Free online ratio calculator
A ratio compares two quantities by division. This calculator simplifies ratios to lowest terms, shows the decimal equivalent, and solves proportion problems.
: A : B
Used to solve A:B = x:C or A:B = C:x
How to use
- Enter values for A and B.
- Optionally enter C to solve proportions (A:B = x:C or A:B = C:x).
- Click Calculate.
- See the simplified ratio, decimal form, and proportion solutions.
Formulas
Simplified ratio: Divide both terms by GCD(A, B).
Decimal: A ÷ B
Proportion (x:C): x = A × C ÷ B
Proportion (C:x): x = B × C ÷ A
Worked example
Ratio 6:8:
- GCD(6, 8) = 2
- Simplified: 6÷2 : 8÷2 = 3:4
- Decimal: 6÷8 = 0.75 (75%)
Proportion: 3:4 = x:12
- x = 3 × 12 ÷ 4 = 9
- So 3:4 = 9:12 ✓
Frequently asked
How do you simplify a ratio?
Find the greatest common divisor (GCD) of both numbers and divide each by it. For 6:8, GCD is 2, so 6÷2 = 3 and 8÷2 = 4, giving simplified ratio 3:4.
What is a proportion?
A proportion states that two ratios are equal. If A:B = x:C, then x = A×C÷B. For example, if 3:4 = x:12, then x = 3×12÷4 = 9.
What is the decimal form of a ratio?
The decimal form of A:B is A÷B. For 3:4, the decimal is 3÷4 = 0.75, which equals 75%.
Can ratios have decimal or fractional parts?
Yes. A ratio like 1.5:2 is equivalent to 3:4. The calculator handles decimal inputs and simplifies them to integer form.
What is a three-term ratio?
A three-term ratio like 2:3:5 compares three quantities simultaneously. It can describe mixtures, scales, or divisions. For example, to split $1,000 in a 2:3:5 ratio, multiply each part by 1000÷10.