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.

What is the Proportion Solver (Cross-Multiplication)?

Free proportion solver. Enter three values of the proportion a/b = c/d and leave one blank to find the missing value by cross-multiplication. Privacy-first and runs entirely in your browser — nothing is sent anywhere. It runs free in your browser on Gera Tools, with nothing uploaded.

Proportion Solver (Cross-Multiplication)

Name: Proportion Solver (Cross-Multiplication)
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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.

Practical situations where proportions arise

Proportions are everywhere in everyday calculation, often disguised as practical questions:

Scaling recipes. A recipe that serves 4 uses 300g of flour. How much flour for 7 servings? Set up 300/4 = x/7 and solve for x. (For this example: x = 300 × 7 ÷ 4 = 525g.)

Map distances. A map scale of 1:50,000 means 1cm on the map represents 50,000cm (500m) in reality. If two points are 4.5cm apart, how far is the real distance? Set 1/50000 = 4.5/d and solve for d.

Mixing solutions. If 5ml of concentrate makes 250ml of solution, how much concentrate is needed for 1 litre? Set 5/250 = x/1000 and solve for x.

Converting units. If 1 mile equals 1.609km, how many kilometres is 13.1 miles? Set 1/1.609 = 13.1/d and solve for d.

In every case the structure is the same: a known ratio on one side, a scaled ratio on the other, and one unknown to find.

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.

Worked examples

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

Setting up a proportion correctly

The key to using a proportion solver is framing your question in the right ratio form. A proportion asserts that two ratios are equal, so both ratios must measure the same thing in the same units. If the left ratio is kilometres per hour, the right ratio must also be kilometres per hour.

A common mistake is inverting one of the ratios. For example, if you know that 2 items cost 5 units and you want to find the cost of 7 items, the correct proportion is 2/5 = 7/x (items per cost) or equivalently 5/2 = x/7 (cost per item). Mixing the order — 2/5 = x/7 — gives a different and wrong answer.

Once you have the two ratios clearly in the same form, fill in the three known values, leave the unknown blank, and the solver handles the cross-multiplication.

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