Mathematical Proportions

Free Online Ratio Calculator

Simplify ratios to lowest terms, solve for missing proportional values (A:B = C:D), and scale aspect ratios for screen resolution, recipes, and geometry.

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Ratio Simplification

Reduce complex integer and decimal ratios to their simplest lowest whole-number terms.

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Solve for Missing X

Solve equivalent proportions with ease using cross-multiplication (A:B = C:X).

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Aspect Ratio Scaling

Scale screen dimensions, photography canvas sizes, and recipe ingredient batches.

Understanding Ratios and Mathematical Proportions

A ratio expresses the quantitative relationship between two numbers, indicating how many times the first value contains the second. Proportions state that two ratios are mathematically equal. They are ubiquitous in graphic design, photography aspect ratios (16:9, 4:3), cooking, and chemistry.

1
Choose Ratio Problem

Select ratio simplification (A:B) or 4-value proportion solving (A:B = C:D).

2
Enter Known Values

Input your integers or decimals into the corresponding terms.

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Calculate Equivalent Ratio

Get the reduced lowest-terms answer and exact missing variable value.

Frequently Asked Questions

How do you simplify a ratio to lowest terms?
Find the greatest common divisor (GCD) of both numbers and divide each number by that GCD. For example, 12:18 divides by 6 to yield 2:3.
How do you solve a proportion like A:B = C:D for an unknown?
Use cross-multiplication: A × D = B × C. If D is unknown, D = (B × C) / A.
What are common aspect ratios used in digital media?
Common aspect ratios include 16:9 (widescreen monitors & YouTube), 9:16 (vertical mobile video & TikTok/Reels), 1:1 (square social posts), and 4:3 (classic displays).