Ratio Calculator – Simplify Ratios, Solve Proportions & More

Use this Ratio Calculator to simplify ratios, solve proportions, find missing values, split totals, convert ratios, compare ratios, calculate aspect ratios, and more.

A ratio is one of the simplest ways to describe the relationship between two or more quantities. You see ratios in math problems, recipes, financial calculations, screen dimensions, measurements, and everyday comparisons.

This Ratio Calculator brings common ratio calculations together in one tool. Depending on what you need to calculate, you can use it to:

• Simplify a ratio
• Find a ratio from two quantities
• Solve a proportion and find a missing value
• Find an equivalent ratio
• Scale a ratio up or down
• Divide a total according to a ratio
• Find a total from a known ratio and part
• Calculate a multi-part ratio
• Convert a ratio to a fraction, decimal, or percentage
• Convert a percentage to a ratio
• Compare two ratios
• Calculate the difference between two ratios
• Calculate an aspect ratio
• Compare quantities with different units

Whether you’re working on a math assignment, checking a proportion, splitting a total, adjusting a recipe, comparing measurements, or calculating a screen’s aspect ratio, you can choose the calculation that matches your problem.

How to Use the Ratio Calculator

The easiest way to use the calculator is to start with the question you are trying to answer.

Step 1: Choose a Calculation Mode

Select the mode that matches your problem:

• Simplify a Ratio — reduce a ratio to its simplest form
• Find a Ratio — calculate the ratio between two quantities
• Find a Missing Value — solve a proportion when one value is unknown
• Find an Equivalent Ratio — create an equivalent ratio with a specified part
• Scale a Ratio — multiply or divide all parts by a factor
• Find Parts from a Total — divide a total according to a ratio
• Find the Total from a Ratio — calculate the total when a ratio and known part are given
• Calculate a Multi-Part Ratio — work with ratios containing more than two parts
• Convert Ratio to Fraction / Decimal / Percentage — express a ratio in other numerical forms
• Convert Percentage to Ratio — turn a percentage into a simplified ratio
• Compare Two Ratios — determine which of two ratios is larger
• Find Ratio Difference — measure the difference between two ratios
• Calculate Aspect Ratio — find or scale a width-to-height ratio
• Compare Quantities with Units — compare measurements after converting them to compatible units

Step 2: Enter Your Values

The required inputs depend on the selected mode.

A ratio may contain two or more parts, depending on the calculation. You can also assign labels such as A, B, C, and so on to make the result easier to understand in a real-world context.

Step 3: Check the Result

The calculator provides the main answer along with useful supporting information when applicable.

Depending on the mode, this may include:

• Simplified ratio
• Greatest common divisor (GCD)
• Decimal form
• Percentage
• Percentage of the total
• Total number of ratio parts
• Scaled values
• Individual amounts after a proportional split

There are also a few mathematical limitations to keep in mind:

• A ratio in which all parts are zero is not meaningful.
• Calculations that divide by a particular ratio part require that part to be nonzero.
• Quantities with different units can only be compared when their units belong to the same measurement category.

What Is a Ratio?

A ratio describes the relative relationship between two or more quantities.

For example, suppose a box contains 4 apples and 8 oranges. The ratio of apples to oranges is:

4:8

This ratio can be simplified to:

1:2

That tells us that for every 1 apple, there are 2 oranges.

A ratio can be written in several equivalent ways, including:

a

or

a/b

A ratio is not necessarily a fraction, even though the two can be written using similar notation. The meaning depends on how the quantities are being compared.

For example, in the ratio 1:3:

• A compared with B is 1/3
• A is 33.33% of B
• A represents 25% of the combined total
• B represents 75% of the combined total

These are different ways of interpreting the same ratio.

Equivalent Ratios

Equivalent ratios describe the same relative relationship.

For example:

2:3 = 4:6 = 10:15

Each ratio can be obtained by multiplying both parts of 2:3 by the same factor.

This is closely related to equivalent fractions. Multiplying or dividing every part of a ratio by the same nonzero number does not change the relationship between the parts.

How to Simplify a Ratio

Simplifying a ratio means reducing all of its parts as much as possible while keeping the same relationship.

