Segment Addition Postulate Calculator

How to use the Segment Addition Postulate Calculator

What this calculator does

This calculator applies the identity AB + BC = AC when point B lies between endpoints A and C on one straight segment. It can find one missing length from the other two, or it can compare three supplied lengths and report whether they are consistent with the postulate. It also converts mixed length units, shows where B falls as a percentage of the whole segment, and creates a validated Excel workbook from the current state. It does not prove from a drawing alone that the points are collinear or that B is between A and C; those geometric conditions must be established by the problem statement, measurement setup, or coordinate data. For a broader introduction to points, lines, and finite segments, see the OpenStax discussion of points, lines, and planes.

When to use it

• Find the total length AC after measuring adjacent pieces AB and BC.
• Find a missing part when the whole AC and the other part are known.
• Check whether three measurements agree with a claimed between-point arrangement.
• Convert a geometry exercise that mixes centimeters, meters, inches, feet, or other supported units.

How to calculate

1. The calculator opens with a complete demonstration: AB length is 10 cm, BC length is 20 cm, and AC length is intentionally blank because it is the unknown. The first result is AC = 30 cm, and Download Excel is ready immediately.
2. Replace any two length values with your known measurements. Leave the value you want to solve blank. Use each adjacent unit selector to choose mm, cm, m, km, in, ft, or yd. When you change a unit for a nonblank field, the current number is converted so the physical length stays the same.
3. Read Primary result for the solved length or verification status. Review the resolved lengths, Point B position, Consistency gap, equation check, and detail table before using the answer.
4. Select Download Excel to export the current validated inputs and outputs as a real .xlsx workbook. Select Reset to clear all three data values and return units to centimeters. Reset removes the demonstration and disables Download Excel until at least two complete valid lengths are entered again.

Input guide

AB length is a required positive decimal whenever AB is one of the two known quantities. It measures the first part from A to B. Enter plain numbers such as 10 or 12.5; a period is the decimal separator, and a comma is accepted only in standard thousands grouping such as 1,250.5. Increasing AB increases AC when AC is unknown, or decreases the remaining BC when AC is fixed. Do not enter a negative number, zero, scientific notation, or a decimal comma such as 1,5.

AB unit defines the unit attached to AB length. The demonstration uses cm. Choose a unit that matches the measurement, and do not manually convert the value immediately before switching units because the selector performs that conversion for you.

BC length follows the same positive-number rules and represents the second part from B to C. The demonstration value is 20 cm. A larger BC makes the whole AC longer when AC is unknown. When AC is known and AB is unknown, BC must remain smaller than AC or the missing part would not be a positive segment.

BC unit identifies the unit for BC and converts a current nonblank value when changed. Mixed units are allowed. For example, AB may be 1 m while BC is 50 cm; the calculator normalizes both before adding.

AC length is the whole distance from A to C. Leave it blank to calculate the total, or supply it with exactly one part to solve the other part. Entering all three lengths changes the calculator to verification mode. The example leaves AC blank. A frequent mistake is entering an AC that is no greater than a known part; that cannot produce a positive missing segment when B is between A and C.

AC unit controls the displayed unit of a calculated AC and converts a supplied AC when changed. The base SI unit for length is the meter, and the NIST length-unit reference explains common metric relationships. For U.S. customary and metric comparisons, NIST also publishes length conversion guidance.

Output guide

Primary result is either the missing segment in its selected unit or a verification message when all three values are present. Calculation mode states whether the calculator added two parts, subtracted a known part from the whole, or checked the complete equation. AB resolved length, BC resolved length, and AC resolved length show the complete solved set, including the inferred value. These are exact consequences of the supplied decimal measurements and conversion factors, not measurements of a drawing.

Point B position is AB divided by AC, expressed as a percentage from endpoint A. A value near 50% means B is near the midpoint; a value near 0% or 100% means B is close to an endpoint. Consistency gap is AB + BC – AC in the output unit. It is zero for a solved case and approximately zero for consistent supplied values. A positive or negative nonzero gap indicates the three entries do not satisfy the claimed segment arrangement. Equation check writes the active numerical relationship in one common display unit.

The Segment details table lists Segment, Current value, Meters, Share of AC, and Interpretation. Current value uses the field's selected unit, Meters is the canonical comparison value, Share of AC shows each segment relative to the whole, and Interpretation identifies whether a row was known, calculated, or verified.

Worked example

In the startup example, AB = 10 cm and BC = 20 cm. Since AC is blank, the calculator uses AC = AB + BC = 10 cm + 20 cm = 30 cm. Point B is 10 ÷ 30 = 0.3333 of the way from A to C, so Point B position is 33.33% from A. The consistency gap is 10 + 20 – 30 = 0 cm. The same resolved values appear in the table and in the downloadable workbook.