Ratio Calculator

Solve proportions and find the missing value in A:B = C:D. Simplify ratios, scale recipes, convert map distances, and work with any proportional relationship.

Solve A:B = C:D. Enter any 3 values and leave one blank.

What Is a Ratio Calculator?

A ratio calculator solves proportions — equations where two ratios are equal. Given three values out of four in the relationship A:B = C:D, it finds the missing number by cross-multiplication. Ratios describe the relative size of two or more quantities and appear everywhere from cooking and construction to chemistry and cartography.

Proportional reasoning is one of the most practical mathematical skills. Builders use ratios for cement mixes (1:2:4 for cement, sand, and gravel). Cooks scale recipes up or down by maintaining ingredient ratios. Map readers convert distances using the scale ratio. Nurses calculate drug dosages based on patient weight ratios. In each case, the underlying maths is the same cross-multiplication method.

This calculator also simplifies ratios to their lowest terms by dividing both sides by their greatest common divisor (GCD). A ratio of 12:8 simplifies to 3:2, making it easier to understand and communicate. Whether you are comparing financial figures, mixing paints, or dividing a sum between people, this tool handles the arithmetic instantly.

How Do You Use This Ratio Calculator?

Enter three of the four values in the proportion A:B = C:D and leave the unknown blank. Click Calculate to solve for the missing value. The calculator also shows the simplified form of each ratio.

Enter the first ratio value (A) in the first field.
Enter the second ratio value (B) in the second field.
Enter the known value from the second ratio (C or D) in the appropriate field.
Leave the unknown field blank — the calculator will solve for it.
Click Calculate to find the missing value using cross-multiplication.
Review the simplified ratio and the full proportion shown in the results.

How Does the Ratio Calculator Formula Work?

The formula used: A/B = C/D → D = (B × C) / A; Simplified ratio: divide both terms by their GCD

Ratios express how two quantities relate. A proportion states that two ratios are equal: A:B = C:D. To find the missing value, cross-multiply and solve.

A/B = C/D → A × D = B × C → D = (B × C) / A

To simplify a ratio, find the greatest common divisor (GCD) of both terms and divide each by it. For example, 18:12 → GCD is 6 → simplified ratio is 3:2. This preserves the proportional relationship while using the smallest whole numbers possible.

What Are Some Example Calculations?

If 3:5 = 12:x, then x = (5 × 12) / 3 = 20. The proportion 3:5 = 12:20 is correct because both ratios simplify to 3:5.

A map has a scale of 1:50,000. A distance on the map measures 3.5 cm. What is the real distance?

1:50,000 = 3.5:x. Cross-multiply: x = 3.5 × 50,000 = 175,000 cm = 1.75 km.

The real distance is 1.75 km (175,000 cm).

A recipe for 4 people uses 300g flour. How much flour for 10 people?

4:300 = 10:x. Cross-multiply: x = (300 × 10) / 4 = 750g.

You need 750g of flour for 10 people.

Divide £600 in the ratio 2:3 between two partners.

Total parts = 2 + 3 = 5. Each part = £600 / 5 = £120. Partner A = 2 × £120 = £240. Partner B = 3 × £120 = £360.

Partner A receives £240 and Partner B receives £360.

When Should You Use a Ratio Calculator?

Use the ratio calculator whenever two quantities must stay in proportion. Scale recipes for different serving sizes, convert map or model distances to real-world measurements, mix materials in specified ratios (concrete, paint, chemical solutions), or divide money, time, or resources between groups. It is also essential for solving proportion problems in GCSE and A-level maths.

The calculator is equally useful in business contexts. Financial analysts compare revenue-to-cost ratios across departments. Marketers track conversion ratios. Engineers maintain gear ratios in mechanical designs. Any situation where one quantity depends proportionally on another calls for ratio mathematics.

What Do These Terms Mean?

Ratio

A comparison of two or more quantities showing their relative sizes, written as A:B or A/B.

Proportion

An equation stating that two ratios are equal, such as A:B = C:D.

Cross-multiplication

A method for solving proportions: multiply the numerator of each fraction by the denominator of the other (A × D = B × C).

Greatest Common Divisor (GCD)

The largest number that divides evenly into both terms of a ratio, used to simplify it to lowest terms.

Scale Factor

The multiplier that converts one ratio term to the corresponding term in an equivalent ratio.

What Are the Best Tips to Know?

Always simplify ratios before comparing them — 12:8 and 9:6 both simplify to 3:2, showing they are equivalent.
When dividing an amount by a ratio, first add the parts to find the total number of shares.
Check your answer by verifying both ratios reduce to the same simplified form.
For three-part ratios like 2:3:5, extend the cross-multiplication to each pair or divide the total by the sum of parts.
Convert units before calculating — mixing cm and metres in the same ratio gives incorrect results.

What Mistakes Should You Avoid?

Cross-multiplying incorrectly — A/B = C/D means AD = BC, not AB = CD.
Forgetting to convert units so both sides of the proportion use the same measurement.
Confusing ratio order — 2:5 is not the same as 5:2. The order must match the quantities described.
Adding ratio parts incorrectly when dividing a total — the sum of all parts is the divisor, not the number of parts.

Frequently Asked Questions

How do I solve A:B = C:? for the missing value?

Use cross-multiplication. If A:B = C:D, then D = (B × C) / A. Enter your three known values and the calculator finds the fourth.

What is the difference between a ratio and a fraction?

A ratio compares two separate quantities (e.g., 3 boys to 5 girls = 3:5). A fraction represents a part of a whole (e.g., 3/8 of the class are boys). The ratio 3:5 corresponds to fractions 3/8 and 5/8.

Can ratios have decimals?

Yes, but they are usually converted to whole numbers for clarity. Multiply both sides by 10, 100, etc. to eliminate decimals. For example, 1.5:2.5 becomes 3:5.

How do I divide an amount into a given ratio?

Add the ratio parts to get the total shares. Divide the amount by this total to find one share. Then multiply each ratio part by the value of one share.

What is a three-part ratio?

A ratio like 2:3:5 compares three quantities. To divide £1,000 in this ratio: total parts = 10, each part = £100, so the split is £200, £300, £500.

Are 2:4 and 1:2 the same ratio?

Yes, they are equivalent ratios. Dividing both terms of 2:4 by their GCD (2) gives 1:2. Equivalent ratios represent the same proportional relationship.

How do ratios relate to percentages?

A ratio can be converted to percentages by dividing each part by the total. The ratio 1:4 means 1/5 = 20% and 4/5 = 80%. This is useful for presenting proportions in reports.

More Maths & Conversion Calculators

Percentage Calculator → Fraction Calculator → Area Calculator → Average Calculator → Quadratic Equation Solver → Exponent Calculator → LCM & HCF Calculator → Roman Numeral Converter → Scientific Notation Converter → Prime Number Calculator →

View all maths & conversion calculators →