Ratio Calculator

A ratio compares two quantities by showing how many times one contains the other. It is written with a colon, such as 3 : 2, or as a fraction, 3/2. If a recipe uses 3 cups of flour for every 2 cups of sugar, the ratio of flour to sugar is 3 : 2. This ratio calculator turns two numbers into a ratio, a decimal value, a percentage and a simplified ratio in lowest terms, draws the ratio as a bar, and lists equivalent ratios.

• Antecedent (first term): the first number in a : b.
• Consequent (second term): the second number in a : b.
• Simplified ratio: the same ratio written with the smallest possible whole numbers, such as 2 : 3 instead of 12 : 18.
• Equivalent ratios: ratios that describe the same comparison, such as 2 : 3, 4 : 6 and 6 : 9.

To simplify a ratio, divide both terms by their greatest common divisor (GCD). Take 12 : 18 as an example.

1. Find the GCD of 12 and 18. The common divisors are 1, 2, 3 and 6, so the GCD is 6.
2. Divide both terms by 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3.
3. The simplified ratio is 2 : 3.
4. Check: 2 × 6 = 12 and 3 × 6 = 18, so it is the same ratio.

If the terms are decimals, first multiply both by 10, 100 or 1,000 until they are whole numbers, then simplify. For 2.4 : 3.6, multiply by 10 to get 24 : 36. The GCD of 24 and 36 is 12, so the ratio simplifies to 2 : 3. For 0.5 : 1.5, multiply by 10 to get 5 : 15, and divide by 5 to get 1 : 3.

Multiply or divide both terms by the same non-zero number and you get an equivalent ratio. From 2 : 3 you get 4 : 6, 6 : 9, 8 : 12 and 10 : 15. To test two ratios, cross-multiply: 2 : 3 and 8 : 12 are equal because 2 × 12 = 24 and 3 × 8 = 24.

To split 200 in the ratio 3 : 2, add the parts (3 + 2 = 5), divide the total by that number (200 ÷ 5 = 40), then multiply each part: 3 × 40 = 120 and 2 × 40 = 80. The shares add back to 200. In percentages, 3 : 2 means 60% and 40%.

• Cooking and mixing: paint, concrete, cleaning liquids and recipes all give ingredients as ratios.
• Maps and models: a scale of 1 : 50,000 means 1 cm on the map is 50,000 cm, which is 500 m, in real life.
• Finance and health: debt-to-income, price-to-earnings and waist-to-hip ratios compare two quantities.
• Screens and photos: an aspect ratio of 16 : 9 means the width is 16 units for every 9 units of height.