Universal Calculator
TAIIR

Ratio Calculator

Solve proportions, simplify ratios, scale to any value, and compare ratios. Instant results with step‑by‑step explanations.

Leave one field empty to solve for the unknown

: = :
A : B = C : D (leave one blank to solve)

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Ratio Formulas

Proportion: A:B = C:D ⇔ A·D = B·C
Simplify: divide by GCD(A, B)
Scale: part = (ratio / sum) × total
Compare: A₁/B₁ vs A₂/B₂

Mastering Ratios and Proportions: The Complete Guide

A ratio is a comparison of two quantities, showing how many times one value contains or is contained within the other. Ratios are ubiquitous in mathematics, science, engineering, cooking, art, and finance. This Professional Ratio Calculator provides four essential tools: solving proportions, simplifying ratios, scaling ratios to a total, and comparing two ratios. Each calculation is accompanied by a clear step‑by‑step explanation and visual breakdown.

Solving Proportions with Cross‑Multiplication

A proportion states that two ratios are equal: A:B = C:D. The most reliable way to solve for an unknown term is cross‑multiplication: A × D = B × C. If one value is missing, you can rearrange to isolate it. For example, to find A when B, C, and D are known: A = (B × C) / D. This method works for any real numbers (provided denominators are non‑zero).

💡 Example: x:5 = 3:15

Cross multiply: x·15 = 5·3 → 15x = 15 → x = 1.

Simplifying Ratios

To simplify a ratio to its lowest terms, divide both sides by their greatest common divisor (GCD). For example, 24:36 simplifies to 2:3 because GCD(24, 36) = 12. If the ratio contains decimals, first multiply by a power of 10 to obtain integers, then simplify. A simplified ratio expresses the same relationship using the smallest possible whole numbers.

Scaling Ratios

Scaling a ratio distributes a total quantity proportionally. Given a ratio A:B and a total T, the two parts are (A/(A+B)) × T and (B/(A+B)) × T. This is essential for dividing resources, mixing ingredients, or allocating budgets according to a specified ratio.

Comparing Ratios

To determine which of two ratios is larger, you can convert each to a decimal (divide the first term by the second) and compare the results. Alternatively, cross‑multiply the ratios as if they were a proportion. The calculator not only tells you which ratio is larger but also simplifies both to their lowest terms for easy comparison.

Frequently Asked Questions

How do I convert a ratio to a percentage?

Add the ratio terms to get the total parts. Then each term's percentage = (term / total) × 100. For 3:4, total = 7 → 3/7 ≈ 42.9% and 4/7 ≈ 57.1%.

What is the golden ratio?

The golden ratio φ ≈ 1.618:1. It appears in nature, art, and architecture. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger quantity.

Can ratios have more than two terms?

Yes. Ratios like 2:3:5 compare three quantities. The Scale tab works with two‑term ratios; for more terms, add the parts and scale each accordingly.

Why do I get a decimal when simplifying?

If the ratio contains decimals, the calculator first multiplies by a power of 10 to clear them, then simplifies. The result is always a whole‑number ratio.

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