Ratio

A ratio compares two or more quantities of the same kind. You write it as a:b and sometimes a:b:c.

This calculator handles four common ratio problems:

• Simplify a ratio to its lowest terms
• Solve a proportion when one value is missing
• Split a total into parts using a ratio
• Compare two ratios to see whether they are equal or which one is larger

Use the tabs in the calculator. Leave blank only the value you want to find, then click Calculate or press Enter.

What This Ratio Calculator Does

Simplify a Ratio

Reduce a ratio to its lowest terms.

For example: 8:12 = 2:3

The calculator also accepts decimals. For example: 2.5:10 = 1:4

Solve a Proportion

Fill in any three values in: A:B = C:D

The calculator finds the missing value using cross-multiplication.

The main relationship is: ad = bc

For example, if: 2:3 = 4:x

then: 2x = 12

so:

x = 6

Split a Total

Use this option when you need to divide an amount according to a ratio.

For example, to split 100 in the ratio 2:3: 2 + 3 = 5 parts

100 ÷ 5 = 20 per part

So the two shares are: 2 × 20 = 40, 3 × 20 = 60

Compare Two Ratios

Compare ratios by converting them to fractions or decimals.

For example: 3:4 = 3 ÷ 4 = 0.75

2:3 ≈ 2 ÷ 3 ≈ 0.667

Therefore: 3:4 is larger than 2:3.

Every result also shows the fraction, decimal, percentage, equivalent ratios, and a check line so you can verify your work.

Ratio Calculator Formulas

Simplifying Ratios

To simplify a ratio, find the greatest common divisor (GCD) of all the terms and divide each term by it.

For example: 8:12 ÷ 4 = 2:3

For a three-part ratio:

12:18:30 ÷ 6 = 2:3:5

The resulting ratio is in its lowest terms.

Solving a Proportion

If: a:b = c:d

then: ad = bc

Depending on which value is missing, you can use: a = bc ÷ d

b = ad ÷ c

c = ad ÷ b

d = bc ÷ a

The calculator requires exactly one unknown value.

If two values are blank, there is not enough information to solve a standard proportion problem.

Splitting a Total

To divide a total according to a ratio:

1. Add all the ratio parts.
2. Divide the total by the sum.
3. Multiply the result by each ratio number.

For example, divide 240 in the ratio 3:5.

3 + 5 = 8 parts

240 ÷ 8 = 30 per part

Therefore:

3 × 30 = 90

5 × 30 = 150

So the answer is: 90:150

Comparing Ratios

To compare two ratios, convert each ratio into a single number.

For example:

3:4 = 3 ÷ 4 = 0.75

2:3 = 2 ÷ 3 ≈ 0.667

Because 0.75 > 0.667, the ratio 3:4 is larger.

You can also compare ratios using cross-products. If: a:b and c:d

then compare: a × d

with: b × c

If the cross-products are equal, the ratios are equal.

Worked Ratio Examples

1. Simplify a Ratio

A class has 16 boys and 24 girls.

The ratio is: 16:24

The GCD of 16 and 24 is 8.

16 ÷ 8 = 2

24 ÷ 8 = 3

Therefore:

16:24 = 2:3

2. Find a Missing Value

A map has a scale of 1:50,000. The map distance is 2 cm.

Set up the proportion: 1:50,000 = 2:d

Using cross-multiplication: 1 × d = 50,000 × 2

d = 100,000 cm

Since: 100,000 cm = 1 km

the actual distance is: 1 km

3. Split Money in a Ratio

Divide $84 in the ratio 3:4.

First add the ratio parts: 3 + 4 = 7

Find the value of one part: $84 ÷ 7 = £12

Now calculate each share:

3 × $12 = $36

4 × $12 = $48

Therefore: $36 and $48

Check: $36 + $48 = $84

4. Three-Part Ratio

A concrete mix uses cement, sand, and gravel in the ratio 1:2:3.

Suppose there are 6 buckets of sand.

Sand represents 2 parts.

Therefore: 6 ÷ 2 = 3 buckets per part

Now calculate the other ingredients:

Cement = 1 × 3 = 3 buckets

Sand = 2 × 3 = 6 buckets

Gravel = 3 × 3 = 9 buckets

Therefore, the mixture is: 3:6:9

5. Compare Two Ratios

Is 3:4 greater than 2:3?

Convert each ratio into a fraction: 3:4 = 3/4 = 0.75

2:3 ≈ 0.667

Because: 0.75 > 0.667

the answer is: Yes, 3:4 is greater than 2:3.

Ratio, Fraction, or Percentage?

A ratio compares parts with each other.

For example: 3:5

A fraction of the whole uses the sum of the ratio parts.

For 3:5: 3 + 5 = 8

So the fractions of the whole are: 3/8 and 5/8

A percentage converts the fraction into a percentage: 3/8 × 100 = 37.5%

5/8 × 100 = 62.5%

So:

Representation	First Part	Second Part
Ratio	3:5	—
Fraction of whole	3/8	5/8
Percentage	37.5%	62.5%

The calculator displays these equivalent forms automatically.

Common Ratio Mistakes This Calculator Helps Prevent

Treating 0:0 as a valid ratio

0:0 is undefined because both sides provide no meaningful comparison.

Dividing by zero

Some proportion problems require division. A value that would make the denominator zero cannot be used.

Leaving Two Values Blank

A standard proportion needs exactly one unknown.

For example: 2:3 = x:y

cannot be solved uniquely because both x and y are unknown.

Comparing Only the First Number

Do not decide that one ratio is larger just because its first number is larger.

For example: 5:9

is not necessarily larger than: 2:3

Compare the complete ratios: 5/9 ≈ 0.556

2/3 ≈ 0.667

Therefore: 2:3 is larger.

Adding the Same Number to Both Terms

Ratios are scaled by multiplication or division, not by simply adding the same number.

For example: 2:3

can become: 4:6

by multiplying both terms by 2.

But adding 2 gives: 4:5

which is a different ratio.

When Should You Use Each Ratio Calculator Tab?

What You Have	Use This Tab
Two messy numbers that need reducing	Simplify
Three known values in a proportion	Proportion
A total that needs to be divided	Split Total
Two complete ratios to compare	Compare

These same ratio calculations can be used for many real-world problems, including aspect ratios, paint mixtures, recipes, map scales, classroom groups, money, speed, and measurements.

Need Practice Material ?

Explore Our Practice Material related to Ratios and Proportions

Basic Unit Rates (Fraction Notation)

Do the ratios form a Proportion?

Identifying and Solving Proportions

Word Problems on Equivalent Ratios

Identifying Equivalent Ratios

Unit Rates (Additional Practice )

Unit Rates with Ratios of Quantities