Proportionality describes a relationship between two quantities where their ratios are constant. There are two main types of proportionality:
Direct Proportionality: As one quantity increases, the other quantity increases at the same rate. If quantity A is directly proportional to quantity B, then A = kB, where k is a constant of proportionality. The ratio A/B is constant.
Inverse Proportionality: As one quantity increases, the other quantity decreases at the same rate. If quantity A is inversely proportional to quantity B, then A = k/B, where k is a constant of proportionality. The product AB is constant.
This calculator specifically deals with direct proportionality, often represented by the equation:
If A is to B as C is to D, then A⁄B = C⁄D.
In this calculator, we are given three values:
Known Value 1 (A): The first known quantity in a proportional relationship.
Known Ratio 1 (B): The second quantity associated with Known Value 1.
Known Ratio 2 (D): The second quantity associated with the unknown value we want to find.
The calculator helps you find the Unknown Value (C) using the formula derived from the proportionality equation.
How the Calculation Works (Direct Proportionality)
We use the relationship:
A⁄B = C⁄D
To solve for C, we can rearrange the formula:
C = (A * D) / B
Where:
A = Known Value 1
B = Known Ratio 1
D = Known Ratio 2
C = Unknown Value (the result)
Use Cases
Proportionality is a fundamental concept used in many real-world scenarios:
Scaling Recipes: If a recipe for 4 servings requires 2 cups of flour, how much flour is needed for 10 servings? (Flour is directly proportional to servings).
Unit Conversions: If 1 inch is equal to 2.54 centimeters, how many centimeters are in 10 inches? (Centimeters are directly proportional to inches).
Maps and Scale Models: A map's scale might state that 1 cm represents 10 km. If two locations are 5 cm apart on the map, their real-world distance is calculated using proportionality.
Physics: Many physical laws involve proportionality, such as Ohm's Law (Voltage is directly proportional to Current if Resistance is constant) or Hooke's Law (Force is directly proportional to extension for an ideal spring).
Cost Calculations: If 3 apples cost $1.50, how much do 7 apples cost? (Cost is directly proportional to the number of items).
This calculator simplifies these calculations, providing quick and accurate results for direct proportionality problems.
function calculateProportionality() {
var value1 = parseFloat(document.getElementById("value1").value);
var ratio1 = parseFloat(document.getElementById("ratio1").value);
var ratio2 = parseFloat(document.getElementById("ratio2").value);
var resultValueElement = document.getElementById("result-value");
if (isNaN(value1) || isNaN(ratio1) || isNaN(ratio2)) {
resultValueElement.textContent = "Invalid Input";
resultValueElement.style.color = "#dc3545"; /* Red for error */
return;
}
if (ratio1 === 0) {
resultValueElement.textContent = "Ratio 1 cannot be zero";
resultValueElement.style.color = "#dc3545"; /* Red for error */
return;
}
var unknownValue = (value1 * ratio2) / ratio1;
resultValueElement.textContent = unknownValue.toFixed(4); /* Display with up to 4 decimal places */
resultValueElement.style.color = "#28a745"; /* Green for success */
}