Ratio & Proportion Solver

What is a ratio?

A ratio compares two or more quantities. The ratio 3:4 means "for every 3 of A, there are 4 of B." Ratios can be simplified by dividing both terms by their GCD. 6:8 simplifies to 3:4.

How decimal ratios are simplified

Decimal ratios are reduced without rounding their terms to whole numbers. The calculator first rewrites both terms with a common power-of-ten denominator, then finds the greatest common divisor of the resulting integers. For example, 1.5:2.5 becomes 15:25 and then 3:5. This is why the simplified answer can be an integer ratio even when the values you enter include decimal places.

Proportions

A proportion states that two ratios are equal: a/b = c/d. Cross-multiplying: a × d = b × c. This is used in scaling recipes, maps, and similar problems.

When you supply all four values, the tool checks that cross-products a × d and b × c agree, allowing only a small floating-point tolerance. A complete but inconsistent proportion is reported as an error, so no entered term is silently ignored. With exactly one blank term, the same cross-multiplication rule solves that missing value.

The golden ratio

The golden ratio φ ≈ 1.618 appears throughout nature and art. It is the ratio where the whole is to the larger part as the larger part is to the smaller part: (a + b) / a = a / b = φ. The Fibonacci sequence converges to φ: 1, 1, 2, 3, 5, 8, 13, 21... (each term divided by the previous approaches 1.618).

Three-part ratios

Ratios can have more than two parts and still be used for precise scaling:

• Concrete mix: 1:2:3 (cement:sand:aggregate) by volume. To make 6 parts total, use 1 part cement, 2 parts sand, 3 parts aggregate.
• Paint mixing: 1:4 base-to-tint gives a light tint; 1:1 gives a mid-tone.
• Fertilizer N-P-K: a 10-20-10 fertilizer has a 1:2:1 ratio of nitrogen to phosphorus to potassium by weight.

Scaling with ratio tables