For a two-part ratio:

a

find the greatest common divisor (GCD) of a and b, then divide both parts by it.

If the GCD is G:

Simplified ratio = (a/G):(b/G)

Example: Simplify 8:12

The greatest common divisor of 8 and 12 is 4.

Divide both parts by 4:

8:12 = 2:3

So the simplest form is:

2:3

The same method works with ratios containing more than two parts. Find the greatest common divisor shared by all parts, then divide every part by it.

For example:

12:18:24

The GCD is 6, so:

12:18:24 = 2:3:4

How to Find a Ratio

If you know two quantities and want to compare them, simply write them in the same order as the comparison.

Suppose you have:

• 4 apples
• 8 oranges

The ratio of apples to oranges is:

4:8 = 1:2

The calculator can also express the relationship numerically:

Decimal ratio = A/B

and, when meaningful:

A as a percentage of B = (A/B) × 100%

For 4 apples and 8 oranges:

4/8 = 0.5

and:

(4/8) × 100% = 50%

So the number of apples is 50% of the number of oranges.

This is different from the percentage each group contributes to the combined total. In this example:

Apples = 4/(4+8) × 100% = 33.33%

Oranges = 8/(4+8) × 100% = 66.67%

Keeping these two interpretations separate helps avoid one of the most common ratio mistakes.

Ratios and Proportions

A proportion states that two ratios are equal.

For example:

A/B = C/D

If three of the four values are known, the fourth can usually be found using cross multiplication.

For example:

A/B = C/D

Then:

A × D = B × C

From this relationship:

• Missing A: A = (B × C) / D
• Missing B: B = (A × D) / C
• Missing C: C = (A × D) / B
• Missing D: D = (B × C) / A

The denominator involved in the calculation cannot be zero.

Example: Solve 3/4 = 9/x

Here, x is the missing value.

Using cross multiplication:

3x = 4 × 9

3x = 36

x = 12

So:

3/4 = 9/12

Both sides equal 0.75, confirming the result.

This same idea appears in many everyday problems.

For example, if 3 items require 4 units of material and the same proportion is maintained, you can use a proportion to determine how much material is needed for 9 items.

Equivalent Ratios and Scaling

Equivalent ratios can be created by multiplying or dividing every part by the same nonzero factor.

For a ratio:

A

multiplying by a factor F gives:

(A × F):(B × F)

Example: Scale 3:4 by 5

Multiply both parts by 5:

3:4 → 15:20

The relationship has not changed.

You can also scale a ratio down:

15:20 → 3:4

by dividing both parts by 5.

Find an Equivalent Ratio With a Target Value

Sometimes you know the ratio and want one part to become a particular value.

For example, suppose the ratio is:

3:4

and you want the second part to become 20.

The scaling factor is:

k = 20/4 = 5

Multiply both parts by 5:

3 × 5 : 4 × 5

= 15:20

So 15:20 is the equivalent ratio with the second part equal to 20.

How to Divide a Total by a Ratio

One of the most useful applications of ratios is splitting a total into proportional parts.

Suppose the ratio is:

r₁₂:…ₙ

and the total is T.

First add all the ratio parts:

S = r₁ + r₂ + … + rₙ

Then calculate the value represented by one ratio unit:

One ratio unit = T/S

Finally, multiply that value by each ratio part:

Partᵢ = rᵢ × (T/S)

Example: Divide 120 in the Ratio 1:2:3

First add the ratio parts:

S = 1 + 2 + 3 = 6

Then calculate one ratio unit:

120/6 = 20

Now multiply:

• First part: 1 × 20 = 20
• Second part: 2 × 20 = 40
• Third part: 3 × 20 = 60

So 120 divided in the ratio 1:2:3 gives:

20:40:60

The values add back to 120:

20 + 40 + 60 = 120

This calculation is useful for dividing bills, allocating budgets, splitting quantities, distributing resources, or adjusting recipe ingredients.

How to Find the Total From a Ratio

The reverse problem is also common.

Suppose you know the ratio and the actual value of one part.

For example, the ratio is:

2:3

and the first part has an actual value of 40.

First determine the scale factor:

k = Known Value / Corresponding Ratio Part

So:

k = 40/2 = 20

The second part is:

3 × 20 = 60

Therefore, the total is:

40 + 60 = 100

The same method works with ratios containing more parts.

