Find the missing value in a proportion. Enter A, B, and C, and the calculator finds X in A : B = C : X, using cross-multiplication.
Two ratios that are equal form a proportion.
Cross-multiplying turns the equation into a simple multiplication.
Dividing by the known term isolates the missing value.
Proportion: A ÷ B = C ÷ X
Cross-multiply: A × X = B × C
Solve: X = B × C ÷ A
A recipe uses 2 cups of rice for 3 people. How much for 6 people?
A (rice): 2
B (people): 3
C (rice needed): 6
Set up: 2 : 3 = 6 : X
Cross-multiply: 2 × X = 3 × 6 = 18
Divide: X = 18 ÷ 2 = 9
Answer: X = 9 people can be served
A proportion calculator solves the equation A : B = C : X for the unknown X. It is the general tool for any statement of the form 'this is to that as this other thing is to what?'. Enter the three known terms and it cross-multiplies to find the fourth.
Proportions appear across school maths, science and daily life. A map scale of 2 cm to 15 km is a ratio, and the real distance for 7 cm on the map is its missing fourth term. The same structure solves recipe scaling, currency conversion at a fixed rate, mixing ratios for paint or cement, and chemical calculations in Class 11 stoichiometry. The calculator does not decide whether your situation truly is proportional; it assumes it is and finds the term that keeps the two ratios equal.
1. Arrange the known values as A : B = C : X, keeping matching quantities in matching positions.
2. Rewrite as fractions: A ÷ B = C ÷ X.
3. Cross-multiply: A × X = B × C.
4. Divide both sides by A: X = (B × C) ÷ A.
5. Check that A and B are not zero, because a ratio with a zero denominator is undefined.
6. Verify by confirming that A ÷ B equals C ÷ X.
A proportion is an equation between two fractions, A ÷ B = C ÷ X. Multiplying both sides by B × X clears both denominators at once, leaving A × X = B × C. This is not a special trick but ordinary algebra applied to fractions. The product of the outer terms, called the extremes, equals the product of the inner terms, called the means. Once the fractions are gone, the unknown appears in a single product and can be isolated by one division.
The two ratios must compare the same kinds of quantity in the same order. If A is map distance and B is real distance, then C must also be a map distance for X to be a real distance. Swapping C into the wrong slot still gives a number, but it answers a different question. A useful habit is to label units next to each term, such as 2 cm : 15 km = 7 cm : X km, and check that each side reads the same way.
A proportion assumes that the ratio between the two quantities stays constant. That holds for scale drawings, fixed prices per unit and fixed recipes. It fails when there is a fixed charge, such as a taxi base fare, or when one quantity falls as the other rises, which is inverse proportion. Using the proportion calculator for workers and days, for example, gives the wrong direction entirely. Always ask whether doubling one quantity should double the other before you set up the equation.
On a district map, Arjun reads the scale as 2 cm for every 15 km and measures 7 cm between his village and the district headquarters.
Write the proportion: 2 : 15 = 7 : X
Cross-multiply: 2 × X = 15 × 7
Solve for X: X = 52.5
Answer: X 52.5
Placing the known values in the wrong positions, so the ratio compares cm with cm on one side and cm with km on the other.
Using a proportion when one quantity decreases as the other increases.
Forgetting a fixed component, such as a delivery charge, that does not scale.
Mixing units, for example grams in one ratio and kilograms in the other.
Converting map or blueprint measurements into real distances using the scale.
Scaling a recipe from 4 servings to 10.
Converting currency or units at a fixed rate.
Mixing cement, sand and aggregate or paint and thinner in a given ratio.
Stoichiometry problems in Class 11 and 12 chemistry.
What is cross-multiplication?
In A/B = C/D, multiplying diagonally gives A × D = B × C. This removes the fractions, and leaves a simple equation to solve.
Why can't a denominator be zero?
A ratio with zero on the bottom does not make sense, because you cannot divide by zero. The calculator rejects this instead of giving a wrong answer.