Math · Ratios and proportions
Ratio calculator.
Simplify a ratio to lowest terms, share a total in a given ratio, or scale a ratio up or down from one known amount.
Inputs
Result
Enter the ratio terms.
How ratios work
A ratio compares values: how much of one thing there is compared to another. The key rule is to multiply or divide every term by the same number, which keeps the relationship the same. 4 : 5 is the same as 8 : 10.
Simplify. Divide every term by their greatest common factor. 12 : 18 has a GCF of 6, so it simplifies to 2 : 3. For 1.5 : 2.5 : 4 the calculator first multiplies by 10 to remove the decimals (15 : 25 : 40), finds a GCF of 5 and gets 3 : 5 : 8.
Split a total. Add the parts, then give each person their part over the sum. Sharing 200 in the ratio 2 : 3 means 2 + 3 = 5 parts, so the shares are 200 × 2/5 = 80 and 200 × 3/5 = 120.
Scale a recipe. A pancake recipe uses 3 cups of flour to 2 cups of milk. For 12 cups of flour the scale factor is 12 ÷ 3 = 4, so you need 8 cups of milk, a ratio of 12 : 8.
Frequently asked questions
How do you simplify a ratio?
Divide every term by the greatest common factor of all the terms. 12 : 18 ÷ 6 = 2 : 3.
How do you simplify a ratio with decimals?
Multiply every term by 10, 100 or 1000 until all are whole numbers, then divide by the GCF. 1.5 : 2.5 : 4 becomes 15 : 25 : 40 and then 3 : 5 : 8.
How do you split an amount in a ratio?
Add the parts of the ratio, divide the total by that sum, and multiply by each part. 200 in the ratio 2 : 3 is 80 and 120.
What is the difference between part-to-part and part-to-whole?
Part-to-part compares one part with another, such as 2 boys to 3 girls (2 : 3). Part-to-whole compares a part with the total, such as 2 boys to 5 pups (2 : 5).
How do I scale a ratio up or down?
Divide the amount you know by its ratio term to get a scale factor, then multiply every term by it. 3 : 2 with 3 equal to 12 uses a factor of 4, giving 12 : 8.
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For learning
Ratio terms must be 0 or more; use at most 6 decimal places. Results are rounded for display. Check with your teacher's required method when you hand in homework.