Ratio Calculator

A ratio compares two quantities - say 16 : 9 for a widescreen display, or 2 : 1 for a cordial mixed with water. This ratio calculator does the three things people actually need: it reduces a ratio to its simplest form, solves a proportion when one value is missing, and scales a ratio up or down. Type 16 : 12, for example, and it instantly returns 4 : 3, the decimal 1.333, and a row of equivalent ratios - the same relationship written with different numbers.

Because a ratio, a fraction, and a percentage are three views of the same comparison, this tool pairs naturally with our Fraction Calculator and Percentage Calculator. Use whichever form fits your problem - the math underneath is identical.

What a ratio is

A ratio is a comparison of two amounts using division. Writing a : b says "for every a of the first thing, there are b of the second." A ratio is closely tied to a fraction: the ratio a : b carries the same information as the fraction a/b. That is why simplifying a ratio works exactly like reducing a fraction - you divide both parts by the same number.

The formulas

Three short rules cover everything this calculator does:

Here g is the greatest common divisor of the two terms, and k is any non-zero scale factor. The proportion rule - called cross-multiplication - is the workhorse: because the two ratios are equal, the products of their diagonals must match, which lets you solve for whichever term is unknown.

How to use this ratio calculator

Pick the tab that matches your task, then fill in the boxes:

1. Simplify: enter both terms (for example 16 and 12). The calculator reduces the ratio, shows the GCD it divided by, and lists equivalent ratios.
2. Solve proportion: enter three of the four values in A : B = C : D and leave the unknown box empty. The result is the missing term, plus the completed proportion.
3. Scale: enter a ratio and a factor. Use a factor above 1 to scale up (double a recipe) or below 1 (such as 0.5) to scale down.

Everything updates as you type - there is no submit button to chase. If you leave a box blank in the wrong place or enter something that cannot be solved (like dividing by zero), the calculator shows a short message instead of a wrong answer.

Who this calculator is for

• Students checking homework on ratios, proportions, and equivalent fractions.
• Cooks and bakers scaling a recipe up or down while keeping the flavor balance.
• DIY and craft users mixing paint, resin, fertilizer, or cleaning solutions to a stated ratio.
• Designers and photographers working with aspect ratios like 16 : 9, 4 : 3, or 3 : 2.
• Hobbyists and makers building scale models or maps where a fixed ratio maps real size to model size.
• Anyone splitting a bill, a prize, or shared costs in a given ratio.

Worked example 1: simplifying

Simplify 18 : 24. The greatest common divisor of 18 and 24 is 6. Dividing both terms by 6 gives 3 : 4. As a decimal that is 3 ÷ 4 = 0.75, and equivalent ratios include 6 : 8, 9 : 12, and 12 : 16 - each one is just 3 : 4 multiplied by the same number.

Worked example 2: solving a proportion

A recipe uses 3 cups of flour for every 4 cups of milk. You have 15 cups of flour - how much milk do you need? Set up 3 : 4 = 15 : D. Cross-multiplying gives 3 × D = 4 × 15, so D = 60 ÷ 3 = 20 cups of milk. In the calculator, type 3, 4, and 15, leave the last box empty, and it returns 20.

Worked example 3: scaling a mixture

A concrete mix is 1 : 4 (cement to sand). You need four times as much, so scale by 4: 1 : 4 becomes 4 : 16. The proportions are unchanged - you simply have more material. To halve a paint mix of 2 : 3, scale by 0.5 to get 1 : 1.5.

Worked example 4: splitting an amount in a ratio

One of the most common real-world ratio tasks is sharing an amount in a given ratio - dividing a bill, profit, or inheritance fairly. Suppose three friends split a $120 prize in the ratio 2 : 3 : 5. First add the parts: 2 + 3 + 5 = 10 total parts. One part is worth $120 ÷ 10 = $12. Multiply each share by the part value: the friends receive 2 × $12 = $24, 3 × $12 = $36, and 5 × $12 = $60. As a check, $24 + $36 + $60 = $120. The same "find one part, then multiply" method works for any split, and it is why counting total parts before you start is so important.