If multiple actual values are provided, they must all correspond to the same scale factor. Otherwise, the values are inconsistent with the stated ratio.

Ratio to Fraction, Decimal, and Percentage

Ratios can often be expressed in several mathematical forms, but the interpretation matters.

For a two-part ratio:

A

you can form the fraction:

A/B

and calculate the decimal:

A/B

For example:

3:4 → 3/4 → 0.75

Convert a Ratio to a Fraction

To convert the first part relative to the second part:

A → A/B

For example:

2:5 → 2/5

This fraction describes how large A is relative to B.

Convert a Ratio to a Decimal

Divide the first part by the second:

Decimal = A/B

For example:

3:4 = 3/4 = 0.75

Convert a Ratio to a Percentage

There are two common percentage interpretations.

A as a Percentage of B

Calculate:

(A/B) × 100%

For example:

1:3

gives:

(1/3) × 100% = 33.33%

So A is 33.33% of B.

Each Part as a Percentage of the Total

If the question is how much each part contributes to the combined total, use:

A percentage = A/(A+B) × 100%

B percentage = B/(A+B) × 100%

For 1:3:

A = 1/(1+3) × 100% = 25%

B = 3/(1+3) × 100% = 75%

The two interpretations answer different questions, so it is important to use the correct one.

Convert a Percentage to a Ratio

A percentage can be converted to a ratio by comparing it with 100.

For a percentage P%:

P% = P:100

Then simplify the resulting ratio.

Example: Convert 40% to a Ratio

Start with:

40:100

The GCD is 20.

Divide both parts by 20:

40:100 = 2:5

Therefore:

40% = 2:5

Another example:

25% = 25:100 = 1:4

This conversion is especially useful when you want to express a percentage as a proportional relationship.

Multi-Part Ratios

Ratios do not have to contain only two parts.

A ratio such as:

1:2:3

describes three quantities in relation to one another.

The total number of ratio units is:

1 + 2 + 3 = 6

Therefore:

• First part: 1/6 = 16.67%
• Second part: 2/6 = 33.33%
• Third part: 3/6 = 50%

A multi-part ratio calculator can also simplify the ratio when all parts have a common divisor.

For example:

6:12:18 → 1:2:3

after dividing every part by 6.

How to Compare Two Ratios

To compare two two-part ratios, convert each ratio to a decimal value.

Suppose you want to compare:

2:3

and:

3:4

Calculate:

2/3 ≈ 0.667

3/4 = 0.75

Since:

0.667 < 0.75

the ratio 2:3 is smaller than 3:4.

The calculator can determine whether one ratio is:

• Less than the other
• Equal to the other
• Greater than the other

Two ratios can also be different in appearance but mathematically equivalent.

For example:

2:3 = 4:6

because:

2/3 = 4/6

How to Calculate the Difference Between Two Ratios

Once two ratios have been converted to numerical values:

r₁ = a₁/a₂

and:

r₂ = b₁/b₂

you can measure their difference in several ways.

Absolute Difference

Absolute difference = |r₁ − r₂|

This gives the direct numerical gap between the two ratio values.

Relative Difference

Using Ratio B as the reference:

Relative difference = |r₁ − r₂| / |r₂| × 100%

This is useful when you want to express the difference relative to a chosen baseline.

Symmetric Percentage Difference

When neither ratio should automatically be treated as the reference:

Symmetric difference = |r₁ − r₂| / ((|r₁| + |r₂|)/2) × 100%

This treats both values symmetrically rather than selecting one as the baseline.

The appropriate measure depends on what you are trying to compare.

Aspect Ratio Calculator

An aspect ratio describes the proportional relationship between the width and height of an image, screen, video, or other rectangular shape.

The aspect ratio is usually written as:

Width

Calculate an Aspect Ratio From Width and Height

To calculate an aspect ratio, simplify the width-to-height ratio.

For example, consider a display measuring:

1280 × 720

The GCD of 1280 and 720 is 80.

Divide both dimensions by 80:

1280/80 = 16

720/80 = 9

Therefore:

1280:720 = 16:9

The aspect ratio is:

16:9

A 1920 × 1080 display produces the same simplified ratio:

1920:1080 = 16:9

This is why screens and videos with different pixel dimensions can still have the same aspect ratio.

