How do you find a missing value in a ratio?

If a:b = c:d and one value is missing, use cross multiplication. Example: 3:4 = x:12 → x = (3×12)÷4 = 9. So 3:4 = 9:12.

What is the difference between a ratio and a proportion?

A ratio compares two quantities (e.g. 3:4). A proportion states that two ratios are equal (e.g. 3:4 = 6:8). Proportions are used to solve problems where one value is unknown.

How do you scale a ratio?

To scale a ratio, multiply (or divide) all parts by the same number. Example: Scale 2:3 by factor 5 → 10:15. To scale to a total of 100, divide each part by the sum then multiply by 100.

📐 Math Calculator

Ratio Calculator

Simplify ratios, solve proportions, find missing values, scale ratios and compare — with step-by-step working shown.

Enter your ratio (A : B)

Result —

—Decimal

—As fraction

—Percentage

Visual ratio

📝 Step-by-step solution

Equivalent ratios

Multiplier	Ratio A	Ratio B	Ratio

Ratio calculator — all modes explained

A ratio expresses the relative size of two or more values. This calculator handles all four key ratio operations: simplifying, solving proportions, scaling and comparing.

🔢 Simplifying ratios

Divide both parts by their GCD (Greatest Common Divisor). Example: 24:16 → GCD=8 → 3:2. The simplified form is the smallest integer ratio that represents the same proportion.

🔍 Finding missing values

Use cross-multiplication: if a:b = c:d and d is unknown, then d = (b×c)÷a. This is used in map scales, recipe adjustments and unit conversions.

📏 Scaling ratios

Multiply each part by a scale factor. To reach a specific total, multiply each part by (target total ÷ sum of parts). Used in mixing, recipes and financial allocations.

⚖️ Comparing ratios

Convert each ratio to a decimal (A÷B) and compare. Equivalent ratios have the same decimal value. Also checks if they share the same simplified form.

Frequently asked questions

How do you simplify a ratio step by step?

Step 1: Find the GCD of both numbers using the Euclidean algorithm. Step 2: Divide both parts by the GCD. Example: Simplify 36:24. GCD(36,24) = 12. 36÷12 = 3. 24÷12 = 2. Answer: 3:2. You can verify by checking that no number greater than 1 divides both 3 and 2 evenly.

How do you convert a ratio to percentage?

To convert ratio A:B to percentages: Total parts = A+B. A% = A/(A+B) × 100. B% = B/(A+B) × 100. Example: 3:2 → Total = 5. A = 3/5 × 100 = 60%. B = 2/5 × 100 = 40%.

What is the difference between ratio and rate?

A ratio compares two quantities of the same unit (e.g. 3 boys to 4 girls). A rate compares two quantities of different units (e.g. 60 km per hour). Both are expressed as fractions, but rates always carry units (km/h, $/kg, etc.).

How are ratios used in real life?

Ratios are everywhere: cooking recipes (2 cups flour : 1 cup sugar), maps (1:50,000 scale), finance (debt-to-equity ratio), photography (aspect ratio 16:9), pharmacy (medication dosages), and construction (concrete mix 1:2:3 cement:sand:aggregate).