# Segment Addition Postulate Calculator

URL: https://speedycalculator.com/calculators/math/segment-addition-postulate/
Last updated: 2026-10-30

> The segment addition postulate calculator uses AB + BC = AC for three collinear points A, B, C (with B between A and C) to find whichever segment length is missing.

## Inputs

- Find
- AB (cm, m, mm, in, ft, yd, km, mi)
- BC (cm, m, mm, in, ft, yd, km, mi)
- AC (cm, m, mm, in, ft, yd, km, mi)

## Results

- Missing segment
- Ratio AB : BC

## Formula

```
AB + BC = AC  (B lies between A and C)
```

## Explanation

The segment addition postulate is one of the basic axioms of geometry: parts of a segment add up to the whole. It is used to set up equations like "AB = 2x + 3, BC = x − 1, AC = 20".

### How to use the Segment Addition Postulate Calculator

- **Find**
- **AB**
- **BC**
- **AC**

Results update as you type, and everything is calculated in your browser.

### How it works

Choose which segment is unknown and enter the other two. The result must be positive; otherwise B cannot lie between A and C.

### Inputs explained

FieldWhat to enterFindChoose one: AC (whole segment), AB, BCABUnits: cm, m, mm, in, ft, yd …BCUnits: cm, m, mm, in, ft, yd …ACUnits: cm, m, mm, in, ft, yd …

### Example values

How the main result changes when **AB** changes and everything else stays at the example values above:

AB (cm)Missing segment (cm)2839410511612814

## Worked example

Inputs — Find: AC (whole segment); AB: 4 cm; BC: 6 cm.

Results — **Missing segment = 10 cm**; Ratio AB : BC = 0.666667.

## Key terms

- **Collinear**: Lying on the same straight line.

## FAQ

**What is a postulate?**
A statement accepted without proof as a starting point.

**What if B is not between A and C?**
Then AB + BC ≠ AC; the formula does not apply.

**How do I solve with algebra?**
Substitute the expressions into AB + BC = AC and solve for x.

**Is there an angle version?**
Yes – the angle addition postulate.


## Sources

- [OpenStax – Prealgebra 2e](https://openstax.org/details/books/prealgebra-2e)