# Ratio Calculator

- **URL:** https://codeasystem.com/calculators/math/ratio-calculator/
- **Category:** math
- **Description:** Simplify any two-term ratio to lowest terms or solve the missing fourth term of a proportion a:b = c:d.
- **Primary output:** Simplified ratio: 8:3

## Inputs
- Mode (name: `mode`, type: select)
- Term a (name: `a`, type: number, example: 48)
- Term b (name: `b`, type: number, example: 18)
- Term c (solve mode) (name: `c`, type: number, example: 8)

## Outputs
- Simplified ratio: 8:3
- Divided both terms by: 6
- Decimal form: 2.666667

## Formula / methodology
```
Simplify: divide both terms by GCD(a, b)
Solve: d = (b × c) / a
```

Simplification divides both terms by their greatest common divisor; Euclid’s algorithm makes that instant even for large numbers. Solving cross-multiplies the proportion: multiplying b by c and dividing by a yields the fourth term that restores equality, with fractional answers kept to six decimals.

## Assumptions & limitations
- Ratio terms must be non-zero.
- Proportions assume term order matters: a corresponds to c, b corresponds to d.
- Fractional missing terms are shown rounded, not truncated.

## How to use
1. **Choose simplify or solve**; Two-term cleanup, or completing the proportion a:b = c:d.
2. **Enter the terms**; Term c only participates in solve mode; the field marks that clearly.
3. **Use the result**; Simplified ratios for recipes and scales; solved terms for scaling quantities up or down.

## Example
The ratio 48:18 simplifies to 8:3 once both terms divide by their GCD of 6.

Result for these inputs:

```
Simplified ratio: 8:3
```

## About this calculator
### Ratios are multiplication in disguise

Saying 48:18 equals 8:3 claims both pairs express the same scaling factor of roughly 2.67-to-1. Simplifying exposes that factor, making it obvious whether two recipes, gear trains or budgets truly match proportionally.

### Cross-multiplication, demystified

If a:b = c:d then a·d = b·c; the diagonals multiply equally. Isolating the unknown gives d = bc/a. This single identity powers unit conversions, map scales, screen aspect ratios and recipe resizing.

### When proportions mislead

Proportions assume linearity. Doubling a cake recipe doubles flour, but doubling a city’s population does not double commute times. Check that the underlying relationship really scales before trusting the fourth term.

## FAQs
### Can ratios contain decimals?

Yes; simplification still applies after scaling; the GCD handles non-integers by working with their exact floating-point values.

### What does solve mode actually find?

Given a, b and c it computes d so that a/b = c/d holds; the classic missing-term proportion problem.

### Why reject zero terms?

A zero term destroys the proportion’s meaning: division by zero is undefined, so validation stops it early.

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Last updated: 2026-08-23 · Version: 1.0.0 · [HTML version](https://codeasystem.com/calculators/math/ratio-calculator/)