What This Proportion Calculator Does
A proportion is a statement that two ratios are equal, written as a:b = c:d. This calculator solves that equation for whichever term you don't know. You supply any three of the four values — a, b, c, and d — and the tool finds the missing fourth so the two ratios match exactly. It's handy for scaling recipes, converting units, resizing images, working out map distances, and solving cross-multiplication problems in homework.
How to Use It
- Enter values for any three of the four fields: a, b, c, or d.
- Leave the field you want to solve for blank.
- The calculator detects the empty term and returns its value instantly.
For example, to solve 2:4 = 3:x, enter a = 2, b = 4, c = 3, and leave d blank.
The Formula
The calculator relies on cross-multiplication. Because a:b = c:d means a × d = b × c, each unknown is found by rearranging that single rule:
$$\frac{\text{A}}{\text{B}} = \frac{\text{C}}{\text{D}}$$- Solve for a: \(\text{A} = \frac{\text{B} \times \text{C}}{\text{D}}\)
- Solve for b: \(\text{B} = \frac{\text{A} \times \text{D}}{\text{C}}\)
- Solve for c: \(\text{C} = \frac{\text{A} \times \text{D}}{\text{B}}\)
- Solve for d: \(\text{D} = \frac{\text{B} \times \text{C}}{\text{A}}\)
If the value needed in the denominator is zero, the calculator can't divide and will return an error instead of an impossible result.
Worked Example
Take the proportion 2:4 = 3:d. With a = 2, b = 4, c = 3 and d left blank, the tool uses the "solve for d" formula:
- \(\text{D} = \frac{\text{B} \times \text{C}}{\text{A}}\)
- \(\text{D} = \frac{4 \times 3}{2}\)
- $$\text{D} = \frac{12}{2} = \mathbf{6}$$
So 2:4 = 3:6, which is correct — both ratios simplify to 1:2.
Frequently Asked Questions
Can I leave more than one field blank? No. The calculator expects exactly three values and one empty field. Leaving two or more blank produces a "Please leave one field blank to calculate" message.
Why do I sometimes get a divide-by-zero error? Solving for a term requires dividing by another value. If that divisor is zero — for instance solving for d when a = 0 — the result is undefined, so the calculator reports an error rather than a wrong answer.
Does it work with decimals? Yes. You can enter whole numbers or decimals, and the calculated value is returned as a precise decimal where needed.
