Ratio Calculator

How to use the ratio calculator

1. Pick a task. “Simplify” reduces a ratio such as 15 : 27 to 5 : 9. “Solve a proportion” fills in the missing fourth number in A : B = C : ?. “Split a total” divides an amount, such as a bill or a batch of concrete, into parts in a given ratio.
2. Enter the numbers. For ratios, type the terms separated by colons. Decimals such as 4.8 : 11.2 are converted to whole numbers for you.
3. Read the answer and the line under it, which shows the step the calculator took. For a two-term ratio you also get the 1 : n and n : 1 forms and the first term as a percent of the total.

Order matters. 2 : 3 and 3 : 2 are different ratios, so enter the terms in the order of your sentence: “flour to sugar” puts flour first.

Simplifying a ratio

A ratio compares quantities by division, and like a fraction it can be scaled up or down without changing its meaning. To simplify, divide every term by their greatest common factor. The open textbook Prealgebra 2e from OpenStax works these in section 5.6:

• 15 to 27 becomes 5 to 9 after dividing by 3, and 45 to 18 becomes 5 to 2 after dividing by 9 (Example 5.58).
• 4.8 to 11.2: move both decimal points one place to get 48 : 112, then divide by 16 to get 3 : 7. 2.7 to 0.54: move two places to get 270 : 54, then divide by 54 to get 5 : 1 (Example 5.59).
• 1¼ to 2⅜: convert to 5/4 and 19/8, divide, and you get 5/4 × 8/19 = 10/19, or 10 : 19 (Example 5.60).

The calculator handles decimals the same way: it multiplies every term by the power of ten that clears the decimals, then divides by the GCF. For a fraction such as 1¼, type the decimal, 1.25.

Unit form. Sometimes it is clearer to scale one term to 1. A 3 : 7 ratio is 1 : 2.333, or 0.4286 : 1. Price per ounce, miles per gallon and students per teacher are all ratios in unit form.

Solving a proportion

A proportion says two ratios are equal. If three of the four numbers are known, cross-multiplying finds the fourth:

OpenStax section 6.5 gives two clean checks. Example 6.42 solves x/63 = 4/7. Read it as 7 : 4 = 63 : x, so x = 4 × 63 ÷ 7 = 36. Example 6.43 solves 144/a = 9/4, read as 9 : 4 = 144 : a, so a = 4 × 144 ÷ 9 = 64.

Scaling a recipe. A pancake recipe uses 2 cups of flour to 3 cups of milk. With 5 cups of flour, enter 2 : 3 = 5 : ?. The answer is 3 × 5 ÷ 2 = 7.5 cups of milk.

Map scales. On a map drawn at 1 : 24,000, 3.5 inches on the map is 3.5 × 24,000 = 84,000 inches on the ground. That is 7,000 feet, or about 1.3 miles.

Unit conversions. If 1 inch is 2.54 centimeters, then 1 : 2.54 = 12 : ? gives 30.48 centimeters in a foot.

A quick check: the two ratios should point the same way. If C is bigger than A, the answer should be bigger than B.

Splitting a total by a ratio

To divide an amount in the ratio 2 : 3 : 5, add the parts (2 + 3 + 5 = 10), find the size of one part (total ÷ 10), then multiply by each term.

This is the method for splitting rent by room size, sharing profits by investment, or mixing materials. A concrete mix of 1 : 2 : 3 cement, sand and gravel means 6 parts in all, so 1/6 of the dry volume is cement, 2/6 is sand and 3/6 is gravel. Check the mix your bag or engineer specifies; the calculator only does the division.

When the shares are money, rounding each one to the cent can leave a penny over or short. The check line shows the sum, so you can see if one share needs adjusting.

Ratios, fractions and percentages

A two-term ratio a : b can be read as the fraction a/b, but the parts-of-a-whole fraction is different. In a class with a 3 : 2 ratio of girls to boys, girls are 3/5 of the class, or 60%, not 3/2. The calculator’s “first as % of total” line makes that conversion.

Ratios with different units need converting first. A ratio of 30 minutes to 2 hours is 30 : 120, or 1 : 4, not 15 : 1.

For screen and photo sizes, the aspect ratio calculator adds named formats such as 16:9 and works out pixel dimensions.

Ratios with three or more terms

The same rules apply to ratios with more than two parts: divide every term by the GCF of all of them. 12 : 18 : 30 has a GCF of 6, so it simplifies to 2 : 3 : 5. A term can’t be dropped or simplified on its own, because each one is compared with all the others. Enter up to ten terms separated by colons.

Ratios as rates: comparing unit prices

A rate is a ratio of two different units, such as dollars to ounces. Turning both options into the same unit form makes them comparable. A 12-ounce box for $3.99 costs 399 ÷ 12 = 33.25 cents an ounce, while an 18-ounce box for $5.49 costs 549 ÷ 18 = 30.5 cents an ounce, so the larger box is cheaper per ounce. Enter 3.99 : 12 in the simplify mode and read the n : 1 line for the price per ounce; for ounces per dollar, read 1 : n.

Sources & assumptions

How this calculator gets its numbers. Full method: our methodology.

• Ratio terms must be positive. Decimals are cleared by multiplying every term by the same power of ten, then divided by their GCF.
• A proportion A : B = C : ? is solved as ? = B × C ÷ A.
• Splitting divides the total by the sum of the terms and multiplies by each term; shares are rounded to the cent for display.

Sources

1. OpenStax (Rice University), Prealgebra 2e, 5.6 Ratios and Rate. Writing ratios as simplified fractions: 15 to 27 = 5/9, 45 to 18 = 5/2, 4.8 to 11.2 = 3/7, 2.7 to 0.54 = 5/1 and 1 1/4 to 2 3/8 = 10/19 (Examples 5.58–5.60).
2. OpenStax (Rice University), Prealgebra 2e, 6.5 Solve Proportions and their Applications. Solving proportions with cross products: x/63 = 4/7 gives 36 and 144/a = 9/4 gives 64 (Examples 6.42 and 6.43).

Last reviewed November 2, 2026. Convert quantities to the same unit before forming a ratio.