Ratio of 2 Numbers Calculator

How to use the ratio of 2 numbers calculator

What this calculator does. This tool compares two numerical quantities written as A : B. It can reduce a ratio to lowest terms, normalize either side to 1, multiply both terms by the same factor, or solve a missing term in the proportion A : B = C : D. It also reports the quotient in both directions and each term's percentage of the combined total. Those percentage shares are useful only when A and B are parts of one meaningful total; they are not a claim that every ratio is automatically a part-to-whole comparison. OpenStax's explanation of ratios and rates gives the underlying fraction interpretation.

When to use it. Use the calculator to reduce recipe quantities such as 200 g to 800 g, compare counts such as 18 wins to 24 losses, normalize a map or model scale to 1 : n, enlarge or shrink a known ratio by a common factor, or complete an equivalent-ratio problem when three of A, B, C, and D are known.

How to calculate. The calculator opens with the demonstration values 200 and 800, so the first result and Excel workbook are ready immediately.

1. Select an Operation. The extra field appears only when the selected operation needs a factor, C, or D.
2. Replace Number A and Number B with your values. Results update as you type; no separate Calculate button is needed.
3. Read Equivalent ratio first, then use the quotient and percentage cards for interpretation. Review Calculation details to see the exact transformation.
4. Select Download Excel to export the current validated inputs and outputs as a real .xlsx workbook. Reset clears the demonstration values and results; Excel export remains disabled until a complete valid state is entered again.

Input guide. Operation is required and determines the formula. “Simplify the ratio” divides both terms by their greatest common factor after converting finite decimals to exact whole-number terms. “Write as 1 : n” requires A greater than zero and calculates n = B ÷ A. “Write as n : 1” calculates n = A ÷ B. “Scale by a factor” requires a positive Scale factor; for example, factor 2.5 turns 3 : 4 into 7.5 : 10. “Find C” requires a positive Known value D and uses C = A × D ÷ B. “Find D” requires A greater than zero plus a positive Known value C and uses D = B × C ÷ A.

Number A is required, may be zero when the selected operation permits it, and accepts an ordinary US-style decimal such as 1,250.5. Number B is required and must be greater than zero. Both fields allow up to six decimal places and values no greater than 1,000,000,000. Decimal commas, scientific notation, units, percent signs, and malformed grouping are rejected rather than silently reinterpreted. Changing A or B changes every output. A common mistake is entering quantities in different units, such as 3 feet and 24 inches; convert them to the same unit first.

Output guide. Equivalent ratio is the transformed or completed ratio and is an exact identity within the accepted decimal precision. A ÷ B states how many B-units correspond to one A-side quotient; B ÷ A is its inverse and is shown as “Undefined” when A is zero. A share of total and B share of total divide each positive term by A + B and display percentages that sum to 100%. A 0% share means that term is zero; larger shares indicate a larger contribution to the combined total. The Calculation details table lists the original ratio, formula step, and result used by both the page and the workbook.

Worked example. With A = 200 and B = 800, both values are whole numbers. Their greatest common factor is 200. Dividing both terms by 200 gives 200 ÷ 200 : 800 ÷ 200 = 1 : 4. The quotient A ÷ B is 0.25, the inverse B ÷ A is 4, and the combined total is 1,000. Therefore A is 200 ÷ 1,000 = 20.00% of the total and B is 80.00%. These exact startup values also populate the initial Excel export.

Learn more. For missing-term problems, see OpenStax's treatment of equivalent ratios and cross products. The Open University also explains how ratios, proportions, and percentages describe related but distinct comparisons.