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Exact ratio and proportion arithmetic

Ratio Calculator with Proportion Solver

Simplify a ratio, multiply it to an equivalent scale, divide a total in a given ratio or solve a missing fourth value in a proportion. Integer results use exact greatest-common-divisor reduction.

Ratio operation

Ratio and proportion result

ratio calculator: formulas, interpretation and worked use

This ratio calculator separates four common tasks that are often mixed together: simplification, equivalent scaling, proportional solving and allocation of a total.

Transparent calculation steps

The ratio calculator displays the intermediate values used in the result so users can audit the calculation rather than receiving an unexplained answer.

Input validation and edge cases

Impossible, incomplete and non-finite inputs are rejected with a specific message. Boundary cases are handled explicitly instead of being silently rounded into a misleading result.

Units and precision

Where units apply, inputs are converted to a consistent internal basis before the formula is evaluated. Results retain enough precision for checking and are then formatted for practical reading.

Worked interpretation

The result panel separates the primary answer, supporting quantities and a formula trace. This makes the calculator suitable for checking homework, planning scenarios and comparing alternatives.

Equivalent ratios and proportional allocation

The ratio calculator simplifies integer ratios with the greatest common divisor, solves missing terms in a proportion by cross multiplication, and divides a total according to entered shares. For a:b = c:x, the missing value is x = bc/a when a is nonzero. Allocation mode first totals all positive ratio parts and then multiplies the available amount by each part’s fraction of that total.

Reading the comparison correctly

The ratio calculator preserves order: 2:3 is not interchangeable with 3:2. Decimal inputs can be scaled into an equivalent whole-number ratio within the selected precision, but recurring decimals may require the user to enter the intended fraction directly. A zero may be meaningful in a ratio, yet a denominator position used for division cannot be zero. For recipes, maps, mixtures and financial splits, make sure all quantities describe comparable units before interpreting a simplified ratio.

Can ratios contain negative values?

The calculator allows signed ratios for algebraic work, but allocation mode requires a positive total and positive ratio parts.

How is a ratio simplified?

Both integer terms are divided by their greatest common divisor, with the sign normalized to the first term.

Can it split a total?

Yes. Divide mode allocates the total according to each part divided by the sum of the ratio parts.