Ratio Calculator

Solve ratio problems, scale ratios, and simplify ratios with step-by-step solutions. Free online ratio calculator for all your proportion needs.

Solve Proportion

Enter any three values of the proportion $a:b = c:d$ to find the missing fourth.

a:b

a:b = c:d

c:d

Missing Value

Enter values and click "Calculate" to see detailed steps.

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Ratio Calculator

This free online ratio calculator solves proportions, scales ratios, and reduces ratios to their simplest form instantly in your browser. No signup, no ads, no server uploads.

What is a Ratio? A ratio is a relationship between two or more numbers that expresses how many times one quantity is contained within another. Ratios are written as $a:b$ (read "a to b") or as a fraction $a/b$. If a recipe calls for 2 cups of flour for every 1 cup of sugar, the ratio of flour to sugar is $2:1$.

What is a Proportion? A proportion is an equation that states two ratios are equal: $a:b = c:d$ or $\frac{a}{b} = \frac{c}{d}$. When three of the four values are known, the missing value can be found using cross-multiplication:

$$a \times d = b \times c$$

Rearranging: - If $a$ is unknown: $a = \frac{b \times c}{d}$ - If $b$ is unknown: $b = \frac{a \times d}{c}$ - If $c$ is unknown: $c = \frac{a \times d}{b}$ - If $d$ is unknown: $d = \frac{b \times c}{a}$

How to Use This Calculator The tool has three modes:

1. Solve Proportion: Enter any three values of $a:b = c:d$ to find the missing fourth. The solution includes the cross-multiplication step and the result.

2. Scale Ratio: Enter a ratio $a:b$ and a scale factor $k$ to get the scaled ratio $(a \times k):(b \times k)$. Useful for recipes, maps, architectural drawings, and model building.

3. Simplify Ratio: Enter a ratio $a:b$ to reduce it to its simplest form. The calculator finds the GCD (greatest common divisor) and divides both terms. It also displays equivalent fractions, decimal value, and percentage.

Applications of Ratios Ratios are used in countless everyday contexts:

- Cooking & Baking: Scaling recipe ingredients up or down - Maps & Scale Drawings: Understanding map scales like $1:100,000$ - Finance: Price-to-earnings ratios, debt-to-income ratios - Engineering: Gear ratios, mixing ratios for concrete or chemicals - Design: Aspect ratios for screens and images ($16:9$, $4:3$) - Education: Student-to-teacher ratios, test score proportions - Photography: Aperture ratios, crop factors

Privacy & Performance All calculations run locally in your browser. No data is transmitted, logged, or stored on any server. Results appear instantly with no page reloads.

🔒 Client-side only⚡ Web Worker processing🌐 Works offline🛡️ Zero server logs

Frequently Asked Questions

Got questions about ratios, proportions, or how to use this tool? We've got answers.

What is a ratio?

A ratio is a comparison of two or more quantities, showing how many times one quantity is contained within another. It is typically written as $a:b$ or $a/b$ and read as "a to b". For example, a ratio of $3:2$ means for every 3 units of the first quantity, there are 2 units of the second.

What is a proportion?

A proportion is an equation stating that two ratios are equal: $a:b = c:d$ or $\frac{a}{b} = \frac{c}{d}$. To solve a proportion, use cross-multiplication: $a \times d = b \times c$. If you know three of the four values, you can find the missing one.

How do you simplify a ratio?

To simplify a ratio $a:b$, find the greatest common divisor (GCD) of $a$ and $b$, then divide both terms by the GCD. For example, $12:8$ simplifies to $3:2$ because $\gcd(12,8) = 4$, and $12 \div 4 = 3$, $8 \div 4 = 2$.

What are equivalent ratios?

Equivalent ratios are ratios that have the same simplified value. For example, $2:3$, $4:6$, $6:9$, and $10:15$ are all equivalent because they all simplify to $2:3$. Multiplying or dividing both terms of a ratio by the same non-zero number produces an equivalent ratio.

What is the golden ratio?

The golden ratio ($\varphi \approx 1.618$) is a special number that appears when two quantities are in proportion such that the ratio of the sum to the larger equals the ratio of the larger to the smaller: $\frac{a+b}{a} = \frac{a}{b} = \varphi$. It appears throughout nature, art, architecture, and mathematics — from the spiral arrangement of sunflower seeds to the proportions of the Parthenon.

How do you scale a ratio?

Scaling a ratio $a:b$ by a factor $k$ means multiplying both terms by $k$ to get $(a \times k):(b \times k)$. For example, scaling $2:3$ by a factor of $5$ gives $10:15$. Scaling preserves the relationship between the quantities — it produces an equivalent ratio.

Is this calculator private?

Yes. All calculations run locally in your browser. No data is transmitted, logged, or stored on any server.