A Ratio Calculator compares two or more quantities by showing how large one value is relative to another.

It can simplify a ratio, create an equivalent ratio, solve a proportion, or divide a total according to a chosen ratio.

For example:

2:3

does not mean the two values differ by 1.

It means that for every:

2 parts of the first quantity

there are:

3 parts of the second quantity

The second quantity is therefore:

3 ÷ 2 = 1.5 times

the first.

Keep the ratio terms in the correct order, convert comparable quantities to the same unit, and divide every term by the same factor when simplifying.

What a ratio tells you

A ratio compares quantities multiplicatively.

Suppose there are:

12 red objects

and:

18 blue objects

The red-to-blue ratio is:

12:18

This ratio can be simplified to:

2:3

That means every group of:

2 red objects

corresponds to:

3 blue objects

The relationship stays the same even though the numbers are smaller.

How to use the Ratio Calculator

1. Enter the ratio terms in the correct order.
2. Choose whether you want to simplify, scale, solve an equivalent ratio, or divide a total.
3. Convert quantities to compatible units when needed.
4. Calculate the result.
5. Check that every ratio term was changed by the same factor.
6. Keep the term labels in the same order when interpreting the answer.

The order matters because:

2:5

and:

5:2

describe different relationships.

Simplifying a ratio

A ratio is simplified by dividing every term by their greatest common factor.

For a two-term ratio:

a

use:

Simplified ratio = (a ÷ GCF):(b ÷ GCF)

where:

GCF

is the greatest common factor of both terms.

Worked simplification example

Consider:

18:24

The greatest common factor of 18 and 24 is:

6

Divide both terms:

18 ÷ 6 = 3

24 ÷ 6 = 4

Therefore:

18:24 = 3:4

The relationship has not changed.

Only the representation has been reduced.

Do not reduce only one side

A ratio such as:

12:18

cannot be simplified by changing only one number.

For example:

12:18 → 2:18

is not equivalent.

Both terms must be divided by the same nonzero factor.

The correct reduction is:

12 ÷ 6 = 2

18 ÷ 6 = 3

So:

12:18 = 2:3

Equivalent ratios

Equivalent ratios represent the same relationship.

For example:

2:3

is equivalent to:

4:6

6:9

10:15

and:

20:30

because both terms are multiplied by the same factor.

For example:

2 × 5 = 10

and:

3 × 5 = 15

So:

2:3 = 10:15

Scaling a ratio

To scale:

a

by a factor:

k

use:

ak

For example, scale:

3:5

by:

4

Then:

3 × 4 = 12

and:

5 × 4 = 20

So:

3:5 = 12:20

Scaling changes the numbers while preserving the relationship.

Solving an equivalent ratio

Suppose:

3:5 = 12

You can solve using cross multiplication:

3 × x = 5 × 12

So:

3x = 60

Then:

x = 20

Therefore:

3:5 = 12:20

Cross-products can check equivalent ratios

Two ratios:

a

and:

c

are equivalent when:

a × d = b × c

For example:

2:3

and:

8:12

Check:

2 × 12 = 24

and:

3 × 8 = 24

The cross-products match.

So the ratios are equivalent.

Part-to-part and part-to-whole ratios are different

Suppose a class has:

12 girls

and:

18 boys

The girl-to-boy ratio is:

12:18

which simplifies to:

2:3

But the total number of students is:

12 + 18 = 30

The girl-to-class ratio is:

12:30

which simplifies to:

2:5

Both ratios are correct.

They answer different questions.

Label the quantities before simplifying

Writing:

2:3

without context may not tell you what is being compared.

A clearer setup is:

Girls : Boys = 2:3

or:

Water : Concentrate = 4:1

or:

Width : Height = 16:9

The labels make the direction clear.

They also help prevent accidental reversal.

Ratio order changes the meaning

If:

Cats : Dogs = 2:5

then there are:

2 cats for every 5 dogs

The reverse comparison is:

Dogs : Cats = 5:2

These are not interchangeable.

The same quantities are involved, but the question is different.

Always preserve the requested order.

Splitting a total by a ratio

A ratio can divide a total into proportional shares.