Calculate a Missing Dimension From an Aspect Ratio

If the aspect ratio and one dimension are known, the other dimension can be calculated.

For an aspect ratio:

Wᵣᵣ

the formulas are:

Width = Height × (Wᵣ/Hᵣ)

and:

Height = Width × (Hᵣ/Wᵣ)

Example: 16:9 With a Height of 1080

Given:

Width = 16:9

and:

Height = 1080

calculate:

Width = 1080 × (16/9)

Width = 1920

So a 16:9 display with a height of 1080 has a width of:

1920

Aspect ratios are commonly used for displays, photographs, video, thumbnails, presentations, and image design.

Comparing Quantities With Different Units

You cannot correctly compare measurements using their numerical values alone when the units are different.

For example:

1 meter : 50 centimeters

should not be written as:

1:50

because the units are different.

First convert the quantities to the same unit:

1 m = 100 cm

So:

100 cm:50 cm = 2:1

The simplified ratio is therefore:

2:1

The calculator can handle compatible units within the same measurement category.

Length

Examples include:

• mm
• cm
• m
• km
• in
• ft
• yd
• mi

Mass

Examples include:

• mg
• g
• kg
• oz
• lb

Volume

Examples include:

• mL
• L
• fl oz
• gal

The important rule is that unit conversion only makes sense within the same physical quantity.

For example, meters and centimeters can be compared after conversion, but meters and kilograms cannot be converted into one another and therefore do not form a meaningful unit-based ratio.

Common Ratio Applications

Ratios appear in many situations beyond textbook math problems.

Recipes and Ingredient Scaling

If a recipe uses ingredients in a fixed ratio, scaling the ratio allows you to increase or decrease the recipe while keeping the same proportions.

For example, a 2:3 ingredient ratio can be scaled to 4:6 or 10:15 without changing the relationship.

Splitting Bills and Budgets

A total amount can be divided according to a ratio.

For example, a $600 budget divided in the ratio 2:1 gives:

• First share: $400
• Second share: $200

The same method works for commissions, investments, expenses, or resource allocation.

Screen and Image Dimensions

Aspect ratios such as 16:9, 4:3, and 1:1 are widely used to describe the shape of screens and images.

Knowing the aspect ratio makes it possible to calculate a missing width or height without changing the shape.

Comparing Measurements

Ratios provide a convenient way to compare quantities once their units have been converted to a common basis.

This is useful for lengths, masses, volumes, and other compatible measurements.

Common Ratio Mistakes

Ratios are straightforward once the quantities are clearly defined, but several mistakes occur frequently.

Reversing the Order

The ratio of apples to oranges is different from the ratio of oranges to apples.

For example:

4 apples : 8 oranges = 1:2

but:

8 oranges : 4 apples = 2:1

Always keep the order consistent with the question.

Forgetting to Simplify

A ratio such as 8:12 is correct, but 2:3 is its simplest form.

When a problem asks for the simplified ratio, divide all parts by their greatest common divisor.

Mixing Units

Do not compare 1 m:50 cm directly.

Convert the units first.

Confusing Ratio With Percentage

For 1:3, A is:

33.33% of B

but A represents:

25% of the combined total

These are not the same calculation.

Scaling Only One Part

If you multiply only one side of a ratio, you change the relationship.

For example:

2:3

cannot be scaled to 4:3 and remain equivalent.

Both parts must be multiplied or divided by the same nonzero factor.

Final Thoughts

Ratios are a simple way to describe relationships, but they appear in many different forms.

You may need to simplify a ratio, solve a proportion, find a missing value, divide a total into proportional parts, convert between ratios and percentages, compare two ratios, or calculate an aspect ratio for a screen or image.

The Ratio Calculator brings these common calculations together so you can choose the method that matches the problem instead of working through each formula manually.

Whether you’re solving a math problem, scaling a recipe, splitting a budget, comparing measurements, or working with image dimensions, enter your values, choose the appropriate mode, and let the calculator handle the arithmetic.

Try the free Ratio Calculator on aicalcory and turn your next ratio problem into a quick calculation.