same line.

The calculator reads AB, BC, and AC, treats any blank field as the unknown, and applies the single rule AB + BC = AC to fill in the missing value, then reports whether the three values are consistent.

• AB: Length of the segment from point A to point B. Leave blank to compute AB as AC minus BC.
• BC: Length of the segment from point B to point C. Leave blank to compute BC as AC minus AB.
• AC: Length of the whole segment from A to C. Leave blank to compute AC as the sum AB + BC.

The calculator treats a blank input as the unknown and applies AB + BC = AC in the appropriate direction. When all three fields are filled, it cross-checks the equality, which is useful for verifying a diagram you typed in from a worksheet.

For coordinate-geometry problems, the same rule shows up as |xB - xA| + |xC - xB| = |xC - xA| for three collinear points on a number line.

According to Wikipedia, the rule states that if point B lies on segment AC and B is between A and C, then AB + BC = AC.

According to Khan Academy, when three points are collinear the distance between the outer two equals the sum of the distances between consecutive points, which is this rule in coordinates.

For coordinate-geometry problems where AB, BC, and AC are the pairwise distances between three collinear points, 2D Distance Calculator handles the distance formula between any two of those points in one step.

Four small ideas cover everything the rule needs: collinearity, betweenness, the part-whole relationship, and the number-line reading of the same formula.

These four ideas travel together: skip the collinearity check and the equality can fail; forget the betweenness condition and the sign convention breaks.

Once you know the radius and segment height, Segment Area Calculator turns the same kind of segment information into the area of a circular segment using the chord, central angle, and sector area.

Type any two of AB, BC, and AC, leave the third blank, and read the result. The calculator updates as you type.

1. 1 Pick which segment is the unknown: Decide which of AB, BC, or AC to solve for. In a 'find the whole' problem the unknown is AC; in a 'find a part' problem the unknown is AB or BC.
2. 2 Enter the two known lengths: Type the two known values into their fields. Leave the third blank so the calculator can use that blank as the unknown.
3. 3 Read the computed segment: The 'Computed Missing Segment' result updates in real time and is labelled with which segment (AB, BC, or AC) it represents, so there is no ambiguity about what was filled in.
4. 4 Check the consistency row: Look at the 'AB + BC = AC?' row. A 'Yes' result means the rule holds for the values you entered; a 'No' result includes the actual sum so you can find the typo.
5. 5 Verify a diagram by filling all three fields: When you already have all three values from a worksheet or drawing, fill in all three fields. The calculator then acts as a consistency checker instead of a solver and tells you whether the diagram satisfies AB + BC = AC.
6. 6 Reset and try the next problem: Press Reset to restore the defaults (AB = 3, BC = 5, AC = 8). The default values satisfy the postulate, so the reset state is a clean starting point for a fresh problem.

Suppose a number line has points A = 1, B = 4, C = 10. AB = 3, BC = 6, AC = 9. Fill all three fields with 3, 6, 9, and the consistency row confirms 3 + 6 = 9.

When the segment lives on a number line or in a coordinate plane and you need to plot the three points, Coordinate Plane Calculator visualizes the points and reads off distances, midpoints, and slopes for the same setup.

A focused SAP calculator saves time on the kind of one-line geometry problems that show up across school, drafting, and programming work.

• • One form replaces three separate problems: The same form handles 'find AC', 'find AB', and 'find BC'. There is no mode toggle to remember, only the rule that whatever you leave blank is the unknown.
• • Consistency check included: When you fill all three fields, the calculator checks AB + BC = AC and reports the actual sum if the values disagree, which is the fastest way to catch a typo on a worksheet.
• • Real-time feedback while you type: The result updates as you change any field, which makes it easy to ask 'what if AC were 20?' without restarting.
• • Defaults match a textbook example: The default values (AB = 3, BC = 5, AC = 8) come from a common geometry textbook problem, so the calculator is in a known-good state the moment the page loads.
• • Negative inputs are handled safely: If you accidentally type a negative value, the calculator treats it as zero and continues, so the page does not throw a runtime error mid-session.
• • Works on number-line problems too: The same AB, BC, AC fields cover the coordinate-geometry version, so the calculator is useful for pure geometry and number-line problems.

The biggest practical win is that the rule becomes a single reading instead of a back-of-the-envelope subtraction or addition.

For the education-side companion that walks through the same collinear-point problems with step-by-step explanations, Distance, Midpoint & Slope Calculator covers distance, midpoint, and slope from the same two-endpoint input style.

A small set of inputs and assumptions decides whether the postulate applies to your problem, and a couple of limitations are worth knowing before you trust the result.

• • The calculator assumes a flat, straight-line geometry. It does not handle curved paths, geodesic distances on a sphere, or piecewise paths with bends.
• • The check is numeric with a tolerance of 0.01, so two values that differ by less than that are treated as equal. That is fine for textbook problems but can hide a tiny rounding mismatch on a very precise problem.

For most homework, drafting, and coordinate problems the rule is exact, and the calculator's numeric check is well below the precision of the input.

According to Wolfram MathWorld, a line segment is a closed interval with two endpoints, and the rule holds whenever the three labeled points sit on the same line.

Before you trust the result, normalize AB, BC, and AC to a single unit so AB + BC = AC compares like with like: the Distance Converter covers centimetre-to-inch, inch-to-foot, kilometre-to-mile, and the rest of the metric, customary, and nautical pairs.