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This ratio calculator simplifies ratios, finds the missing ratio value, creates equivalent ratios, and scales ratios up or down. Plus, we show the work for the calculations.

Use the ratio calculator when working with proportions to make sure ratios are equivalent. When scaling ratios the calculator can verify that your new proportions values remain true to the original ratios.

The ratio calculator takes integers, decimals and scientific e notation with a max of 15 characters.

Simplify Ratios

Enter A and B, and the calculator simplifies the ratio A : B dividing by the greatest common denominator if possible. If not, the calculator finds an equivalent ratio by multiplying each A and B value by 2 to create values for C and D. The ratio calculator uses the same process for 3-term ratios A : B : C, or D : E : F.

Solve for the Missing Ratio Value

For two pair of ratios enter 3 values to find the 4th. For example enter A, B and C to find D.
The calculator shows the steps and solves using the ratio equation D = C * (B/A)

Or enter A, B and D to find C.
The calculator shows the steps and solves using the ratio equation C = D * (A/B)

The calculator uses the same process for 3-term ratios. If you want to solve for a 3-term ratio by hand you can still use the above equations. Just solve for one term at a time using the corresponding known ratio and a value from the ratio with the missing term.

Evaluate Equivalent Ratios

Enter two ratios to find if the ratio A : B is equivalent to the ratio C : D. The calculator solves the ratios as fractions, comparing A/B and C/D. If the fractions can be simplified to the same fraction in lowest terms the ratios are equivalent. If the fractions are not equivalent the calculator indicates which fraction is larger and which is smaller using greater than or less than signs.

Practical Example: Concrete Mix Ratios

A common concrete recipe mixes cement, sand and gravel in a 1:2:3 ratio by volume. The mix includes 1 part cement, 2 parts sand, and 3 parts gravel. Say you had 7 buckets of sand and wanted to know much cement and gravel you needed to use up all this sand on a concrete project. In the calculator select the A:B:C = D:E:F calculation. Input A, B and C as 1, 2 and 3 which is your concrete mix ratio. Then input 7 for the E value and click calculate. The resulting ratio is 3.5 : 7 : 10.5. So you need 3.5 buckets of cement for your concrete mix. And 10.5 or 10 and a half buckets of gravel to use up all your sand on this project.

Practical Example: Scaling a Recipe

Sometimes you need to scale a favorite recipe up or down. Say you know the ratio of macaroni, milk and cheese for your grandmother's famous mac and cheese recipe: it's a 1-pound box of macaroni, 2.5 cups milk, and 6.5 cups of cheese. You're having a party and want to make 3 times as much as you normally get from one recipe -- how much do you need of each ingredient? Select Scale A:B:C in the calculator and input A, B, and C as 1, 2.5 and 6.5. Select Multiply, enter 3 as your scale factor and click calculate. The resulting ratio is 3 : 7.5 : 19.5. So you need 3 boxes of noodles, 7.5 cups of milk, and 19.5 cups of cheese to scale the recipe by 3.

About Ratios

A ratio is a comparison of the relative size of two or more numbers.

Part-to-part ratios compare relative quantities to each other, regardless of the greater whole. If you had a salad and compared the ratio of cucumber to tomato pieces, your part-to-part cucumber:tomato ratio might be 5:4. For every 5 cucumber pieces there are 4 tomato pieces. This would be true regardless of the other salad ingredients, or how big the salad was.

This calculator works with part-to-part ratios and relative scaling.

Part-to-whole ratios compare the quantity of a part to the total quantity in the whole. In the salad example if there were a total of 50 pieces of vegetables, your part-to-whole cucumber:vegetables ratio would be 5:50. You could read this as a fraction and know that 5/50, or 1/10 of the salad vegetables are cucumber pieces.

Convert Ratio to Fraction

A part-to-part ratio states the proportion of the parts in relation to each other. The sum of the parts makes up the whole. The ratio 1 : 2 is read as "1 to 2." This means of the whole of 3, there is a part worth 1 and another part worth 2.

To convert a part-to-part ratio to fractions:

1. Add the ratio terms to get the whole. Use this as the denominator.
   1 : 2 => 1 + 2 = 3
2. Convert the ratio into fractions. Each ratio term becomes a numerator in a fraction.
   1 : 2 => 1/3, 2/3
3. Therefore, in the part-to-part ratio 1 : 2, 1 is 1/3 of the whole and 2 is 2/3 of the whole.

Related Calculators

To reduce a ratio to lowest terms in whole numbers see our Ratio Simplifier.

To simplify a fraction into a reduced fraction or mixed number use our Simplifying Fractions Calculator.