This ratio calculator helps you work with A and B as a ratio string, or solve a simple proportion using A, B, and D. In simplify mode the primary result is A:B. In proportion mode the solve uses x = (A × D) ÷ B.
Students, cooks, and makers use ratios for mixes, scales, and homework. For percent form of a part over a whole, also see the percentage calculator.
How the formula works
Simplify mode reports the pair you entered as A:B. Proportion mode scales A across B to match D, which is the classic cross multiply pattern when one term is missing.
Worked example
Default simplify inputs A=2 and B=4. Primary result = 2:4.
| Input | Value |
|---|---|
| A | 2 |
| B | 4 |
| Mode | Simplify |
| Result | 2:4 |
How to use the fields
- A and B define the base ratio pair.
- D is used when solving a proportion against that pair.
- Mode chooses simplify versus proportion behavior.
Reading 2:4
The pair means two parts of A for every four parts of B. You can think in halves as 1:2, but this tool’s simplify primary keeps the numbers you typed. That helps when labels on a recipe or drawing already use 2 and 4.
Proportion solves
When you know three of the four related values, proportion mode fills the missing scale. Keep units aligned: cups with cups, pixels with pixels, dollars with dollars.
Common mistakes
- Flipping A and B when reading a word problem
- Mixing units on opposite sides of a proportion
- Dividing by a zero B value
- Expecting automatic reduction in the primary simplify string
Practical checklist
- Write the known pair first.
- Decide whether you need the displayed ratio or a scaled amount.
- Check that B is not zero before proportion solves.
- Convert to percents only after the ratio relationship is clear.
Recipes and mixes
Scale a sauce by keeping the same A:B relationship while changing total volume. Solve for the new amount on one side, then adjust the other side to match the ratio.
Maps and models
Map scales are ratios too. If 2 cm represents 4 km in a simplified example sense, the same cross multiply idea sizes other distances. Always confirm the legend units before you trust the draw length.
Scaling recipes without waste
If a recipe uses 2 cups stock to 4 cups water style ratios, keep A and B in the same units. Scale total volume by solving the proportion for the new batch size, then measure once. Changing only one side breaks the taste balance the ratio was protecting.
For baker percentages, convert the ratio into baker percent after you trust A:B. This page stays on simple two part relationships first.
Finance and allocation ratios
Portfolio mixes such as 2:4 risk to stable assets are the same math as classroom ratios. Confirm whether you mean dollars or percents before you rebalance. A 2:4 dollar mix is one third risk assets by value, which is easier to check with a percentage view afterward.
Debt to income conversations use ratios too, but they often need payment and income fields rather than a bare A:B pair. Use the right calculator when underwriting language appears.
Teaching the cross multiply habit
Write A/B = C/D, cross multiply, then solve for the missing term. Proportion mode follows that idea when D is known and C is missing. Keeping a paper sketch beside the tool reduces flipped fraction mistakes.
Maps, models, and print scales
Scale bars on maps are ratios in disguise. If 2 cm on paper represents 4 km on land in a teaching example, every other paper length follows the same proportion. Measure carefully and keep cm with cm before you convert to km.
3D print scaling uses the same idea when you enlarge a model uniformly. Changing only one axis breaks fit with mating parts.
Limitations
The calculator does not reduce fractions in the primary simplify result and does not handle three part ratios like A:B:C. For part of whole as a percent, use the percentage calculator linked above.