Math calculator
Proportion Calculator
Solve a four-value proportion and see the cross multiplication used.
For a ÷ b = c ÷ d, leave exactly one box blank. b and d cannot be zero.
d equals
12
What counts as a valid entry
The calculator holds four boxes — a, b, c, d — standing for the equation a ÷ b = c ÷ d. Fill in exactly three of them and leave one blank; that blank is what gets solved for. Filling in all four, or leaving more than one blank, produces no result, since the tool needs precisely one unknown to solve for.
b and d play the role of denominators, so if you type a value into either box it cannot be 0 — a proportion with a zero denominator has no defined value on that side. There's no such restriction on a and c; those numerators, along with any filled-in b or d, can be decimals or negative numbers without issue.
The result box updates as soon as three valid values are present and labels which letter it just solved, so you always know which position the answer belongs to.
Cross multiplication, step by step
Cross multiplication turns the two fractions into one equation with no division: multiply a by d, multiply b by c, and set them equal. Solving for whichever letter is missing just means isolating it algebraically. For 5/6 = c/18 with c missing, cross multiplying gives 5 × 18 = 6 × c, so 90 = 6c, and c = 15.
The same equation solves for any position. Take 4/b = 10/15 with b missing: cross multiplying gives 4 × 15 = b × 10, so 60 = 10b, and b = 6. In both cases the two ratios end up equal — 5/6 and 15/18 both simplify to about 0.8333, and 4/6 and 10/15 both simplify to about 0.6667.
Proportion versus ratio, and how to check one
A single ratio, like 3:4, just compares two quantities. A proportion is a statement that two ratios are equal — it's the equation, not just one side of it. That's why this tool always needs four numbers arranged as two paired ratios, rather than the two or more terms a plain ratio simplifier works with.
To check whether two ratios actually form a true proportion, cross multiply both and compare. 3/4 and 6/8: 3 × 8 = 24 and 4 × 6 = 24 — equal, so it's a genuine proportion. 3/4 and 6/9: 3 × 9 = 27 but 4 × 6 = 24 — not equal, so despite looking similar, 3/4 and 6/9 are not proportional.
Common setup mistakes
The most frequent error is multiplying straight across instead of diagonally — treating a × b = c × d rather than a × d = b × c. Straight-across multiplication doesn't preserve the equality and gives a wrong answer for any position except when the proportion happens to be symmetric.
A second mistake is misaligning units between the two ratios: if a and b are measured in minutes and hours, then c and d need to follow the same order, minutes over hours, or the cross products won't represent anything meaningful even though the arithmetic still runs.
Situations that reduce to a proportion
Any problem with two paired quantities that scale together can be set up as a/b = c/d:
- Recipe scaling – if 2 cups of rice serves 5 people, how many cups serve 12? 2/5 = c/12 gives c = 4.8 cups
- Map reading – if 3 cm on a map equals 45 real km, how many km does 7 cm represent? 3/45 = 7/d gives d = 105 km
- Speed and distance – if a car covers 120 miles in 2 hours, how far in 5 hours at the same pace? 120/2 = d/5 gives d = 300 miles
- Currency conversion – if $50 converts to €46, how many euros does $120 convert to? 50/46 = 120/d gives d ≈ 110.4
- Paint mixing – if 4 parts blue mix with 9 parts white, how much white pairs with 10 parts blue? 4/9 = 10/d gives d = 22.5 parts
- Fuel efficiency – if a tank of 12 gallons drives 348 miles, how far on 20 gallons? 12/348 = 20/d gives d = 580 miles
Frequently asked questions
What exactly is a proportion in math?
It's a statement that two ratios are equal, written a/b = c/d. A single ratio like 3/4 only describes one relationship; a proportion links two of them together and lets you solve for a missing piece.
How does cross multiplication work here?
Multiply diagonally across the equals sign — a times d, and b times c — then set those two products equal and solve for whichever value is missing. For 5/6 = c/18, that's 5 × 18 = 6 × c, giving c = 15.
Which value am I allowed to leave blank?
Any one of the four — a, b, c, or d. The only extra rule is that if you do fill in b or d, neither can be zero, since both sit in the denominator position.
Why can't b or d be zero?
Both represent denominators, and a ratio divided by zero is undefined. Entering 0 in either box leaves the calculator without a valid equation to solve, so no result is shown.
Are decimal and negative values allowed?
Yes, in any of the four positions, including the ones you leave filled in. A proportion like −4/2 = c/6 solves the same way as a positive one: c = (−4 × 6) ÷ 2 = −12.
How can I tell if two ratios actually form a true proportion?
Cross multiply both sides and compare the products. 3/4 and 6/8 give 3 × 8 = 24 and 4 × 6 = 24, so they match and form a true proportion. 3/4 and 6/9 give 27 and 24, which don't match, so they aren't proportional even though the numbers look close.