Suppose:

$500

must be divided in the ratio:

2:3

First add the ratio terms:

2 + 3 = 5 total parts

Find the value of one part:

500 ÷ 5 = 100

Now calculate each share:

2 × 100 = 200

and:

3 × 100 = 300

So:

$500 divided in a 2:3 ratio = $200 and $300

The general formula for splitting a total

For a total:

T

divided in the ratio:

a

the first share is:

First share = T × a/(a + b)

The second share is:

Second share = T × b/(a + b)

For:

T = 500

and:

a = 2:3

First share:

500 × 2/5 = 200

Second share:

500 × 3/5 = 300

Always check the shares add back to the total

After dividing a total:

200 + 300 = 500

The allocated amounts should reproduce the original total.

This is a simple way to catch a ratio-entry or arithmetic mistake.

The larger ratio term should receive the larger share

If a total is split:

2:5

the second quantity should receive more than the first.

If the calculator shows the opposite, check:

• the ratio order;
• the inputs;
• and the labels.

The result should reflect the relative size of the terms.

Three-part ratios work the same way

Ratios are not limited to two terms.

Consider:

2:3:5

Total parts:

2 + 3 + 5 = 10

Suppose:

240

must be divided according to that ratio.

One part is:

240 ÷ 10 = 24

Then:

2 × 24 = 48

3 × 24 = 72

5 × 24 = 120

So:

Ratio part	Share
2	48
3	72
5	120
Total	240

The order of the three terms must remain unchanged.

Four-part and longer ratios use the same method

Suppose:

1:2:3:4

The total number of parts is:

1 + 2 + 3 + 4 = 10

If the total is:

1,000

then one part is:

1,000 ÷ 10 = 100

The shares are:

100

200

300

and:

400

which add to:

1,000

Ratios with decimal values

Ratios can contain decimals.

For example:

1.5:2.5

To make the relationship easier to read, multiply both values by:

10

Then:

15:25

Simplify by 5:

3:5

Therefore:

1.5:2.5 = 3:5

Clear decimals using the same power of ten

Consider:

0.25:1.5

The greatest number of decimal places is:

2

Multiply both terms by:

100

Then:

25:150

Reduce by 25:

1:6

So:

0.25:1.5 = 1:6

Multiplying both terms by the same factor preserves the ratio.

Ratios with fractions

Fractions can also appear inside ratios.

For example:

1/2 : 3/4

To clear the denominators, multiply both terms by:

4

Then:

2:3

So:

1/2 : 3/4 = 2:3

This is often easier to interpret than leaving fractional ratio terms.

Another fraction-ratio example

Consider:

2/3 : 5/6

The least common denominator is:

6

Multiply both terms by 6:

4:5

Therefore:

2/3 : 5/6 = 4:5

Units must be compatible before comparing

Consider:

2 ft : 8 in

Writing:

2:8

would be incorrect because the quantities use different units.

Convert first:

2 ft = 24 in

Now:

24 in : 8 in

Simplify:

24:8 = 3:1

So the correct ratio is:

3:1

Units may cancel after conversion

Once comparable quantities use the same unit:

24 in : 8 in

the inches appear on both terms.

So the simplified ratio:

3:1

can often be written without unit labels.

But the unit conversion must happen first.

Not every ratio should lose its units

Some comparisons deliberately involve different types of quantities.

For example:

60 miles : 2 hours

describes:

30 miles per hour

This is better interpreted as a rate rather than a dimensionless ratio.

The Ratio Calculator can perform the numeric comparison, but the units remain meaningful.

Ratios and rates are related but not identical

A ratio may compare quantities with the same unit:

3 apples : 5 apples

which simplifies to:

3:5

A rate often compares different units:

150 miles : 3 hours

which gives:

50 miles per hour

Do not automatically remove units from a rate.

Recipe scaling with ratios

Suppose a drink mix uses:

Water : Concentrate = 4:1

There are:

4 + 1 = 5 total parts

If you want:

15 liters

of finished mixture:

One part:

15 ÷ 5 = 3 liters

Water:

4 × 3 = 12 liters

Concentrate:

1 × 3 = 3 liters

So the mix requires:

12 L water

and:

3 L concentrate

Recipe ratios describe proportions, not automatically safe formulations

A ratio calculation can correctly scale quantities mathematically.

But some mixtures also have:

• concentration limits;
• safety requirements;
• manufacturer instructions;
• or regulatory requirements.

The calculator cannot determine whether a chosen ratio is appropriate for a chemical, medical, or technical mixture.

