What Is a Proportion?
A proportion is a statement that two ratios are equal: A/B = C/D. Given any three of the four values, the fourth can be found by cross-multiplication — the foundational rule that A × D = B × C.
Proportions appear throughout everyday life and every scientific discipline. Recipe scaling, map distances, architectural blueprints, chemical dilutions, currency exchange, shadow geometry, dosage calculations, financial ratios, and screen aspect ratios are all solved with the same A/B = C/D structure.
How to Solve a Proportion — Step by Step
The Proportion Formula
AB
=
CD
⟺
A × D = B × C
AFirst numerator — top-left value
BFirst denominator — bottom-left value
CSecond numerator — top-right value
DSecond denominator — bottom-right value
Solve for A
A = (B × C) ÷ D
e.g. ?/5 = 6/10 → A = (5×6)/10 = 3
Solve for B
B = (A × D) ÷ C
e.g. 3/? = 6/10 → B = (3×10)/6 = 5
Solve for C
C = (A × D) ÷ B
e.g. 3/5 = ?/10 → C = (3×10)/5 = 6
Solve for D
D = (B × C) ÷ A
e.g. 3/5 = 6/? → D = (5×6)/3 = 10
Real-World Applications of Proportions
Recipe ScalingA recipe uses 2 cups flour for 12 cookies. For 30 cookies: 2/12 = x/30 → x = 5 cups. Proportions make scaling any recipe trivial.
Map & Scale DistancesA map uses 1 cm = 50 km. If two cities are 3.5 cm apart, the real distance: 1/50 = 3.5/x → x = 175 km.
Blueprints & ArchitectureScale 1:100 means 1 cm on the drawing = 100 cm in reality. Find any real dimension from blueprint measurements instantly.
Chemistry & DilutionsDiluting a 5% solution to 2%: 5/100 = 2/x tells you how much water to add. Proportions underpin molarity and concentration calculations.
Screen & Image Aspect RatiosA 16:9 screen is 1920 px wide. The height: 16/9 = 1920/x → x = 1080 px. Proportions keep images and videos correctly sized.
Finance & CurrencyExchange rate 1 USD = 0.93 EUR. For $250: 1/0.93 = 250/x → x = €232.50. Financial proportions power every currency conversion.
Frequently Asked Questions
Cross-multiplication is the rule that if A/B = C/D, then A × D = B × C. To find the missing value, you rearrange this equation. For example, if C is unknown: C = (A × D) / B. Cross-multiplication works because multiplying both sides of A/B = C/D by B × D gives A × D = B × C.
A ratio is a comparison of two quantities (e.g. 3:5 or 3/5). A proportion is a statement that two ratios are equal (e.g. 3/5 = 6/10). All proportions contain ratios, but a single ratio is not a proportion — you need two equal ratios to form one.
Yes. If all four fields are filled, the calculator checks whether A × D equals B × C and reports whether the proportion is true or false. It also shows the decimal value of each ratio so you can see how close they are.
You need exactly three values to solve for the fourth. If two or more values are blank, the proportion has infinitely many solutions and the calculator will show an error asking you to fill in at least three fields.
After solving, the calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it. For example, 6/10 simplifies to 3/5 because GCD(6,10) = 2. Simplified ratios are often more intuitive and required in many exam answers.
The five presets load realistic example values for common use cases: recipe scaling (2/12 = ?/30), map scale (1/50 = 3.5/?), blueprint (1/100 = 4.5/?), chemistry dilution (5/100 = 2/?), and screen aspect ratio (16/9 = 1920/?). Clicking a preset fills in three values so you can immediately see how the calculation works for that scenario.
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