Ratio & Proportion Calculator (A:B = C:D)
Solve proportions (A : B = C : D), simplify multi-term ratios, and divide amounts proportionally.
Ratio Calculator — interactive calculator, computed instantly in your browser.
Ratio & Proportion Guide: Simplification, Scaling & Parts Partition
Proportion Equality & Cross-Multiplication
Cross-Product Invariant: For any valid proportion $A/B = C/D$, the cross products are always strictly equal: $A \times D = B \times C$.
A ratio compares two quantities by division, indicating how many times one number contains another. A proportion is an equation stating that two ratios are equivalent ($A:B = C:D$). Ratios are used in culinary scaling, architectural blueprints, financial liquidity analysis, and screen display aspect ratios (16:9, 21:9).
1. Fundamental Proportion Solving Formula
To solve for an unknown variable $X$ in a proportion:
2. Dividing a Total Amount by Ratio Parts
To distribute a total quantity $T$ into ratio parts $A : B : C$:
Example: Splitting $\$1,200$ among three partners in ratio $2 : 3 : 5$:
- Total Parts = $2 + 3 + 5 = 10$ parts
- Partner 1: $\$1,200 \times (2 / 10) = \mathbf{\$240}$
- Partner 2: $\$1,200 \times (3 / 10) = \mathbf{\$360}$
- Partner 3: $\$1,200 \times (5 / 10) = \mathbf{\$600}$
🔗 Proportions & Aspect Ratio Tools
Ratios compare relative quantities in geometry, chemistry, recipe scaling, and screen aspect dimensions. Explore our full ➗ Math Hub.
Convert ratios to percentages or solve fraction arithmetic using the cross-references below.
Frequently Asked Questions (Ratio Calculator)
An aspect ratio is the proportional relationship between the width and height of an image or screen. For example, modern 1080p and 4K displays use 16:9, meaning for every 16 units of width, there are 9 units of height.
The Golden Ratio (denoted $\phi \approx 1.618033$) is a mathematical proportion where the ratio of the sum of quantities to the larger quantity equals the ratio of the larger to the smaller: $(a+b)/a = a/b = \phi$.