What is the Golden Ratio?

The Golden Ratio (phi = 1.618...) is an irrational number where a/b = (a+b)/a. It appears in nature (spiral shells, flower petals), art (Renaissance compositions), and architecture (Parthenon proportions), though some claims are debated.

How do I simplify a ratio?

Divide both numbers by their Greatest Common Divisor (GCD). For 1920:1080, the GCD is 120, giving 16:9. The calculator finds the GCD automatically and shows the simplified form.

What are common screen aspect ratios?

4:3 for classic TV/monitors, 16:9 for HDTV and most screens, 21:9 for ultrawide monitors, 9:16 for vertical video, and 1:1 for square social media content. Film uses 1.85:1 and 2.39:1.

How do I convert a ratio to a percentage?

Divide the first number by the sum of both numbers and multiply by 100. A 3:2 ratio means 3/(3+2) * 100 = 60% for the first part and 40% for the second.

What is the difference between a ratio and a fraction?

A ratio (3:2) compares two quantities to each other. A fraction (3/5) represents a part of the whole. The ratio 3:2 means 3 parts to 2 parts; as fractions, that is 3/5 and 2/5 of the total.

How do I use this tool in Claude/Cursor?

You can use this tool via MCP. Add the Toolypet MCP server to your AI agent configuration with 'npx -y @toolypet/mcp-server@latest'. Then ask your AI to use mcp__toolypet__ratio_calculator with your parameters.

What is MCP and why does Toolypet support it?

MCP (Model Context Protocol) is an open standard that lets AI agents like Claude and Cursor use external tools. Toolypet supports MCP so you can use all 65+ tools both in the browser and through AI agents, making calculations and operations seamlessly integrated into your AI workflow.

Ratio Calculator

What Is This?

Ratio Calculator simplifies, scales, and compares ratios. It finds equivalent ratios, solves proportions, converts ratios to fractions/decimals/percentages, and helps with design aspect ratios, recipe scaling, and mathematical proportion problems.

Input

First Value (A)

Second Value (B)

Formula: A:B = ?

How to Use

Enter a ratio like 16:9 or values as A:B. The tool simplifies it to lowest terms, shows equivalent ratios, and converts to fraction and decimal forms. For scaling, enter a target value for one side to find the proportional other side.

Deep Dive

The Golden Ratio (phi, approximately 1.618:1) has fascinated mathematicians since ancient Greece. Two quantities are in the golden ratio when their ratio equals the ratio of their sum to the larger quantity: (a+b)/a = a/b. It appears in the Fibonacci sequence (each consecutive pair's ratio approaches phi), sunflower seed spirals (137.5-degree divergence angle), and the proportions of a regular pentagon. In design and media, aspect ratios define the relationship between width and height. The most common screen ratios tell a story of technological evolution: 4:3 (1.33:1) dominated early television and CRT monitors. 16:9 (1.78:1) became the HDTV standard in the 1990s, chosen as a mathematical compromise between 4:3 and the wider cinema formats. 21:9 (2.33:1) ultrawide monitors approximate the cinema standard. Film uses 2.39:1 (CinemaScope/anamorphic widescreen) and 1.85:1 (standard US theatrical). Mobile devices introduced new ratios: 9:16 (vertical video), 19.5:9 (modern smartphones like iPhone), and 20:9 (many Android devices). Instagram uses 1:1 (square), 4:5 (portrait), and 1.91:1 (landscape). Understanding these ratios is essential for responsive design - a 16:9 image cropped to 1:1 loses 44% of its width. In cooking, scaling ratios preserves flavor balance. Baker's percentages express all ingredients as a percentage of flour weight, making it trivial to scale: 60% hydration bread uses 600g water per 1000g flour, regardless of batch size.

Examples

Simplify the ratio 1920:1080 to its lowest terms: 16:9 (dividing both by GCD of 120)
Scale a recipe from 4 servings to 6: multiply all ingredient ratios by 1.5
Find the missing value in a proportion: if 3:5 = x:20, then x = 12

Install Toolypet MCP Server

Add Toolypet tools to your AI agent with a single command. Works with Claude Desktop, Claude Code, Cursor, and any MCP-compatible client.

Quick Start

npx -y @toolypet/mcp-server@latest

MCP Client Configuration

{
  "mcpServers": {
    "toolypet": {
      "command": "npx",
      "args": [
        "-y",
        "@toolypet/mcp-server@latest"
      ]
    }
  }
}

Tool Name:mcp__toolypet__ratio_calculator

Example Prompt

Use mcp__toolypet__ratio_calculator to ...

Frequently Asked Questions

What is the Golden Ratio?: The Golden Ratio (phi = 1.618...) is an irrational number where a/b = (a+b)/a. It appears in nature (spiral shells, flower petals), art (Renaissance compositions), and architecture (Parthenon proportions), though some claims are debated.
How do I simplify a ratio?: Divide both numbers by their Greatest Common Divisor (GCD). For 1920:1080, the GCD is 120, giving 16:9. The calculator finds the GCD automatically and shows the simplified form.
What are common screen aspect ratios?: 4:3 for classic TV/monitors, 16:9 for HDTV and most screens, 21:9 for ultrawide monitors, 9:16 for vertical video, and 1:1 for square social media content. Film uses 1.85:1 and 2.39:1.
How do I convert a ratio to a percentage?: Divide the first number by the sum of both numbers and multiply by 100. A 3:2 ratio means 3/(3+2) * 100 = 60% for the first part and 40% for the second.
What is the difference between a ratio and a fraction?: A ratio (3:2) compares two quantities to each other. A fraction (3/5) represents a part of the whole. The ratio 3:2 means 3 parts to 2 parts; as fractions, that is 3/5 and 2/5 of the total.
How do I use this tool in Claude/Cursor?: You can use this tool via MCP. Add the Toolypet MCP server to your AI agent configuration with 'npx -y @toolypet/mcp-server@latest'. Then ask your AI to use mcp__toolypet__ratio_calculator with your parameters.
What is MCP and why does Toolypet support it?: MCP (Model Context Protocol) is an open standard that lets AI agents like Claude and Cursor use external tools. Toolypet supports MCP so you can use all 65+ tools both in the browser and through AI agents, making calculations and operations seamlessly integrated into your AI workflow.