Math

Ratio Calculator

Simplify and convert ratios.

CALCULATOR

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THE NUMORIX GUIDE

How to use the Ratio Calculator

Last reviewed September 14, 2026

What this calculator does

Find gcd(a,b) to reduce a:b, compute decimal = a/b, and compute each share of the pair as percentA = 100a/(a+b) and percentB = 100b/(a+b).

Formula and method

Find gcd(a,b) to reduce a:b, compute decimal = a/b, and compute each share of the pair as percentA = 100a/(a+b) and percentB = 100b/(a+b).

Variables and inputs

Value A defaults to 12 and Value B to 8. The inputs are nonnegative in the UI, but a nonzero divisor and positive total are needed for meaningful percentages.

Worked example

For 12:8: gcd(12,8)=4, so simplified ratio = 3:2; decimal ratio = 12/8 = 1.5; total = 20, so shares are 12/20 = 60% and 8/20 = 40%.

How to interpret the result

A ratio compares relative amounts; the two displayed percentages describe each amount's share of their combined total.

Common mistakes to avoid

Do not reverse the ratio when interpreting decimal a/b. Reduce both terms by the same GCD, not by unrelated factors.

Assumptions and limitations

The recursive GCD helper is intended for integer-like values; decimal inputs can produce awkward remainders. Division by zero or a zero total is not a useful ratio case.

Practical use and checks

The Ratio Calculator is useful for comparing compatible quantities and for showing each quantity's share of a combined total. Enter A = 12 and B = 8 as a check; the simplified ratio should be 3:2, the decimal ratio A/B should be 1.5, and the shares should be 60% and 40%. That example shows why reducing both terms by their greatest common divisor changes the notation but not the relationship. If the question is "how many of A per B," keep the order A:B consistent when interpreting the decimal. Use ratios for recipes, staffing, mixtures, or financial splits only when the units have a meaningful comparison. A ratio of dollars to dollars can be unitless, while grams to liters may describe a density only when the context says so. Do not confuse a share percentage with a percent change, and do not divide by zero. Decimal inputs can create awkward greatest-common-divisor behavior in a tool intended for integer-like values, and a zero total cannot produce meaningful shares. Negative values may be algebraically possible but are rarely sensible for a count or allocation. State the numerator and denominator labels next to the result so a simplified ratio is not detached from the decision it is meant to support.

Sources and references

COMMON QUESTIONS

Frequently asked questions

Do the two percentages always add to 100%?

When the total a+b is positive, yes; they are the two shares of the combined amount.

Is 12:8 different from 3:2?

No, they express the same relative comparison because both terms were divided by 4.