Free Online Ratio Calculator

Solve ratios, find missing values, and scale proportions easily.

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Solve Ratio Proportion

Find X in: A:B = C:X

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Understanding Ratios

A ratio compares two quantities. It can be written as A:B, A/B, or "A to B." Ratios are used in cooking, mixing, scaling, and many applications.

Solving Proportions

If A:B = C:X, then X = (B × C) ÷ A

Example: If 2:3 = 10:X, find X

X = (3 × 10) ÷ 2 = 30 ÷ 2 = 15

Common Applications

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What is a Ratio?

A ratio compares two or more quantities, showing how much of one there is relative to another. Written as 3:4, it says that for every three units of the first quantity there are four of the second. Ratios underpin recipe scaling, map reading, mixing concrete, screen dimensions and financial analysis. A ratio calculator simplifies ratios, scales them and solves proportions where one value is unknown.

How to Use This Ratio Calculator

  1. Enter the ratio you have.Type both parts, such as 18 and 24, and the calculator reduces it to its simplest form.
  2. Solve for a missing value.Enter three known values in a proportion and leave the fourth blank to find it by cross-multiplication.
  3. Scale as needed.Multiply or divide every part by the same factor to enlarge or reduce while keeping the proportion intact.

Simplifying a Ratio

Simplifying means expressing the same relationship with the smallest whole numbers possible. The method is to divide every part by their greatest common factor.

Simplify: divide each part by the greatest common factor (GCF)
Solve a proportion: if a : b = c : x, then x = (b x c) / a
Scale: multiply every part by the same factor

Worked Example: Simplifying and Scaling

A concrete mix given as 90:180:270 (cement : sand : gravel)

Step 1: Find the greatest common factor

Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90 The largest number dividing 90, 180 and 270 evenly is 90

Step 2: Divide every part by 90

90 / 90 = 1 180 / 90 = 2 270 / 90 = 3

Step 3: Scale to a real batch needing 4 buckets of cement

Scaling factor = 4 / 1 = 4 1 : 2 : 3 becomes 4 : 8 : 12

The mix simplifies to 1:2:3, which for 4 buckets of cement means 8 sand and 12 gravel

Solving Proportions by Cross-Multiplication

A proportion states that two ratios are equal. When one value is missing, cross-multiplication finds it in one step.

A map scale where 2 cm represents 5 km. How far is 7 cm?

Set up the proportion: 2 : 5 = 7 : x Cross-multiply: 2 x X = 5 x 7 2x = 35 x = 17.5

7 cm on the map represents 17.5 km on the ground

Common Ratios You Meet Every Day

ContextTypical RatioMeaning
Widescreen displays16:916 units wide for every 9 tall
A-series paper1:1.414Halving keeps the same proportion
Standard concrete1:2:3Cement, sand, gravel by volume
Rice and water1:2One cup rice to two cups water
Golden ratio1:1.618Used in design and architecture
Debt-to-equityVariesCompany debt relative to shareholder equity
Keep the order consistent

The order of a ratio carries meaning. A cement-to-water ratio of 2:1 is not the same as 1:2, and confusing them ruins the mix. When setting up a proportion, make sure both sides list quantities in the same order, or the cross-multiplication will produce a wrong answer that looks perfectly reasonable.

Ratios in Practice

Cooking and baking

Baking is essentially applied ratios. A basic shortcrust pastry is often given as 1:2:3 by weight for sugar, fat and flour. Because the relationship rather than the absolute quantity determines the result, the same ratio works for a small tart or a large one.

Maps, models and drawings

A scale of 1:25,000 means one unit on the map equals 25,000 of the same units on the ground. Architectural drawings and scale models work identically, which is why proportion problems are the everyday mathematics of construction.

Business and finance

Financial analysis is largely ratio work: current ratio, debt-to-equity, price-to-earnings. Each compresses two figures into one comparable number, which is what makes companies of different sizes comparable at all.

Ratios with more than two parts

Ratios extend to any number of quantities, such as 2:3:5 for a three-way split. To divide a total using such a ratio, add the parts to get the total share count, then divide. Splitting 500 in the ratio 2:3:5 means ten shares of 50, giving 100, 150 and 250.

People Also Ask

Divide every part of the ratio by their greatest common factor. For 18:24, the greatest common factor is 6, so dividing both gives 3:4. A ratio is fully simplified when no whole number greater than one divides all parts evenly.
Cross-multiply. If 3:4 equals 9:x, multiply 3 by x and 4 by 9, giving 3x equals 36, so x is 12. Cross-multiplication works because equal ratios have equal cross products, which is the defining property of a proportion.
A fraction compares a part to the whole, while a ratio usually compares one part to another part. If a class has 12 boys and 18 girls, the ratio of boys to girls is 12:18 or 2:3, but the fraction of the class that is boys is 12 out of 30, which is 2/5. Both use division, but they answer different questions.
Find the scaling factor by dividing your target quantity by the original, then multiply every ingredient by that same factor. A recipe for four scaled to six has a factor of 1.5, so every ingredient increases by half. Keeping all parts in the same proportion is what preserves the result.
The golden ratio is approximately 1.618 to 1, a proportion that appears in geometry and has been used in art and architecture for centuries. It has the unusual property that the ratio of the whole to the larger part equals the ratio of the larger part to the smaller. Claims about its universal appearance in nature are often overstated, but the mathematics itself is genuine.

📚 Sources & References

  1. National Council of Teachers of Mathematics — Standards for teaching ratio and proportional reasoning.
  2. Khan Academy — Free lessons on ratios, rates and proportions.
  3. NIST — Measurement standards relevant to scaling and proportion.

This calculator is provided for educational purposes. For engineering, construction or structural applications, follow the specifications set by a qualified professional and applicable standards.