Find the missing value in a direct proportion.
Cross-multiplication solves for the unknown value, the same method used in the general Proportion calculator.
Solve: A:B = C:X, cross-multiplied
A direct proportion calculator finds the missing value when two quantities rise and fall together at a constant rate. If 4 kg of rice costs ₹260, it tells you what 7 kg costs, assuming the price per kilogram stays the same. You enter the known pair and the new value of the first quantity, and it returns the matching value of the second.
This is the unitary method from Class 6 and 7 in calculator form. It covers price and quantity, distance and fuel at a steady mileage, wages and days worked at a fixed daily rate, and ingredient scaling. The defining test is simple: if doubling one quantity doubles the other, they are in direct proportion and this calculator applies.
1. Check the relationship is direct: doubling one quantity should double the other, and zero of one should give zero of the other.
2. Write the known pair as A : B, where A is the first quantity and B the matching second quantity.
3. Write the new pair as C : X, with C the new first quantity and X unknown.
4. Set A ÷ B = C ÷ X and cross-multiply: A × X = B × C.
5. Solve X = B × C ÷ A.
6. Alternatively, use the unitary method: find B ÷ A for one unit, then multiply by C.
Saying y is directly proportional to x means y = k × x for some fixed number k. Here k is the rate: rupees per kilogram, kilometres per litre or wages per day. Any two pairs share the same k, so y₁ ÷ x₁ = y₂ ÷ x₂. With 4 kg costing ₹260, k = 65 rupees per kg, and 7 kg costs 7 × 65 = ₹455. The cross-multiplication formula and the unitary method are two ways of writing the same fact.
Plotting y against x for a direct proportion gives a straight line through the origin with slope k. The 'through the origin' part is essential. A taxi fare with a fixed ₹50 base charge plus ₹18 per km is linear but not proportional, because 0 km still costs ₹50. Using this calculator on such a fare would give the wrong answer. The line passing through zero is the quick visual test that separates direct proportion from other straight-line relationships.
In direct proportion the ratio y ÷ x stays constant, while in inverse proportion the product x × y stays constant. More workers finish a job in fewer days, so workers and days are inversely proportional, and using the direct method would make the answer move the wrong way. Before choosing a method, ask whether an increase in one quantity should increase or decrease the other. If it increases, and zero gives zero, the relationship is direct.
Latha paid ₹260 for 4 kg of sona masoori rice at her local store and wants to know what 7 kg will cost at the same rate.
Write the proportion: 4 : 260 = 7 : X
Cross-multiply: 4 × X = 260 × 7
Solve for X: X = 455
Answer: X (where A:B = C:X) 455
Using direct proportion for workers and days, which are inversely proportional.
Applying it to prices with a fixed charge or bulk discount, where the rate is not constant.
Putting C in the position of B, so the ratio compares kilograms with rupees in the wrong order.
Ignoring unit changes, such as grams in one pair and kilograms in the other.
Finding the cost of a different quantity at the same unit price.
Estimating fuel needed for a trip from a known mileage.
Calculating wages for a number of days at a fixed daily rate.
Scaling ingredients in a recipe for more or fewer people.
Converting between currencies or units at a fixed rate.
What makes a proportion 'direct'?
In a direct proportion, both amounts go up or down together, at the same rate. If you double one, the other one doubles too.