Find the Percentage (Part) — (Rate % of Base)
Find the Rate (%) — (Part is what % of Base)
Find the Base (Whole) — (Part is Rate % of what?)
Result:
Understanding the Percentage, Base, and Rate
In mathematics, the relationship between three distinct values—the Base, the Rate, and the Percentage (Part)—forms the foundation of most commercial and scientific calculations. This calculator is designed to solve for any of these variables while providing a detailed step-by-step solution to help you understand the logic behind the math.
The Variables Defined
Base (B): The whole amount or the total value. For example, in the phrase "20% of 500", 500 is the base.
Rate (R): The ratio or fraction expressed as a percentage. It is usually followed by the percent sign (%). In the phrase "20% of 500", 20% is the rate.
Percentage (P): Often referred to as the "Part," this is the result of applying the rate to the base. In "20% of 500 is 100", 100 is the percentage.
Fundamental Formulas
Depending on which value you are missing, you can use one of the following three variations of the percentage formula:
Finding the Part: $P = B \times (R / 100)$
Finding the Rate: $R = (P / B) \times 100$
Finding the Base: $B = P / (R / 100)$
Example Real-World Scenarios
Scenario 1: Finding the Part You have a grocery bill of 150 and want to calculate a 10% tip. Here, the Base is 150 and the Rate is 10. The Part (Percentage) is $150 \times 0.10 = 15$.
Scenario 2: Finding the Rate If a student scores 45 out of 60 on a test, what is their percentage? Here, the Part is 45 and the Base is 60. The Rate is $(45 / 60) \times 100 = 75\%$.
Scenario 3: Finding the Base An item is on sale for $40, which is 20% of its original price. What was the original price? Here, the Part is 40 and the Rate is 20. The Base is $40 / (20 / 100) = 200$.
function updateFields() {
var mode = document.getElementById("calcMode").value;
var labelA = document.getElementById("labelA");
var labelB = document.getElementById("labelB");
var inputA = document.getElementById("inputA");
var inputB = document.getElementById("inputB");
if (mode === "part") {
labelA.innerText = "Rate (%)";
labelB.innerText = "Base (Whole)";
inputA.placeholder = "e.g. 20";
inputB.placeholder = "e.g. 500";
} else if (mode === "rate") {
labelA.innerText = "Percentage (Part)";
labelB.innerText = "Base (Whole)";
inputA.placeholder = "e.g. 100";
inputB.placeholder = "e.g. 500";
} else if (mode === "base") {
labelA.innerText = "Percentage (Part)";
labelB.innerText = "Rate (%)";
inputA.placeholder = "e.g. 100";
inputB.placeholder = "e.g. 20";
}
document.getElementById("resultArea").style.display = "none";
}
function calculatePercentage() {
var mode = document.getElementById("calcMode").value;
var valA = parseFloat(document.getElementById("inputA").value);
var valB = parseFloat(document.getElementById("inputB").value);
var resultDisplay = document.getElementById("mainResult");
var solutionDisplay = document.getElementById("stepSolution");
var resultArea = document.getElementById("resultArea");
if (isNaN(valA) || isNaN(valB)) {
alert("Please enter valid numbers in both fields.");
return;
}
var result = 0;
var solutionHtml = "";
if (mode === "part") {
// Find Part: P = B * (R/100)
result = valB * (valA / 100);
resultDisplay.innerText = result.toLocaleString(undefined, {maximumFractionDigits: 4});
solutionHtml = "Step 1: Identify the formula for the Part: P = Base × (Rate / 100)" +
"Step 2: Convert the rate to a decimal: " + valA + " / 100 = " + (valA / 100) + "" +
"Step 3: Multiply the Base by the decimal: " + valB + " × " + (valA / 100) + " = " + result + "";
} else if (mode === "rate") {
// Find Rate: R = (P / B) * 100
if (valB === 0) {
alert("Base cannot be zero.");
return;
}
result = (valA / valB) * 100;
resultDisplay.innerText = result.toLocaleString(undefined, {maximumFractionDigits: 4}) + "%";
solutionHtml = "Step 1: Identify the formula for the Rate: R = (Part / Base) × 100" +
"Step 2: Divide the Part by the Base: " + valA + " / " + valB + " ≈ " + (valA / valB).toFixed(4) + "" +
"Step 3: Multiply by 100 to get the percentage: " + (valA / valB).toFixed(4) + " × 100 = " + result.toFixed(2) + "%";
} else if (mode === "base") {
// Find Base: B = P / (R / 100)
if (valB === 0) {
alert("Rate cannot be zero.");
return;
}
result = valA / (valB / 100);
resultDisplay.innerText = result.toLocaleString(undefined, {maximumFractionDigits: 4});
solutionHtml = "Step 1: Identify the formula for the Base: B = Part / (Rate / 100)" +
"Step 2: Convert the rate to a decimal: " + valB + " / 100 = " + (valB / 100) + "" +
"Step 3: Divide the Part by the decimal: " + valA + " / " + (valB / 100) + " = " + result + "";
}
solutionDisplay.innerHTML = solutionHtml;
resultArea.style.display = "block";
}