# Proportion Calculator

> Solves the proportion a / b = c / x for the unknown fourth term by cross-multiplication (x = b × c / a) and reports the common scale factor.

- Calculator id: `proportion` · Category: Math (`math`) · Tool name: `solve_proportion`
- Canonical page: https://tttkmbb.com/math/proportion · This document: https://tttkmbb.com/math/proportion.md · JSON definition: https://tttkmbb.com/math/proportion.json

## Purpose

Solves the proportion a / b = c / x for the unknown fourth term by cross-multiplication (x = b × c / a) and reports the common scale factor.

**Use when:** Three terms of a proportion are known and you need the fourth, e.g. converting a recipe, map scale or unit rate.

**Do not use when:** You only want to simplify a ratio (use ratio) or the unknown is a percentage (use percentage).

## Input

| Parameter | Type | Unit | Required | Description |
| --- | --- | --- | --- | --- |
| `a` | number |  | required | First term (numerator of the known ratio). Must not be 0. |
| `b` | number |  | required | Second term (denominator of the known ratio). Must not be 0. |
| `c` | number |  | required | Third term: the numerator paired with the unknown x. Must not be 0. |

## Output

| Field | Type | Unit | Description |
| --- | --- | --- | --- |
| `x` | number |  | The unknown fourth term, b × c / a. |
| `scale_factor` | number |  | c / a = x / b: the multiplier from the first pair to the second. |
| `ratio` | number |  | The common value of both fractions, a / b = c / x. |
| `equation` | string |  | The proportion with x filled in, e.g. '2/3 = 4/6'. |

## Formula

`a / b = c / x  ⇒  a × x = b × c  ⇒  x = b × c / a; scale_factor = c / a`

## Data Sources

- Wikipedia – Cross-multiplication — https://en.wikipedia.org/wiki/Cross-multiplication (reference, retrieved 2026-09-23)
- Wikipedia – Proportionality (mathematics) — https://en.wikipedia.org/wiki/Proportionality_(mathematics) (reference, retrieved 2026-09-23)

Data freshness: `static`. Deterministic formula with fixed constants; results never go stale. Inputs supplied by the caller determine the output.

## API

- `GET https://tttkmbb.com/api/v1/calculate/proportion?a=…&b=…&c=…`
- `POST https://tttkmbb.com/api/v1/calculate/proportion` with JSON body `{"inputs": {…}}`
- Response: unified envelope (`success`, `request`, `result.values`, `result.units`, `sources`, `freshness`, `timestamp`, `next_actions`, `links`); see https://tttkmbb.com/docs/response-format.md
- Schema: https://tttkmbb.com/api/v1/calculators/proportion · OpenAPI operationId `solve_proportion` in https://tttkmbb.com/openapi.json
- Authentication: none. Rate limit: fair use, see https://tttkmbb.com/docs/rate-limits.md.

## MCP

- Server: `https://tttkmbb.com/mcp` (Streamable HTTP, JSON-RPC 2.0, no auth)
- Tool:  `run_calculator` with `{"calculator_id": "proportion", "inputs": {…}}`

## Example

- 2/3 = 4/x: inputs `{"a":2,"b":3,"c":4}` → `{"x":6,"scale_factor":2,"ratio":0.666667,"equation":"2/3 = 4/6"}`
- 5/8 = 12.5/x: inputs `{"a":5,"b":8,"c":12.5}` → `{"x":20,"scale_factor":2.5,"ratio":0.625}`

```
GET https://tttkmbb.com/api/v1/calculate/proportion?a=2&b=3&c=4
```

## Limitations

You only want to simplify a ratio (use ratio) or the unknown is a percentage (use percentage). All values are computed from the formula above; no measurement or live data is involved.

## FAQ

**What if the unknown is in a different position?**

Rearrange so the unknown is last: a/b = c/x is equivalent to b/a = x/c, c/a = x/b and so on; all give x = b × c / a.

**Does this handle inverse proportion?**

No. For inverse proportion (a × b = c × x) compute x = a × b / c directly.

## Related

- [Ratio Calculator](https://tttkmbb.com/math/ratio.md) — Simplify or scale the ratio a:b.
- [Recipe Scaler](https://tttkmbb.com/food/recipe-scaler.md) — Proportional scaling of recipe quantities.
- [Percentage Calculator](https://tttkmbb.com/math/percentage.md) — Proportions with 100 as the base.