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Proportion Calculator

Solve any proportion instantly. Find missing values, cross multiply, and verify if two ratios are proportional.

a / b = c / d

Leave one field empty to solve for the unknown

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Check if a/b = c/d

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Direct Proportion: y = kx

When x increases, y increases proportionally

Inverse Proportion: y = k/x

When x increases, y decreases proportionally

Quick Examples

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Proportion Formulas

Cross Multiplication:
a/b = c/d ⇔ a·d = b·c

Direct Proportion:
y = k·x, k = y₁/x₁ = constant

Inverse Proportion:
x·y = k, k = x₁·y₁ = constant

Mastering Proportions: The Complete Guide

A proportion is an equation that states two ratios are equal. Proportions are fundamental in mathematics, appearing in scaling, unit conversion, similarity, and countless real‑world applications. This Professional Proportion Calculator provides four essential tools: solving for a missing term in a proportion, checking whether two ratios form a proportion, and working with direct and inverse proportional relationships.

Solving Proportions with Cross Multiplication

Given a proportion a/b = c/d, cross multiplication gives a·d = b·c. If one value is unknown, you can isolate it algebraically. For example, to find a when b, c, and d are known: a = (b·c)/d. This method is reliable and works for any real numbers (provided denominators are non‑zero).

💡 Example: x/5 = 3/15

Cross multiply: x·15 = 5·3 → 15x = 15 → x = 1.

Direct Proportion

Two quantities are directly proportional if their ratio is constant: y/x = k or y = kx. As one quantity increases, the other increases at the same rate. Examples include distance traveled at constant speed, cost of items at a fixed price, and conversion between units (e.g., inches to centimeters).

Inverse Proportion

Inverse proportion describes a relationship where the product of two quantities is constant: xy = k or y = k/x. As one quantity increases, the other decreases. Common examples include the relationship between speed and travel time for a fixed distance, or the number of workers and the time needed to complete a job.

Checking Proportionality

To verify whether two ratios a/b and c/d form a proportion, compare their cross products: if a·d = b·c, the ratios are proportional. This is more reliable than comparing decimal approximations, which can suffer from rounding errors.

Frequently Asked Questions

How do I solve a proportion with a variable in the denominator?

Cross multiply as usual. For example, 3/x = 6/10 → 3·10 = 6·x → 30 = 6x → x = 5. The process is identical regardless of the variable's position.

What is the constant of proportionality?

It is the constant ratio k in direct proportion (y = kx) or the constant product in inverse proportion (k = xy). It characterizes the relationship between the variables.

Can proportions involve fractions or decimals?

Yes. The calculator accepts any real numbers, including fractions (entered as decimals) and negative numbers. Cross multiplication works exactly the same way.

How are proportions used in scaling recipes?

If a recipe serves 4 and you need to serve 10, set up the proportion 4/10 = (ingredient amount)/x. Cross multiply to find the scaled amount x.

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