Ratio Calculator

How to use this calculator

1. Enter the two sides of the ratio as whole numbers.
2. The calculator divides both by their greatest common divisor to reach the simplest form.

The formula

GCD

Greatest common divisor — the largest whole number dividing both A and B

How it works

Two ratios are equivalent when one is a scaling of the other. 24:36 is the same relationship as 2:3 because both sides were divided by 12.

The greatest common divisor is found with the Euclidean algorithm: repeatedly replace the larger number by the remainder of the division until the remainder is zero.

Simplifying and comparing ratios

Reducing a ratio works exactly like reducing a fraction: divide every term by their greatest common divisor. The ratio 120:180 becomes 2:3, which is far easier to hold in your head and to communicate on a drawing or a label.

To compare two ratios, convert each to a single number by dividing the first term by the second, or rewrite both with a common second term. 5:8 and 7:11 are close, but 0.625 versus 0.636 settles which is larger.

Solving proportions with cross multiplication

When two ratios are equal, the product of the outer terms equals the product of the inner terms. Given a : b = c : x, the missing value is x = (b × c) ÷ a. This one identity underpins map scales, unit pricing, recipe scaling, model dimensions, and dosage calculations.

Keep the order consistent. If the first ratio lists parts as concentrate to water, the second must list them in the same order, or the answer will be inverted.

Part-to-part versus part-to-whole

A ratio of 3:2 means three parts of one thing for every two of another, making five parts in total. The first item is therefore 3/5, or 60%, of the whole — not 3/2. Confusing part-to-part with part-to-whole is the most common ratio error in mixing, budgeting, and reporting.

When a ratio has more than two terms, the same logic applies: sum all terms to find the whole, then express each term over that total to convert to fractions or percentages.

Scaling ratios up and down

Multiplying or dividing every term of a ratio by the same number leaves it unchanged. 3:2 is the same relationship as 6:4 and 30:20, just at a different scale.

This is what makes ratios useful for recipes, mixes, and models — you fix the relationship once and scale it to whatever total quantity you need.

To hit a specific total, add the parts, divide the total by that sum, and multiply each part by the result. Splitting 450 in a 3:2 ratio gives 450 / 5 = 90 per part, so 270 and 180.

Ratios, fractions, and percentages

A part-to-whole ratio converts directly to a fraction and then to a percentage. In 3:2, the first part is 3/5 of the total, or 60%.

A part-to-part ratio does not convert directly — 3:2 is not 3% and 2%. Add the parts first to get the whole, then express each share against it.

Being explicit about which kind of ratio you have prevents most of the confusion in mixing instructions and financial ratios alike.

Common mistakes with ratios

Reversing the order changes the meaning. A 2:1 concentrate mix is not the same as 1:2, and the difference matters for paint, fuel, and chemicals.

Adding ratios together is not valid. Two batches at 3:2 and 5:1 combine only once you convert both to actual quantities.

Confusing '1:4' with 'one in four' is common. In mixing conventions, 1:4 usually means one part to four parts, giving five parts total, whereas one in four means 25%.

Solving proportions in practice

A proportion is two equal ratios: a/b = c/d. Cross-multiplying gives ad = bc, and you solve for whichever term is unknown.

Map scales, currency conversion, unit pricing, and dosage calculations are all proportions. If 3 metres of cable costs 7.50, then 8 metres costs 8 x 7.50 / 3 = 20.

Always check that the units line up on both sides before cross-multiplying — mismatched units are the main source of wrong answers here.

Where ratios are used

In cooking and mixing: water to rice, concrete to sand, fuel to oil, concentrate to water. In business: debt-to-equity, current ratio, staff-to-customer, cost-to-income.

In design and photography: aspect ratios such as 16:9 and 3:2 describe shape independently of size, which is why they survive every resolution change.

In sport and education: win-loss records, pupil-teacher ratios, and odds are all ratios read as relationships rather than absolute counts.

Glossary and verification

Term: each number in the ratio. Antecedent: the first term. Consequent: the second. Simplified ratio: all terms divided by their greatest common divisor.

Verify a split by adding the resulting parts and confirming they equal the original total.

Verify a simplification by dividing the terms of both the original and the simplified version — the quotients should match, for example 30 / 20 = 3 / 2 = 1.5.

Ratios, fractions, and rates

A ratio compares two quantities of the same kind, a fraction expresses a part of a whole, and a rate compares different units such as kilometres per hour. Mixing them is the source of most ratio confusion.

A mix of 2:3 means five parts in total, so the first component is two fifths — 40% — not two thirds. Reading a ratio as a fraction of the other part rather than of the whole is a routine error.

Ratios can be scaled freely as long as every term is multiplied by the same number, which is exactly what makes them useful for recipes and mixes.

Scaling mixtures and sharing amounts

To share 840 in the ratio 3:4:5, add the parts to get twelve, divide the total by twelve to get 70 per part, then multiply out to 210, 280, and 350.

The same method scales concrete mixes, paint tints, fuel-oil blends, and staffing ratios. Always confirm the shares add back to the original total.

For dilution ratios, check whether the notation means part-to-part or part-to-total — 1:4 can mean one in five or one in four depending on the industry.

Aspect ratios and geometry

Screen and image sizes use ratios such as 16:9 and 4:3. Resizing while preserving the ratio means multiplying both dimensions by the same factor.

Scale models, map scales, and architectural drawings work identically: a 1:50 drawing means one unit on paper equals fifty in reality.

Distorting an image comes from applying different factors to width and height, which is a broken ratio rather than a rounding issue.

Verification

Simplify by dividing every term by their greatest common divisor, then confirm the simplified ratio still reproduces the original quantities when scaled.

Convert each part to a percentage of the total and check they sum to 100%.

For proportion problems, cross-multiply and confirm both products match.

Ratios, rates, and proportions

A ratio compares two quantities of the same kind, a rate compares different kinds such as miles per hour, and a proportion states that two ratios are equal. Mixing the three leads to unit errors.

Solving a proportion means cross-multiplying and dividing, which is the arithmetic behind scaling recipes, maps, and drawings alike.

Part-to-part ratios and part-to-whole ratios answer different questions: three to one is the same mixture as three quarters to one quarter, stated differently.

Always label which quantity comes first, because reversing a ratio inverts the relationship entirely.

Mixing and dilution

Concrete, fuel mixes, fertiliser, and cleaning solutions are all specified as ratios, and getting the order wrong can ruin a batch or damage equipment.

To find the amount of each part, add the ratio terms to get the total number of parts, divide the batch size by that total, then multiply by each term.

A one-to-fifty two-stroke mix means one part oil to fifty parts fuel, giving fifty-one parts in total — not one part in fifty.

When scaling a mix up or down, scale every term by the same factor; changing one term alone changes the product, not just its quantity.

Ratios in analysis and finance

Financial ratios such as debt to equity or price to earnings compress two figures into one comparable number, but only compare meaningfully within the same industry.

Aspect ratios describe shape rather than size, so a sixteen-to-nine image keeps its proportions at any resolution.

Gear and pulley ratios trade speed against torque; doubling the ratio halves the output speed and roughly doubles the turning force.

Expressing a ratio in the form n to one makes comparison across cases immediate, since only one number then varies.

When this calculator is useful

• Scaling recipes
• Mixing paint, concrete, or fertilizer
• Comparing screen aspect ratios
• Map and model scales