Ratio Tool
Explore two-part ratios with simplified forms, equivalent values, proportional allocations, and side-by-side comparisons. Adjust decimal precision, swap terms, inspect percentages and detailed results, and view responsive charts for clearer understanding of proportional relationships.
Ratio breakdown
Relative share of both terms
Detailed results
Values and formulas at a glance
| Measure | Value |
|---|
Table of Contents
Highlights
- Simplify whole-number and decimal ratios
- Solve missing terms in equivalent ratios
- Split totals into proportional shares
- Compare ratios using cross-products
- Visualise percentages and export CSV, JSON or PNG
How Ratio Tool Works?
A ratio expresses the relative sizes of two quantities as A : B. To simplify a ratio, express both terms as whole numbers and divide them by their greatest common divisor (GCD). For decimal terms, the tool first scales both values by a power of ten, using up to eight decimal places.
Equivalent ratios multiply both terms by the same factor. Given a new first term X and an original ratio A : B, the corresponding second term is X × B ÷ A. Conversely, given a new second term Y, the first term is Y × A ÷ B.
To split a total T in the ratio A : B, allocate T × A ÷ (A + B) to the first part and T × B ÷ (A + B) to the second part. A comparison of A : B and C : D checks whether the cross-products A × D and C × B match. Scaling multiplies or divides both terms by the chosen factor.
| Mode | Example | Outcome |
|---|---|---|
| Simplify | 16 : 8 | 2 : 1 |
| Equivalent | 3 : 2, new A = 12 | 12 : 8 |
| Split a total | 3 : 2, total = 100 | 60 and 40 |
| Compare | 2 : 3 versus 4 : 6 | Equal ratios |
| Scale | 2 : 3 multiplied by 4 | 8 : 12 |
The results also show both term shares as percentages of their sum, the sum, absolute difference, and quotients where defined. A stacked bar and chart illustrate the proportions.
Practical Use Cases
Home cooks: Scale a 2 : 3 ingredient proportion for a larger recipe while preserving the flavour balance.
Teachers and students: Reduce ratios to simplest form, solve missing equivalent terms, and check exercises through cross-products.
Designers: Compare two width-to-height proportions to see whether layouts preserve the same relative dimensions.
Project managers: Divide a shared total between two teams according to a chosen workload ratio, then review each team’s percentage share.
Small business owners: Split a promotional budget across two activities using a target allocation ratio and inspect the resulting amounts.
Sports analysts: Compare two non-negative performance ratios and visualise each side’s share of the combined figures.
Accuracy and Limitations
The tool uses browser JavaScript floating-point arithmetic and displays results to 2, 4, 6, or 8 decimal places. Decimal simplification considers at most eight fractional digits and may become unavailable when scaled terms exceed JavaScript’s safe-integer range. Inputs must be finite and non-negative; both ratio terms cannot be zero. Equivalent-term solving requires a non-zero original term on the selected side, and dividing by a zero scale factor is rejected. Ratio comparisons use a relative cross-product tolerance of 1 × 10−10, so extremely close ratios may be labelled equal. With a zero denominator, the corresponding quotient is undefined; chart percentages are relative to the two-term sum.
