#rule-of-three-container h2 { color: #2c3e50; margin-top: 30px; border-bottom: 2px solid #3498db; padding-bottom: 8px; }
#rule-of-three-container .calc-box { background-color: #f8f9fa; padding: 20px; border-radius: 8px; border: 1px solid #dee2e6; margin-bottom: 30px; }
#rule-of-three-container .input-row { display: flex; align-items: center; justify-content: center; margin-bottom: 20px; flex-wrap: wrap; gap: 10px; }
#rule-of-three-container .proportion-box { display: flex; flex-direction: column; align-items: center; gap: 15px; }
#rule-of-three-container .fraction { display: flex; flex-direction: column; align-items: center; }
#rule-of-three-container .fraction input { width: 100px; padding: 10px; border: 1px solid #ccc; border-radius: 4px; text-align: center; font-size: 16px; }
#rule-of-three-container .line { width: 110px; height: 2px; background-color: #333; margin: 8px 0; }
#rule-of-three-container .equals { font-size: 24px; font-weight: bold; margin: 0 15px; }
#rule-of-three-container .result-area { margin-top: 20px; padding: 15px; background-color: #e8f4fd; border-radius: 6px; text-align: center; font-weight: bold; font-size: 1.2em; display: none; }
#rule-of-three-container .calculate-btn { display: block; width: 200px; margin: 20px auto; padding: 12px; background-color: #3498db; color: white; border: none; border-radius: 5px; cursor: pointer; font-size: 16px; font-weight: bold; transition: background 0.3s; }
#rule-of-three-container .calculate-btn:hover { background-color: #2980b9; }
#rule-of-three-container .formula-display { font-style: italic; color: #666; margin-bottom: 10px; text-align: center; }
#rule-of-three-container .mode-selector { text-align: center; margin-bottom: 20px; }
#rule-of-three-container select { padding: 8px; border-radius: 4px; border: 1px solid #ccc; }
@media (max-width: 480px) {
#rule-of-three-container .input-row { flex-direction: column; }
#rule-of-three-container .equals { transform: rotate(90deg); margin: 10px 0; }
}
function updateLabels() {
var mode = document.getElementById("calcMode").value;
var formulaText = document.getElementById("formulaText");
if (mode === "direct") {
formulaText.innerHTML = "Formula: (B × C) / A = X";
} else {
formulaText.innerHTML = "Formula: (A × B) / C = X";
}
document.getElementById("resultDisplay").style.display = "none";
document.getElementById("valX").value = "?";
}
function calculateRuleOfThree() {
var a = parseFloat(document.getElementById("valA").value);
var b = parseFloat(document.getElementById("valB").value);
var c = parseFloat(document.getElementById("valC").value);
var mode = document.getElementById("calcMode").value;
var resultDisplay = document.getElementById("resultDisplay");
var xField = document.getElementById("valX");
if (isNaN(a) || isNaN(b) || isNaN(c)) {
resultDisplay.style.display = "block";
resultDisplay.style.backgroundColor = "#fce4e4";
resultDisplay.innerHTML = "Please enter valid numbers for A, B, and C.";
return;
}
if (a === 0 || c === 0) {
resultDisplay.style.display = "block";
resultDisplay.style.backgroundColor = "#fce4e4";
resultDisplay.innerHTML = "Values cannot be zero for this calculation.";
return;
}
var result;
if (mode === "direct") {
// Direct: A/B = C/X => X = (B*C)/A
result = (b * c) / a;
} else {
// Inverse: A*B = C*X => X = (A*B)/C
result = (a * b) / c;
}
var formattedResult = Number.isInteger(result) ? result : result.toFixed(4).replace(/\.?0+$/, "");
xField.value = formattedResult;
resultDisplay.style.display = "block";
resultDisplay.style.backgroundColor = "#e8f4fd";
resultDisplay.innerHTML = "The value of X is: " + formattedResult;
}
Rule of Three Calculator
Solve direct and inverse proportions instantly.
Direct Proportion (If A increases, B increases)
Inverse Proportion (If A increases, B decreases)
=
Formula: (B × C) / A = X
What is the Rule of Three?
The Rule of Three is a mathematical method used to solve proportions and find an unknown fourth value when three other values are known. It is one of the most practical mathematical tools used in daily life, from adjusting cooking recipes to calculating fuel consumption or currency conversions.
There are two types of relationships handled by this calculator:
- Direct Proportion: As one value increases, the other increases at the same rate. (e.g., If 2 apples cost 4, 4 apples cost 8).
- Inverse Proportion: As one value increases, the other decreases. (e.g., If 2 workers finish a job in 4 hours, 4 workers finish it in 2 hours).
How to Use the Rule of Three Calculator
To use this calculator effectively, follow these steps:
- Identify your pairs: Determine which two values are related (A and B).
- Identify your third value: Determine the new value (C) for which you want to find the corresponding result (X).
- Select the relationship: Choose "Direct" if the values move in the same direction, or "Inverse" if they move in opposite directions.
- Calculate: Input the numbers and hit calculate to see the result.
Real-World Examples
Example 1: Cooking (Direct Proportion)
Suppose a recipe for 4 people requires 200g of flour. How much flour is needed for 10 people?
- Value A: 4 people
- Value B: 200g
- Value C: 10 people
- Calculation: (200 × 10) / 4 = 500g.
Example 2: Travel Speed (Inverse Proportion)
If you drive at 60 km/h, it takes 2 hours to reach your destination. How long will it take if you drive at 80 km/h?
- Value A: 60 km/h
- Value B: 2 hours
- Value C: 80 km/h
- Calculation: (60 × 2) / 80 = 1.5 hours.
The Math Behind the Calculation
For a Direct Proportion, we set up the equation as a fraction equality: A / B = C / X. By cross-multiplying, we get A * X = B * C, which simplifies to X = (B * C) / A.
For an Inverse Proportion, the product of the variables remains constant: A * B = C * X. Therefore, the formula is X = (A * B) / C.
Note: Always ensure that Value A and Value C are in the same units (e.g., both in hours, or both in kilograms) to ensure the calculation is accurate.