A ratio calculator solves a proportion when one of the four terms is missing. Given three values in the relation A:B = C:D, the calculator finds the fourth using cross-multiplication: A × D = B × C, so D = (B × C) ÷ A.
Useful for scaling recipes, mixing chemicals, converting map distances, setting machine ratios, comparing equivalent fractions, and any setting where two quantities are linked in a fixed proportion. This calculator solves for the fourth term D; if you need a different unknown, rearrange your inputs so the missing term lands in the D position.
Key takeaway
A proportion is two fractions set equal to each other: A/B = C/D. Cross-multiplying eliminates the fractions and turns the equation into A × D = B × C. From there, any single unknown comes out by dividing, there's no algebraic gymnastics, just the cross-multiply and one divide. This single technique covers all four "missing term" variations.
How it's calculated
Starting from the proportion A:B = C:D (read "A is to B as C is to D"), the cross-multiplication rule says:
A × D = B × C
Solving for each variable in turn:
- D unknown:
D = (B × C) ÷ A(this calculator) - C unknown:
C = (A × D) ÷ B - B unknown:
B = (A × D) ÷ C - A unknown:
A = (B × C) ÷ D
All four are the same equation rearranged, pick the form where your unknown is on the left. This calculator solves the most common shape (D unknown); for the others, swap your inputs into the A/B/C slots so the result you're after becomes D.
Real-world use: recipe scaling. If a recipe serves 4 people and uses 6 oz of flour, scaling to 10 people sets up 4:6 = 10:?, and the calculator gives 15 oz. The same shape covers map scales (1:24,000), gear ratios, and any "if X then Y" rule where X and Y scale together.
Source: Cross-multiplication identity, for A:B = C:D, then A × D = B × C
Examples
Recipe scaling: 2 cups serves 3, how much for 10 servings?
- A (first ratio, left) 3
- B (first ratio, right) 2
- C (second ratio, left) 10
With the proportion
3:2 = 10:?(3 servings uses 2 cups; 10 servings uses ? cups), cross-multiplying gives(2 × 10) ÷ 3 ≈ 6.67 cups. Round up to 7 in practice, round numbers work better in the kitchen than fractions.Map scale: 4 cm = 12 km, then 7 cm = ? km
- A (first ratio, left) 4
- B (first ratio, right) 12
- C (second ratio, left) 7
4:12 = 7:?solves to 21 km. The map scale is "1 cm represents 3 km" (12 ÷ 4), and 7 cm × 3 = 21. The proportion form makes scale-conversion mechanical without needing to compute the per-unit factor first.
Frequently asked questions
What is a proportion?
A proportion is a statement that two ratios are equal, for example, 2:3 = 4:6. Both ratios reduce to the same simplest form (2:3), so they represent the same relationship between quantities. Proportions are the engine behind scaling: any time you have a known relationship between two quantities and want to apply it to new values, you're using a proportion.
How does cross-multiplication work?
Cross-multiplication is a shortcut for solving equations of the form a/b = c/d. Multiply both sides by b × d and the fractions disappear, leaving a × d = b × c. The "cross" name comes from the visual of drawing an X across the equation, the diagonals are equal. From there, any unknown solves with one division.
Are ratios and fractions the same thing?
Closely related but framed differently. A fraction like 3/4 represents a part of a whole. A ratio like 3:4 represents a relationship between two independent quantities (for example, 3 cups of flour for every 4 cups of water). Mathematically they behave the same way under cross-multiplication and equivalent-fraction rules. The distinction is mostly about context.
What if my ratio has more than two terms (like 1:2:3)?
Multi-term ratios scale all parts by the same multiplier. To split a quantity in a 1:2:3 ratio, divide by the sum of the parts (1+2+3 = 6) and multiply by each part's share. For example, splitting $60 in 1:2:3 ratio gives $10, $20, $30. This calculator handles two-term ratios; multi-term problems work by similar logic but need a different setup.