Ratios vs rates: when units differ

A plain ratio compares two quantities in the same unit - 3 cups to 4 cups, or 2 liters to 5 liters - and is unitless once simplified. A rate compares two different units, such as miles per hour, dollars per pound, or words per minute. A unit rate reduces the second term to 1: if 6 apples cost $3, the unit rate is $0.50 per apple. Mechanically the math is the same division, but the meaning differs - a ratio answers "how do these two like things compare?" while a rate answers "how much of one thing per single unit of another?" When the two numbers carry different units, you are working with a rate, and you should keep the unit labels attached so the answer stays meaningful.

Common aspect ratios (reference)

Aspect ratios are one of the most common everyday uses of ratios. Here are the standard ones and their decimal width-to-height values:

Key terms explained

• Term: one of the numbers in a ratio. In 3 : 4, the terms are 3 and 4.
• Antecedent & consequent: the first term is the antecedent, the second is the consequent.
• Greatest common divisor (GCD): the largest whole number that divides both terms exactly - used to simplify.
• Proportion: an equation stating that two ratios are equal, such as 1 : 2 = 4 : 8.
• Cross-multiplication: the method of solving a proportion by setting the diagonal products equal.
• Equivalent ratios: different number pairs that reduce to the same simplest form, like 2 : 3 and 10 : 15.

Ratios, fractions, and percentages

These three are closely related ways of expressing the same relationship. The ratio 1 : 4 is the fraction 1/4 when comparing the first part to the second, which equals 0.25 as a decimal or 25%. But be careful with "parts": if a mixture is 1 : 3, the first ingredient is 1 out of 4 total parts, which is 1/4 = 25% of the whole - not 1/3. Deciding whether you are comparing part-to-part or part-to-whole is the single most common source of mistakes.

Tips for working with ratios

• Always simplify first. A reduced ratio is easier to compare and scale.
• Keep the order fixed. Decide which quantity is "first" and never swap it mid-problem.
• Match the units. Convert both quantities to the same unit before forming the ratio (for example, both in grams).
• Use cross-multiplication to check equality. If A × D equals B × C, the two ratios are equivalent.
• For three-part ratios, divide every part by their shared GCD - the same idea, extended.

Common pitfalls

• Confusing part-to-part with part-to-whole. A 1 : 3 ratio means 4 total parts, not 3.
• Adding ratios incorrectly. You cannot add 1 : 2 and 1 : 3 term by term; combine the underlying quantities instead.
• Reversing the order. 3 : 4 and 4 : 3 describe opposite relationships.
• Mixing units. 500 g : 1 kg is really 1 : 2 once both are in the same unit.

Related concepts and next steps

Once you are comfortable with ratios, the next steps are rates (a ratio of two different units, such as miles per hour), scale factors (the single number that maps one figure to a similar larger or smaller one), and percentages (a ratio out of 100). Each is a special case of the same comparison-by-division idea.

How it compares to related calculators

This page answers "simplify, solve, or scale a ratio." If your question is shaped a little differently, a sister tool fits better:

• To reduce, add, or convert a fraction directly, use the Fraction Calculator - a ratio a : b is the same as the fraction a/b.
• To turn a part-to-whole ratio into a percent, or to find "x% of a number," use the Percentage Calculator.
• To find the mean of several values rather than compare two, use the Average Calculator.
• For roots and powers that come up when scaling areas and volumes, use the Square Root Calculator and the Scientific Calculator.

A useful rule when scaling shapes: lengths scale by the ratio k, but areas scale by k² and volumes by k³. So doubling a model's linear dimensions (a 1 : 2 length ratio) makes it four times the surface area and eight times the volume - a frequent source of confusion in scale-model and recipe work.

Method note

The simplify step uses the Euclidean algorithm for the greatest common divisor - the standard method taught in arithmetic and number theory. Proportions are solved by cross-multiplication, and scaling multiplies both terms by the same factor. These are universal arithmetic rules, so this page cites no external authority: the math is the same everywhere.