What is cross-multiplication?

Cross-multiplication is a shortcut for solving proportions of the form a/b = c/d. Multiplying both sides by b and d gives a*d = b*c, so any one of the four values can be isolated: a = b*c/d, b = a*d/c, c = a*d/b, or d = b*c/a.

When do you use cross-multiplication?

Any time you know three out of four numbers in a proportion — scaling a recipe, converting units, working out a percentage, finding a map distance, or solving a maths word problem. It is one of the most frequently used techniques in everyday arithmetic.

Can I solve for any of the four variables?

Yes. The "Solve for" dropdown lets you pick a, b, c, or d. The calculator automatically rearranges the formula and computes the missing value from the other three.

What happens if a denominator is zero?

Division by zero is undefined, so the calculator shows an error message instead of a number. Make sure the value in the denominator position (b or d) is non-zero before solving.

Is cross-multiplication the same as simplifying a fraction?

Not quite. Simplifying a fraction reduces a single ratio to lowest terms. Cross-multiplication compares two ratios and lets you find an unknown in one of them. They are complementary techniques but serve different purposes.

How accurate are the results?

The calculator uses JavaScript 64-bit floating-point arithmetic and rounds to 10 significant figures, which is more than enough for everyday calculations. For very large or very small numbers it uses standard scientific notation automatically.

Cross-Multiplication Calculator

Cross-multiplication is the go-to method whenever you need to find an unknown value inside a proportion. A proportion is simply a statement that two ratios are equal:

a / b = c / d

If you know any three of those four numbers, cross-multiplication finds the fourth in a single step. This calculator does exactly that — pick which variable you want, enter the other three, and the answer appears immediately alongside the full working.

How it works

The core identity behind every proportion is:

a × d = b × c

This comes from multiplying both sides of a/b = c/d by b and by d. Once you accept that the two cross-products are equal, you can solve for any variable by dividing:

Solve for a: a = (b × c) / d
Solve for b: b = (a × d) / c
Solve for c: c = (a × d) / b
Solve for d: d = (b × c) / a

The SVG diagram in the calculator shows the two diagonals — the blue arrow represents the cross-product being computed, and the grey arrow represents the one being divided by.

Worked example

Suppose a recipe uses 3 cups of flour for 4 servings, and you want to make 9 servings. How many cups of flour do you need?

Set up the proportion: 3/4 = x/9.

Here a = 3, b = 4, c = x, d = 9 — so solve for c:

c = (a × d) / b = (3 × 9) / 4 = 27 / 4 = 6.75 cups

Enter a = 3, b = 4, d = 9, select “Solve for c”, and the calculator returns 6.75 immediately. The proportion check confirms that 3/4 = 6.75/9 — both equal 0.75.

Formula note

The general formula a/b = c/d holds as long as b and d are both non-zero. When one denominator is zero, the proportion is undefined — the calculator displays an error message rather than returning an incorrect result. All arithmetic is performed in 64-bit floating-point (IEEE 754 double precision), rounded to 10 significant figures for clean display.

Common use cases

Situation	Known values	Solve for
Scaling a recipe	original amount, original servings, new servings	new amount
Unit conversion	1 unit, its equivalent, quantity to convert	converted quantity
Map scale	map distance, scale factor, real distance	any unknown
Percentage of a total	part, whole, reference percentage	scaled part
Similar triangles	three of four corresponding side lengths	missing side

In every case the setup is the same: identify the four slots a, b, c, d; fill in the three you know; let the calculator find the fourth.