Ratio to Fraction Calculator

How to Convert a Ratio to a Fraction

Quick answer: To convert a ratio A:B to a fraction, write A over B, then divide the numerator and denominator by their greatest common divisor. For example, the ratio 6:8 becomes 6/8, which simplifies to 3/4. The calculator above performs this conversion instantly and also shows the equivalent decimal and percentage.

What is a ratio?

A ratio compares two quantities. A ratio written as 3:4 means there are three units of the first quantity for every four units of the second. Ratios appear in recipes, maps, classroom problems, construction measurements, design proportions and financial comparisons. A fraction is another way to express the same comparison when you want to divide the first quantity by the second. In this context, 3:4 is written as 3/4.

Be careful about what the quantities represent. A ratio of boys to girls of 3:4 gives the fraction 3/4 for boys divided by girls, but the fraction of the whole group who are boys is 3/(3+4), or 3/7. These are different questions and require different calculations.

Ratio to fraction formula

For a ratio A:B, the equivalent fraction is A/B, provided B is not zero. If A and B are whole numbers, simplify by dividing both by their greatest common divisor (GCD). For decimal values, first multiply both numbers by a suitable power of ten to remove decimal places, then simplify.

How to use this calculator

1. Enter the first number in the ratio in the A field.
2. Enter the second number in the B field. This number cannot be zero.
3. Select Calculate Fraction to display the simplified fraction.
4. Review the decimal, percentage and calculation explanation.
5. Use Swap to reverse the ratio or Copy Results to reuse the answer.

Worked examples

Example 1 — 6:8: Write the ratio as 6/8. The greatest common divisor of 6 and 8 is 2. Divide both numbers by 2 to get 3/4. As a decimal, 3 ÷ 4 = 0.75, and as a percentage it equals 75%.

Example 2 — 12:18: The fraction is 12/18. Both values can be divided by 6, giving 2/3. Its decimal representation is approximately 0.666667, or 66.6667%. A repeating decimal does not mean the fraction is inaccurate; 2/3 is the exact value.

Example 3 — 1.5:2.5: Convert the ratio to 1.5/2.5. Multiply the top and bottom by 10 to obtain 15/25. Divide both by 5, producing 3/5. The decimal is 0.6 and the percentage is 60%.

Example 4 — 2:5: The equivalent fraction is already in simplest form: 2/5. Dividing 2 by 5 gives 0.4, or 40%. This is useful when comparing quantities or converting a ratio into a numerical rate.

Ratio to fraction versus part of a whole

One of the most common errors is confusing a part-to-part ratio with a part-to-whole fraction. Suppose a paint mixture uses two parts blue paint and three parts white paint. The blue-to-white ratio is 2:3, so blue divided by white equals 2/3. However, the mixture has five total parts. Blue therefore makes up 2/5 of the complete mixture, while white makes up 3/5. To find a part of the total from A:B, calculate A/(A+B) or B/(A+B), not simply A/B.

How to simplify a fraction from a ratio

Reducing a fraction means finding an equivalent fraction with smaller whole-number values. Start by identifying the greatest common divisor. For 24:36, the GCD is 12. Dividing 24 and 36 by 12 gives 2/3. The ratio 24:36 and the fraction 2/3 describe the same proportional relationship, even though their numbers look different. Simplifying makes the relationship easier to read and compare.

Converting fractions to decimals and percentages

After simplifying a fraction, divide its numerator by its denominator to obtain the decimal. Multiply the decimal by 100 to express the result as a percentage. For example, 7:20 becomes 7/20, then 0.35, then 35%. Some fractions produce repeating decimals. In those cases, the calculator displays a rounded decimal and percentage while retaining the exact simplified fraction.

Where ratio-to-fraction conversions are useful

Cooking: A recipe may use a 1:3 ratio of concentrate to water. The fraction of concentrate relative to water is 1/3, while its share of the combined mixture is 1/4. Education: Students use conversions to compare fractions, ratios and percentages. Construction: Material mixes are often described in parts, such as cement to sand. Business: Ratios can express relationships between quantities, sales categories or operating metrics. In each case, make sure the numerator and denominator correspond to the quantities you actually want to compare.

Important limitations

The calculator converts the first ratio value divided by the second; it does not automatically calculate the first value as a share of their combined total. The second value must be nonzero. Decimal inputs are treated as exact decimal values as entered, within the calculator’s supported precision. Results involving repeating decimals are rounded for display. For scientific measurements or financial reporting, consider the original measurement precision and any rounding requirements.

Frequently asked questions

How do I turn a ratio into a fraction?

Write the first ratio number above the second, then simplify. For example, 4:6 becomes 4/6 and reduces to 2/3.

What is 3:4 as a fraction?

The ratio 3:4 is 3/4. It is already in simplest form, and its decimal value is 0.75.

What is 2:5 as a fraction?

The ratio 2:5 becomes 2/5, which equals 0.4 or 40% when interpreted as 2 divided by 5.

Can a ratio contain decimals?

Yes. For example, 0.5:1.5 equals 1:3 after multiplying both values by 2, so the simplified fraction is 1/3.

Is a ratio the same as a fraction?

A ratio compares quantities, while a fraction can express division or a part of a whole. A:B can be written as A/B, but a part-to-part ratio is not automatically the same as the first part’s share of the total.

How do I find a fraction of the total from a ratio?

For a two-part ratio A:B, add A and B, then divide the part of interest by that total. In a 2:3 ratio, the first part is 2/5 of the whole.

Can the second number in a ratio be zero?

A ratio such as 5:0 can be written symbolically, but 5/0 is undefined as a numerical fraction. The calculator therefore rejects a zero denominator.

Why does my decimal result have rounded digits?

Some fractions, such as 1/3, have infinitely repeating decimal representations. The calculator rounds the decimal display while preserving the exact simplified fraction.