Proportion Calculator

What is a proportion calculator?

A proportion calculator solves the equation a/b = c/d for whichever single value you leave blank, using cross-multiplication. You type the three numbers you know, leave one box empty, and the tool returns the missing value along with the completed proportion. A proportion is simply a statement that two ratios are equal — the relationship between a and b matches the relationship between c and d.

This is one of the most common setups in everyday maths: scaling recipes, converting map distances, working out unit prices, mixing solutions, and any “if this much gives that, how much gives the other” question. Instead of rearranging the equation by hand, you let the calculator cross-multiply and divide for you.

How does the proportion calculator work?

The tool treats your four boxes as the proportion a/b = c/d and finds the one value you left blank. The core idea is cross-multiplication: in any true proportion, the product of one numerator and the opposite denominator equals the product of the other pair.

The exact relationship the widget uses is:

a/b = c/d → a · d = b · c

From that single rule, every position has a direct formula. Whichever box is blank, the tool isolates it by dividing the cross-product by the remaining known value:

• Missing d = b × c ÷ a
• Missing c = a × d ÷ b
• Missing b = a × d ÷ c
• Missing a = b × c ÷ d

In words: multiply the two numbers that sit diagonally opposite the gaps, then divide by the number next to the blank. The only requirement is that the divisor — the known value the formula divides by — must not be 0, because division by zero is undefined.

Terms and units. Here a, b, c and d are just the four numbers in the two ratios; a/b is the first ratio and c/d the second. Whatever units you use, keep matching quantities in matching positions — if a and c are both “cups of flour”, then b and d should both be “servings”.

Examples

Each example below leaves one value blank and solves it with the formulas above.

Example 1 — missing d. Solve 3/4 = 9/d.

• Blank is d, so use d = b × c ÷ a.
• d = 4 × 9 ÷ 3 = 36 ÷ 3 = 12.
• The complete proportion is 3/4 = 9/12.

Example 2 — missing c (the unknown x). Solve 2/5 = x/20.

• Here x sits in the c position, so use c = a × d ÷ b.
• x = 2 × 20 ÷ 5 = 40 ÷ 5 = 8.
• The complete proportion is 2/5 = 8/20.

Example 3 — missing b. Solve 6/b = 3/2.

• Blank is b, so use b = a × d ÷ c.
• b = 6 × 2 ÷ 3 = 12 ÷ 3 = 4.
• The complete proportion is 6/4 = 3/2.

You can always verify an answer by cross-multiplying the finished proportion: for 3/4 = 9/12, check that 3 × 12 = 36 and 4 × 9 = 36 — equal, so it is correct.

Quick reference: which formula for which blank?

This table maps the blank position to its formula and shows the worked result from the examples above.

Blank position	Formula	Example	Result
Missing d	d = b × c ÷ a	3/4 = 9/d	12
Missing c	c = a × d ÷ b	2/5 = x/20	8
Missing b	b = a × d ÷ c	6/b = 3/2	4
Missing a	a = b × c ÷ d	a/4 = 9/12	3

Notice that opposite corners share a formula shape: the two numerators-and-denominators that are not adjacent to the blank get multiplied, and the neighbour gets divided.

What are common uses for a proportion calculator?

Proportions show up wherever two quantities change together at a fixed rate:

• Recipes and cooking. Scale ingredients while keeping the balance — 2 cups flour for 5 servings means x cups for 20 servings (2/5 = x/20 → 8 cups).
• Maps and scale drawings. Convert a map measurement to a real distance using the map’s scale ratio.
• Unit pricing. Compare value by solving for price-per-item or cost at a different quantity.
• Mixing and dilutions. Keep a fixed concentrate-to-water ratio when you change the batch size.
• Similar shapes and models. Matching sides of similar triangles or scale models stay in proportion, so a missing length is one cross-multiplication away.

For percentage-style comparisons you may prefer the percentage calculator, and for reducing whole numbers the LCM and GCF calculator is a close companion.

Tips and common mistakes

A few pointers help you trust the result:

• Keep matching units in matching positions. If a is “miles”, c must also be “miles”, and b and d share the other unit.
• Multiply diagonally, divide by the neighbour. The number sitting next to the blank is always the divisor.
• Watch the order of operations. The formula is (b × c) ÷ a, done as one multiplication then one division — not b × (c ÷ a) written carelessly.
• Sanity-check the size. If the second ratio is larger than the first, the missing value should grow accordingly; a wildly off answer usually means a swapped position.
• Verify by cross-multiplying. Once solved, the two cross-products should be equal.

Limitations and notes

This calculator solves one blank in a single two-ratio proportion a/b = c/d. It does not handle proportions with two unknowns, three-part ratios, or non-linear relationships. The value the chosen formula divides by must not be 0, since division by zero is undefined — for a missing d that divisor is a, for a missing c it is b. Results may be rounded for display, so a long repeating decimal can appear slightly shortened.

The tool runs entirely in your browser — nothing you type is uploaded or stored — so it works offline and keeps your numbers private. The figures here are for general educational and everyday use; double-check any value that feeds an important calculation.

Looking for related math tools? Try the modulo calculator for remainders and the prime number calculator for factor checks, or browse the full math calculators category.