Use the required formulation instructions.

Map scales are ratios

A map scale such as:

1:50,000

means:

1 unit on the map

represents:

50,000 of the same units in reality

For example:

1 cm on the map

represents:

50,000 cm in reality

Convert:

50,000 cm = 500 m

So:

1 cm on the map = 500 m on the ground

The same unit must be understood on both sides before converting to a more convenient unit.

Drawing scales use the same principle

A drawing scale of:

1:50

means one unit on the drawing represents 50 of the same units in the real object.

For example:

4 cm on the drawing

represents:

4 × 50 = 200 cm

which is:

2 m

The direction matters.

A scale of:

1:50

should not accidentally be treated as:

50:1

Aspect ratios compare dimensions

Screen and image dimensions are often expressed as ratios.

For example:

1920:1080

Both terms can be divided by:

120

giving:

16:9

So a 1920 × 1080 display has a:

16:9 aspect ratio

The same aspect ratio can apply to many resolutions.

Ratios can compare areas or volumes, but meaning matters

Suppose one area is:

100 ft²

and another is:

150 ft²

The ratio is:

100:150 = 2:3

That is valid because both quantities use square feet.

But do not compare:

100 ft²

directly with:

150 ft

because area and length are different dimensions.

Compatible units must represent compatible types of quantities.

A ratio is not a difference

Consider:

2:3

The numerical difference is:

3 − 2 = 1

But the ratio describes:

3 ÷ 2 = 1.5

So the second quantity is:

1.5 times

the first.

Ratios describe multiplicative relationships.

Differences describe additive relationships.

They answer different questions.

Ratios and fractions are closely related

The ratio:

2:3

can also be represented as:

2/3

when you are expressing the first quantity relative to the second.

But the notation emphasizes different ideas.

2:3

highlights a comparison.

2/3

behaves as a fraction or quotient.

This connection is useful when solving proportions.

Part-to-whole ratio can become a fraction of the total

Suppose:

Red : Blue = 2:3

Total parts:

2 + 3 = 5

The fraction of the total that is red is:

2/5

The fraction that is blue is:

3/5

As percentages:

2/5 = 40%

and:

3/5 = 60%

Notice that the original red-to-blue ratio:

2:3

is not the same as the red-to-total ratio:

2:5

Ratios can be converted into percentages

If you want to express:

2:3

as the first quantity relative to the second:

2 ÷ 3 × 100 ≈ 66.67%

That means the first quantity is about:

66.67% of the second

But if you want the first quantity as a percentage of the combined total:

2 ÷ (2 + 3) × 100 = 40%

These are different percentage questions.

State which relationship you mean.

Zero in ratios needs context

A ratio such as:

0:5

can meaningfully describe:

0 of the first quantity

for every:

5 of the second

But the quotient:

0 ÷ 5 = 0

is valid.

The reverse ratio:

5:0

creates a problem if interpreted as:

5 ÷ 0

because division by zero is undefined.

So zero can appear in some ratio notation, but not every ratio can be treated as an ordinary finite quotient.

0:0 does not provide a meaningful ordinary ratio

The ratio:

0:0

does not establish a unique relative size.

Both values are zero, so there is no meaningful scaling relationship to simplify into one ordinary ratio.

Treat this as a special or undefined comparison rather than forcing a result.

Negative ratios need interpretation

Mathematically, ratios can contain negative values.

For example:

−2:4

can be reduced algebraically to:

−1:2

But many practical ratio problems involve quantities that cannot be negative, such as:

• ingredient amounts;
• counts of people;
• physical lengths;
• material quantities.

Use negative ratios only when the underlying problem allows signed quantities.

Simplifying more than two terms

Consider:

12:18:30

Find a common factor shared by all terms.

The greatest common factor is:

6

Divide every term:

12 ÷ 6 = 2

18 ÷ 6 = 3

30 ÷ 6 = 5

So:

12:18:30 = 2:3:5

Do not simplify different terms by different factors.

Never delete a term when simplifying

A ratio such as:

2:3:5

contains three distinct quantities.

It cannot be simplified to:

2:3

just because one term seems less important.

Every position represents a specific quantity.

Changing the number of terms changes the meaning of the ratio.

Checking an equivalent ratio

Suppose you calculate:

4:7 = 20:35

Check the scale factor.

