How do I simplify a ratio?

Find the Greatest Common Divisor (GCD) of both numbers and divide each by it. For example, 12:8 has GCD 4, so it simplifies to 3:2.

How do I solve a proportion?

Use cross-multiplication. For A:B = X:D, multiply A × D = B × X, then solve for X = (A × D) / B.

What is the difference between a ratio and a fraction?

A ratio compares two quantities (3:2 means 3 parts to 2 parts). A fraction represents a part of a whole (3/5 means 3 out of 5 total parts).

How do I scale a ratio to a specific total?

Add the ratio parts, then divide the target total by that sum to get the multiplier. Multiply each part by the multiplier. For 3:2 scaled to 100: sum=5, multiplier=20, result=60:40.

Can ratios have more than two parts?

Yes. Ratios like 2:3:5 are common in recipes and mixing. The same simplification rules apply — divide all parts by their GCD.

Ratio Calculator — Simplify & Solve Ratios

Simplify any ratio to its lowest terms, scale a ratio to a target total, or solve a proportion with a missing value. It is useful for common searches like 4 to 3 ratio calculator, 2 3 ratio calculator, and 3 2 ratio calculator.

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How This Ratio Calculator Works

This ratio calculator simplifies ratios, scales them to a total, and solves missing values in proportions. If you searched for a 4 to 3 ratio calculator, 2 3 ratio calculator, or 3 2 ratio calculator, enter those numbers directly above and the tool will show the simplified result and the working behind it.

What Are Ratios?

A ratio compares two or more quantities, showing how much of one thing there is relative to another. Written as A:B, it means "for every A of the first quantity, there are B of the second." Ratios are used everywhere — in cooking recipes (flour to sugar), map scales (1:50,000), financial analysis (debt-to-income), and mixing solutions (paint, concrete, cocktails).

Key Ratio Formulas

Simplify: A:B → (A/GCD) : (B/GCD)

Scale: A:B to total T → A×(T/(A+B)) : B×(T/(A+B))

Proportion: A:B = C:D → A×D = B×C (cross-multiply)

Common Ratio Calculator Examples

4:3 ratio calculator: Scale 4:3 to 70 total and you get 40:30 because the seven total parts divide evenly into the target.

3:2 ratio calculator: Scale 3:2 to 100 and you get 60:40, a common use case for recipes, screen crops, and budget splits.

2:3 ratio calculator: Scale 2:3 to 50 and you get 20:30, which is useful for mixture problems and allocation planning.

Recipes: A bread recipe calls for flour to water in a 5:3 ratio. If you use 500g of flour, you need 300g of water. Scaling up: for 2kg flour, you need 1.2kg water.

Maps: A 1:25,000 map scale means 1 cm on the map equals 25,000 cm (250 meters) in real life. A 4 cm distance on the map represents 1 km.

Finance: A debt-to-income ratio of 36:100 (or 0.36) means 36% of your income goes to debt payments. Lenders prefer this ratio below 43%.

Simplifying and Scaling Ratios

To simplify a ratio, find the Greatest Common Divisor (GCD) of all parts and divide each part by it. The GCD is found using the Euclidean algorithm: repeatedly divide the larger number by the smaller and take the remainder until the remainder is zero. For example, GCD(12, 8): 12 = 1×8 + 4, then 8 = 2×4 + 0. GCD = 4. So 12:8 = 3:2.

Solving Proportions and Cross-Multiplication

A proportion states that two ratios are equal: A/B = C/D. To find a missing value, cross-multiply: A×D = B×C. Then solve for the unknown. This technique is used in scale drawings, unit conversions, recipe scaling, and similarity problems in geometry. Proportional reasoning is one of the most practical math skills, appearing in everything from calculating exchange rates to resizing images without distortion. Mastering cross-multiplication allows you to solve any proportion problem quickly and confidently.