Ratio Calculator
Simplify, Solve & Scale Ratios
Understanding Ratios & Proportions
A ratio compares two quantities, while a proportion says two ratios are equal — together they're the backbone of scaling recipes, mixing solutions, reading maps, and splitting shared costs fairly.
Just like a fraction, a ratio can be reduced to its simplest form by dividing both terms by their greatest common factor — 8:12 and 2:3 describe exactly the same relationship.
When two ratios are set equal to each other, cross-multiplication lets you solve for any single unknown term — the technique behind unit conversions, map scales, and recipe adjustments.
Cross-Multiplication
This single formula solves any proportion problem: convert both ratios to fractions, cross-multiply, and isolate the unknown term.
Scaling a Ratio
Multiplying every term of a ratio by the same factor never changes what it represents — 1:2 and 50:100 are the same proportion. This calculator's "scale to total" mode goes one step further, finding the exact terms needed so they add up to a specific number while keeping the original proportion intact — perfect for splitting a bonus, a bill, or a batch of ingredients.
Every ratio has one lowest-terms representation, found via the GCF.
The key technique for solving any proportion problem.
Splits a target sum according to a given proportion.
Key Takeaways
- Simplifying a ratio uses the same GCF technique as simplifying a fraction.
- Cross-multiplication solves any proportion for a single missing term, given the other three.
- Scaling to a total preserves the original proportion while making the terms add up to any target sum.
Frequently Asked Questions
- On the Simplify tab, enter A and B to reduce a ratio to lowest terms.
- On the Proportion tab, enter A, B, and C to solve
A:B = C:xfor the missing term x. - On the Scale tab, enter A and B, choose whether to scale by a multiplying factor or to a target total, and enter that value.
- Click "Calculate" to see the result.
Simplifying a ratio works exactly like simplifying a fraction: find the greatest common factor (GCF) of both terms and divide each term by it. For example, the ratio 8:12 shares a GCF of 4, so it simplifies to 2:3. Decimal ratios are first scaled up to whole numbers before this step.
A proportion states that two ratios are equal, written A:B = C:D. If three of the four terms are known, the fourth can always be found using cross-multiplication: A × D = B × C. Solving for the missing term D gives D = (B × C) / A, which is exactly what this calculator computes.
Scaling by a factor multiplies both terms of the ratio by the same number, keeping the ratio's proportion identical (2:3 scaled by 4 becomes 8:12). Scaling to a total instead finds new terms that add up to a target sum while preserving the original proportion — useful for splitting a fixed amount, like a bonus or a recipe, according to a given ratio.
The formula for the missing term divides by A (x = (B × C) / A), and division by zero is undefined. If A is zero, the proportion 0:B = C:x can't be solved for a finite x unless C is also zero, in which case x could be anything — so the calculator blocks A = 0 entirely.
Ratio terms are conventionally zero or positive, since a ratio compares the relative size of two non-negative quantities (like ingredients in a recipe, or a screen's width to its height). Decimal values are fully supported for simplifying and scaling — the calculator scales them to whole numbers internally before finding the simplest form.