How does cross-multiplication solve a proportion?

For a/b = c/d the cross products are equal, so a × d = b × c. Rearranging gives each unknown — for example the missing d = (b × c) ÷ a. The tool applies whichever rearrangement matches the blank field.

How accurate is the result?

It uses standard double-precision arithmetic rounded to six decimals for display. Results are exact for typical use; the solver reports an error if the rearrangement would divide by zero.

What is a proportion?

A proportion is a statement that two ratios are equal, written a/b = c/d. It says a relates to b in the same way c relates to d, which lets you find a fourth value from three known ones.

How do I solve for x in a proportion?

Put x in one of the four slots and leave it blank. The tool cross-multiplies and divides to isolate x — for example x/4 = 9/12 gives x = (4 × 9) ÷ 12 = 3.

What is a real-world use for a proportion?

Scaling recipes, converting units, working out map distances, mixing solutions and adjusting quantities all rely on proportions — keeping one ratio fixed while finding the matching value for a new amount.

Why might the solver show an error?

If the rearrangement needed to isolate the unknown would divide by zero (because a required denominator is 0), the answer is undefined and the tool flags it rather than returning a meaningless number.

Are my numbers sent anywhere?

No. The solver is privacy-first — everything is computed in your browser and no values are sent to any server.

Proportion Solver (Cross-Multiplication)

Proportion solver

Solve the proportion a / b = c / d for any one missing term. Enter the three values you know, leave the unknown blank, and the tool finds it by cross-multiplication. It is handy for scaling recipes, converting units, reading maps and any “if this, then how much of that” question.

How it works

In a true proportion the cross products are equal, which the tool rearranges to isolate whichever box you leave empty:

a/b = c/d   ⟹   a × d = b × c
solve a = (b × c) ÷ d      solve b = (a × d) ÷ c
solve c = (a × d) ÷ b      solve d = (b × c) ÷ a

If the required denominator is zero, the result is undefined and the solver says so instead of returning a bad value.

Example

Solve 3 / 4 = 9 / d:

Cross-multiply: 3 × d = 4 × 9 = 36
d = 36 ÷ 3 = 12

Proportion	Unknown	Result
3/4 = 9/d	d	12
a/5 = 6/10	a	3
2/b = 8/12	b	3

It is privacy-first: all of the maths happens locally in your browser, so nothing you type ever leaves your device.