Finance & Tax Date & Time Health & Lifestyle Math Geometry Advanced Math Unit Converters Energy & Home Construction Developer Tools Text Utilities Lifestyle Converters Image & File Tools

Ratio Calculator

Solve ratio proportions a:b = c:d. Enter three values and find the missing one with step-by-step working.

: = :
Missing Value
—
Simplified First Ratio
—
Simplified Second Ratio
—

Step-by-Step Solution

    Formula

    Proportion: a : b = c : d
    Cross-multiplication: a × d = b × c

    To find the missing value, isolate the unknown using cross-multiplication. For example, if d is unknown: d = (b × c) / a

    Examples

    How It Works

    A ratio compares two quantities, written as a:b. A proportion is a statement that two ratios are equal: a:b = c:d. Proportions appear everywhere — scaling recipes, converting units, working with maps, mixing concentrations, or resizing images. As long as you know any three of the four values, the fourth is determined uniquely.

    The mathematical tool that solves a proportion is cross-multiplication. Because a:b = c:d is equivalent to a/b = c/d, multiplying both sides by b and d gives a × d = b × c. From this single identity you can isolate whichever variable is missing — for example, d = (b × c) / a, or a = (b × c) / d. This calculator performs that algebra automatically and also reduces each ratio to its simplest whole-number form using the greatest common divisor (GCD).

    Tips & Best Practices

    Leave exactly one field blank — the calculator will solve for whichever value is missing.
    Cross-multiplication works in any direction: a × d always equals b × c when the ratios are equal.
    A simplified ratio uses the smallest whole numbers that preserve the same relationship — e.g. 4:6 simplifies to 2:3.
    Watch the units: a ratio is dimensionless only if both quantities share the same unit. 2 km : 500 m should be rewritten as 2000 m : 500 m = 4:1.
    If one of the known values is zero, the proportion may have no unique solution — check that you have not mistyped a value.

    Related Calculators

    Cross Multiplication Calculator
    Math
    Fraction Calculator
    Math
    Percentage Calculator
    Finance & Tax
    Circle Calculator
    Geometry

    Frequently Asked Questions

    What is the difference between a ratio and a proportion?

    A ratio compares two quantities (e.g. 3:4). A proportion states that two ratios are equal (e.g. 3:4 = 6:8). This calculator solves proportions — given three of the four values, it finds the fourth.

    For a proportion a:b = c:d, the cross products are equal: a × d = b × c. This identity comes from multiplying both sides of a/b = c/d by b × d. Once you know three values, you can rearrange the identity to solve for the fourth.

    Yes. The proportion identity a × d = b × c holds for any real numbers, so you can enter decimals like 2.5:3.7 = 5:d. The calculator returns the missing value but only simplifies to whole-number ratios when all four values are integers.

    A proportion has no unique solution when the value you would divide by is zero. For example, solving for d in 0:5 = 3:d requires dividing by 0. Double-check your inputs — usually a zero appears by mistake.

    Find the greatest common divisor (GCD) of both numbers and divide each by it. For example, 12:18 has GCD 6, so it simplifies to 2:3. The calculator does this automatically when both values are whole numbers.