From:

4 → 20

the multiplier is:

5

Then:

7 × 5 = 35

So the ratio is consistent.

You can also check cross-products:

4 × 35 = 140

7 × 20 = 140

Both checks confirm equivalence.

Checking a total split

Suppose:

420

is divided:

2:5

Total parts:

7

One part:

420 ÷ 7 = 60

Shares:

2 × 60 = 120

5 × 60 = 300

Check:

120 + 300 = 420

And because:

5 > 2

the second share is appropriately larger.

Common ratio calculation mistakes to avoid

Reversing the term order

2:5

does not mean the same thing as:

5:2

Reducing only one term

All ratio terms must be divided by the same factor.

Comparing different units directly

Convert to compatible units first.

Treating a ratio as subtraction

A ratio compares multiplicatively.

Using the wrong total number of parts

For:

2:3

the total is:

5 parts

not:

3 parts

Dropping a term in a multi-part ratio

Every position represents a separate quantity.

Mixing part-to-part with part-to-whole

2:3

and:

2:5

can describe the same group from different perspectives.

Ignoring labels

A numerical ratio without labels can easily be interpreted backwards.

A compact comparison of ratio tasks

Task	Example	Result
Simplify	18:24	3:4
Scale	2:3 × 5	10:15
Solve equivalent ratio	3:5 = 12	x = 20
Divide a total	500 in 2:3	200 and 300
Simplify three terms	12:18:30	2:3:5
Convert units first	2 ft : 8 in	3:1

These operations all use the same principle: preserve the relative size of every term.

When to use another calculator

Use the Proportion Calculator when you need to solve an equation involving two equivalent ratios.

Use the Fraction to Decimal Calculator when a ratio or fraction needs to be expressed in decimal form.

For ordinary arithmetic and order-of-operations checks, use the Basic Calculator.

FAQ

How do I simplify 12:18?

Find the greatest common factor:

6

Then:

12 ÷ 6 = 2

18 ÷ 6 = 3

So:

12:18 = 2:3

Does ratio order matter?

Yes.

2:5

and:

5:2

describe opposite comparisons.

How do I split a total in the ratio 2:3?

Add the parts:

2 + 3 = 5

Divide the total by 5, then allocate two parts to the first quantity and three parts to the second.

How do I know whether two ratios are equivalent?

Check the cross-products.

For:

a = c

the ratios are equivalent when:

a × d = b × c

Can ratios contain decimals?

Yes.

You can multiply every term by the same power of ten to convert them to whole numbers when useful.

Can ratios contain fractions?

Yes.

Multiply every term by a common denominator to clear the fractions.

Can ratios use different units?

Only after compatible quantities are converted to a common unit if you want a dimensionless ratio.

Different-unit comparisons may instead represent a rate.

Is 2:3 the same as 2/3?

They are closely related.

The fraction:

2/3

expresses the first term relative to the second, while the colon notation emphasizes the comparison between the two quantities.

Is a 2:3 ratio the same as 40%?

Not directly.

In a two-part group with ratio:

2:3

the first part is:

2/(2 + 3) = 40%

of the combined total.

But the first quantity is:

2/3 ≈ 66.67%

of the second quantity.

Can a ratio have zero?

Sometimes.

0:5

can describe zero of the first quantity compared with five of the second.

A ratio with zero as the reference denominator, such as 5:0, cannot be interpreted as an ordinary finite quotient.

Can I use a ratio to scale a recipe?

Yes mathematically.

Add the ratio parts and divide the required total accordingly.

For regulated, chemical, or safety-sensitive mixtures, follow the required formulation instructions as well.

Can the calculator handle three-part ratios?

Yes, when supported.

Add all the terms to determine the total number of parts, then allocate the total according to each term.

Mathematics reference

For additional explanations and worked examples involving ratios, rates, fractions, and proportions, see:

OpenStax — Prealgebra 2e

Keep the labels attached to the ratio

A Ratio Calculator can simplify numbers quickly, but the meaning comes from the quantities those numbers represent.

A ratio of:

2:3

could describe people, ingredients, dimensions, money, colors, or many other relationships.

Keep the terms in order.

Convert comparable measurements to the same unit.

Apply the same scaling factor to every term.

And when dividing a total, check that the shares add back to the original amount.

That keeps the arithmetic correct without losing the meaning of the comparison.