Ratio Calculator

Simplify ratios, convert ratios to fractions and percentages, and find equivalent ratios with our free ratio calculator

Available Calculators

What is a Ratio?

A ratio is a comparison of two quantities, expressed as a:b or a/b. It shows how many times one value contains or is contained within the other. Ratios are fundamental in mathematics and appear in many real-world applications, from cooking recipes to financial analysis.

Ratio Properties

Key properties of ratios include:

If a:b = c:d, then ad = bc (cross multiplication)

Applications

Ratios are used in many real-world scenarios, including scaling recipes (2:3 flour to sugar), mixing solutions (1:4 concentrate to water), calculating proportions in design (16:9 aspect ratio), and analyzing financial data (debt-to-equity ratios).

Examples of Ratio Calculations

Here are several everyday situations that show how easy it is to use our ratio calculator.

Example 1: Simplify Ratio 12:8

Simplify the ratio 12:8 to its simplest form.

You can use our calculator by entering:

What is 12:8 in simplest form?

The calculator returns: 3:2

GCD of 12 and 8 = 4
12 ÷ 4 = 3, 8 ÷ 4 = 2
Simplified ratio: 3:2

The formula used is:

12:8 = (12 ÷ 4):(8 ÷ 4) = 3:2

Example 2: Ratio to Fraction

Convert the ratio 3:5 to a fraction.

You can use our calculator by entering:

What fraction represents 3:5?

The calculator returns: 3/8

Total parts: 3 + 5 = 8
Fraction: 3/8

The formula used is:

(3 ÷ (3 + 5)) = (3 ÷ 8)

Example 3: Ratio to Percentage

Convert the ratio 3:7 to a percentage.

You can use our calculator by entering:

What percentage is 3 out of the total?

The calculator returns: 42.86%

Total parts: 3 + 7 = 10
Percentage: (3/10) × 100% = 42.86%

The formula used is:

(3 ÷ (3 + 7)) × 100% = 42.86%

Example 4: Equivalent Ratios

Find equivalent ratios for 2:3.

You can use our calculator by entering:

What are some equivalent ratios to 2:3?

The calculator returns: 2:3, 4:6, 6:9, 8:12, 10:15

Simplified form: 2:3
Equivalent ratios: 2:3, 4:6, 6:9, 8:12, 10:15

The formula used is:

2:3 = 4:6 = 6:9 = 8:12 = 10:15

Example 5: UK Recipe Scaling

A traditional British recipe from a cookbook calls for flour and sugar in a 2:1 ratio. If you use 4 cups of flour, how much sugar?

You can use our calculator by entering:

What is the amount of sugar?

The calculator returns: 2 cups

Ratio: 2:1 (flour:sugar)
4 cups flour = 2 × 2
Sugar needed: 2 × 1 = 2 cups

The formula used is:

2:1 = 4:x x = 2

Example 6: Mixing Solution

A cleaning solution uses concentrate and water in a 1:4 ratio. How much concentrate for 20 parts water?

You can use our calculator by entering:

What is the amount of concentrate?

The calculator returns: 5 parts

Ratio: 1:4 (concentrate:water)
20 parts water = 4 × 5
Concentrate needed: 1 × 5 = 5 parts

The formula used is:

1:4 = x:20 x = 5

Example 7: Aspect Ratio

A screen has a 16:9 aspect ratio. If the width is 1920 pixels, what is the height?

You can use our calculator by entering:

What is the height?

The calculator returns: 1080 pixels

Ratio: 16:9 (width:height)
1920 pixels width = 16 × 120
Height: 9 × 120 = 1080 pixels

The formula used is:

16:9 = 1920:x x = 1080

Example 8: UK School Student-Teacher Ratio

A UK secondary school in Manchester has a student-teacher ratio of 25:1. If there are 500 students, how many teachers?

You can use our calculator by entering:

How many teachers are needed?

The calculator returns: 20 teachers

Ratio: 25:1 (students:teachers)
500 students = 25 × 20
Teachers needed: 1 × 20 = 20

The formula used is:

25:1 = 500:x x = 20

Example 9: UK Company Financial Ratio

A UK company has a debt-to-equity ratio of 2:3. If debt is £400,000, what is equity?

You can use our calculator by entering:

What is the equity?

The calculator returns: £600,000

Ratio: 2:3 (debt:equity)
£400,000 debt = 2 × £200,000
Equity: 3 × £200,000 = £600,000

The formula used is:

2:3 = 400000:x x = 600000

Example 10: Paint Mixing

Paint is mixed in a 3:2:1 ratio of red, blue, and yellow. If you use 6 parts red, how much blue and yellow?

You can use our calculator by entering:

What are the amounts of blue and yellow?

The calculator returns: 4 parts blue, 2 parts yellow

Ratio: 3:2:1 (red:blue:yellow)
6 parts red = 3 × 2
Blue: 2 × 2 = 4 parts
Yellow: 1 × 2 = 2 parts

The formula used is:

3:2:1 = 6:4:2

Summary

These examples show how our ratio calculator can handle:

  • •Simplifying ratios (12:8 = 3:2)
  • •Converting ratios to fractions (3:5 = 3/8)
  • •Converting ratios to percentages (3:7 ≈ 42.86%)
  • •Finding equivalent ratios (2:3 = 4:6 = 6:9 = ...)

You can adapt any real-life situation involving ratios to one of these patterns and let the calculator do the work for you.

How to Use

  1. Enter the two numbers of the ratio (a:b).
  2. Select the type of calculation you need (simplify, convert to fraction, convert to percentage, or find equivalent ratios).
  3. View the result and step-by-step calculation breakdown.

Frequently asked questions

What is a ratio?

A ratio is a comparison of two quantities, expressed as a:b or a/b. It shows how many times one value contains or is contained within the other.

How do you simplify a ratio?

To simplify a ratio, divide both numbers by their greatest common divisor (GCD). For example, 12:8 simplifies to 3:2 by dividing both by 4.

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About this tool

Published by Online Tools Center

Last updated:

Check the units, assumptions and rounding before using a result. Health and financial estimates are educational and do not replace individual professional advice.

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