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Ratio Calculator
Simplify a ratio, build an equivalent ratio, convert part-to-part into part-to-whole, or solve one missing term in a:b = c:d.
One part of the ratio, such as 4
The part it is compared with, such as 6
Leave blank for a two-part ratio
Enter two parts to simplify a ratio. A third part is optional.
Enter two parts to simplify a ratio. A third part is optional.
This ratio calculator is for middle-school classwork on ratios. It simplifies two or three parts to lowest terms, including a short decimal such as 1.5:3, by clearing the decimal and dividing by the greatest common divisor. It builds an equivalent ratio from a multiplier or by making one part a chosen number, and it turns a part-to-part ratio into part-to-whole fractions. A missing term in a:b = c:d is solved with cross products, still written with colons. The fraction form a/b = c/d belongs to the proportion calculator.
How to find a ratio and simplify it
A ratio compares quantities with a colon. Four blue counters and six red counters are the ratio 4:6, read as 4 to 6. The ratio formula for two parts is a:b, and the same comparison extends to three parts, a:b:c. Order matters, so 4:6 is not the same comparison as 6:4.
To simplify, divide every part by the greatest common divisor, the largest whole number that divides each part evenly. The greatest common divisor of 4 and 6 is 2, and dividing both parts by 2 gives 2:3. For three parts, use one divisor for all of them. The greatest common divisor of 2, 4, and 6 is 2, so 2:4:6 simplifies to 1:2:3. A short decimal is cleared before that division. 1.5 and 3 are multiplied by 10 to clear the decimal, which gives 15:30, and dividing by the greatest common divisor 15 gives 1:2. A zero part is allowed: 0:5 simplifies to 0:1, which means none of the first quantity for every 1 of the second. This calculator does not use a negative part.
Equivalent ratios and how to solve a ratio
Equivalent ratios name the same comparison. Multiply or divide every part by the same non-zero number, called the multiplier, and the ratio does not change. 2:3 multiplied by 4 is 8:12, and 8:12 simplifies back to 2:3. You can also start from the part you want. If the first part of 2:3 should become 8, the multiplier is 8 ÷ 2 = 4, and the second part is 3 × 4 = 12, so the equivalent ratio is 8:12.
How to solve ratios with one missing term uses that same equality, written a:b = c:d. The cross products are equal: a × d = b × c. In 2:3 = ?:12, 2 × 12 = 3 × the missing part, so the missing part is 24 ÷ 3 = 8 and the ratios are 2:3 = 8:12. A proportion is the same equality written as fractions, a/b = c/d. The proportion calculator solves that fraction form. This page keeps the colon. Dividing by zero, or a result that would be 0:0, is explained in a sentence instead of a number.
Part-to-part and part-to-whole
A part-to-part ratio compares the parts with each other. In a tray of 2 apple slices and 3 orange slices, the part-to-part ratio of apple to orange is 2:3. A part-to-whole ratio compares one part with the whole group. Add the parts to get the whole: 2 + 3 = 5. Apple compared with the whole is 2:5, which is the fraction 2/5. Orange compared with the whole is 3:5, which is 3/5. The first part of 2:3 is 2/5 of the whole, and the second part is 3/5 of the whole. The same addition works for three parts: the whole is the sum, and each fraction is that part over the sum.
When the ratio is written as fractions
Frequently Asked Questions
How do you simplify a ratio?
Divide each part by the greatest common divisor. For 4 and 6, that divisor is 2, so 4:6 = 2:3. For 2, 4, and 6, the divisor is 2, so 2:4:6 = 1:2:3. For 1.5 and 3, multiply by 10 to clear the decimal, then 15:30 divides by 15 to give 1:2.
How do you find equivalent ratios?
Multiply or divide every part by the same number. To make the first part of 2:3 into 8, use the multiplier 4, because 2 × 4 = 8 and 3 × 4 = 12. The equivalent ratio is 8:12. Another shared multiplier gives another equivalent ratio, such as 2:3 × 2 = 4:6.
What is a part-to-part ratio?
A part-to-part ratio compares one part with another part, not with the total. 2:3 means 2 of the first quantity for every 3 of the second. The part-to-whole ratios for that pair are 2:5 and 3:5, because the whole is 2 + 3 = 5. As fractions of the whole, the parts are 2/5 and 3/5.
How do you solve a ratio with a missing number?
Write the ratios as a:b = c:d and leave the unknown blank. Set the cross products equal, a × d = b × c, then divide. For 2:3 = ?:12, 2 × 12 = 3 × the blank, so the blank is 8. The proportion calculator solves the same equality when it is written as the fractions a/b = c/d.
What is the ratio formula?
The ratio formula is a:b for two quantities, or a:b:c for three. Simplify by dividing every part by the greatest common divisor. An equivalent ratio is a×k:b×k for a multiplier k other than 0. The fraction of the whole for the first part is a/(a + b), so in 2:3 the first part is 2/5 and the second part is 3/5.