body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 1200px;
margin: 0 auto;
padding: 20px;
background-color: #f9f9f9;
}
.calculator-container {
background: #ffffff;
padding: 30px;
border-radius: 12px;
box-shadow: 0 4px 20px rgba(0,0,0,0.1);
margin-bottom: 40px;
border: 1px solid #e0e0e0;
}
.calculator-title {
font-size: 24px;
font-weight: 700;
margin-bottom: 25px;
color: #2c3e50;
text-align: center;
border-bottom: 2px solid #3498db;
padding-bottom: 10px;
}
.input-grid {
display: grid;
grid-template-columns: repeat(auto-fit, minmax(250px, 1fr));
gap: 20px;
margin-bottom: 25px;
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: #555;
font-size: 14px;
}
.input-group input {
padding: 12px;
border: 1px solid #ddd;
border-radius: 6px;
font-size: 16px;
transition: border-color 0.3s;
}
.input-group input:focus {
border-color: #3498db;
outline: none;
box-shadow: 0 0 0 3px rgba(52, 152, 219, 0.1);
}
.calc-btn {
width: 100%;
padding: 15px;
background-color: #3498db;
color: white;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: 600;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
.calc-btn:hover {
background-color: #2980b9;
}
.results-section {
margin-top: 30px;
background-color: #f8f9fa;
border-radius: 8px;
padding: 20px;
display: none;
border: 1px solid #e9ecef;
}
.result-row {
display: flex;
justify-content: space-between;
align-items: center;
padding: 12px 0;
border-bottom: 1px solid #e0e0e0;
}
.result-row:last-child {
border-bottom: none;
}
.result-label {
font-weight: 600;
color: #666;
}
.result-value {
font-weight: 700;
font-size: 18px;
color: #2c3e50;
}
.highlight-result {
color: #27ae60;
font-size: 24px;
}
.article-content {
background: #fff;
padding: 40px;
border-radius: 12px;
box-shadow: 0 2px 10px rgba(0,0,0,0.05);
}
.article-content h2 {
color: #2c3e50;
margin-top: 30px;
font-size: 22px;
}
.article-content h3 {
color: #34495e;
font-size: 18px;
margin-top: 25px;
}
.article-content p, .article-content li {
color: #555;
line-height: 1.8;
margin-bottom: 15px;
}
.formula-box {
background-color: #f1f8ff;
padding: 20px;
border-left: 4px solid #3498db;
margin: 20px 0;
font-family: monospace;
font-size: 1.1em;
}
.example-box {
background-color: #fff8e1;
padding: 20px;
border-left: 4px solid #f1c40f;
margin: 20px 0;
}
@media (max-width: 768px) {
.input-grid {
grid-template-columns: 1fr;
}
.article-content {
padding: 20px;
}
}
function calculateDiscount() {
// Get Input Values
var listPriceInput = document.getElementById("listPrice").value;
var d1Input = document.getElementById("discount1").value;
var d2Input = document.getElementById("discount2").value;
var d3Input = document.getElementById("discount3").value;
// Parse Inputs
var listPrice = parseFloat(listPriceInput);
var d1 = parseFloat(d1Input) || 0;
var d2 = parseFloat(d2Input) || 0;
var d3 = parseFloat(d3Input) || 0;
// Validation: Ensure valid percentages
if (d1 < 0 || d2 < 0 || d3 < 0) {
alert("Discounts cannot be negative.");
return;
}
// Convert percentages to decimal complements (e.g., 20% discount = 0.8 multiplier)
var c1 = 1 – (d1 / 100);
var c2 = 1 – (d2 / 100);
var c3 = 1 – (d3 / 100);
// Calculate Net Price Equivalent Rate (NPER)
// Multiplier = (1-d1) * (1-d2) * (1-d3)
var nperDecimal = c1 * c2 * c3;
// Calculate Single Equivalent Discount Rate (SEDR)
// SEDR = 1 – NPER
var sedrDecimal = 1 – nperDecimal;
// Format Percentages for Display
var sedrPercent = (sedrDecimal * 100).toFixed(2);
var nperPercent = (nperDecimal * 100).toFixed(2);
// Display Percentage Results
var resultSection = document.getElementById("resultSection");
var monetarySection = document.getElementById("monetaryResults");
resultSection.style.display = "block";
document.getElementById("equivalentRate").innerHTML = sedrPercent + "%";
document.getElementById("nperDisplay").innerHTML = nperPercent + "%";
// Handle Monetary Calculations if List Price is provided
if (!isNaN(listPrice) && listPriceInput !== "") {
var netPrice = listPrice * nperDecimal;
var totalSaved = listPrice – netPrice;
monetarySection.style.display = "block";
document.getElementById("displayListPrice").innerHTML = "$" + listPrice.toFixed(2);
document.getElementById("netPrice").innerHTML = "$" + netPrice.toFixed(2);
document.getElementById("totalSaved").innerHTML = "$" + totalSaved.toFixed(2);
} else {
monetarySection.style.display = "none";
}
}
How to Calculate Single Equivalent Rate of Discount
In business, retail, and supply chain management, discounts are often stacked. A wholesaler might offer a trade discount series like "20/10/5", meaning a 20% discount, followed by an additional 10% off the remaining balance, followed by another 5% off that.
A common misconception is that you can simply add these percentages together ($20\% + 10\% + 5\% = 35\%$). However, because each subsequent discount applies to a smaller principal amount, the actual total reduction is less than the sum of the parts. This tool helps you find the Single Equivalent Discount Rate—the one percentage that represents the total reduction from the original list price.
Why Can't You Just Add the Discounts?
Trade discounts are applied successively, known as "chain discounts."
- First Discount: Calculated on the full List Price.
- Second Discount: Calculated on the Net Price after the first discount is removed.
- Third Discount: Calculated on the Net Price after the second discount is removed.
Because the base amount shrinks with every step, a 10% discount on the second step is worth less in absolute dollars than a 10% discount on the first step.
The Formula
To calculate the single equivalent rate of discount manually, you first determine the Net Price Equivalent Rate (NPER).
NPER = (1 – d1) × (1 – d2) × (1 – d3)…
Single Equivalent Rate = 1 – NPER
Where d1, d2, and d3 are the discount percentages expressed as decimals (e.g., 20% = 0.20).
Calculation Example
Let's say a supplier offers a trade discount series of 20/10 on an item with a list price of $1,000.
Step 1: Convert to complements
Discount 1: 20% → Complement is 0.80 (100% – 20%)
Discount 2: 10% → Complement is 0.90 (100% – 10%)
Step 2: Multiply complements (NPER)
0.80 × 0.90 = 0.72
(This means the customer pays 72% of the list price)
Step 3: Calculate Single Equivalent Rate
1.00 – 0.72 = 0.28
Result: 28%
Notice that simply adding 20% + 10% would suggest a 30% discount. The actual mathematical discount is only 28%. On a $1,000 order, that 2% difference equals $20, which is significant for profit margins.
Real-World Applications
Understanding how to calculate the single equivalent rate of discount is crucial for:
- Accounts Payable/Receivable: Verifying that invoices match purchase orders.
- Pricing Strategy: Retailers determining the final cost of goods sold (COGS) to set appropriate profit margins.
- Negotiation: Comparing different discount offers from vendors. For example, is "25/5" better than "20/10/5"? Use the calculator to find out.
Frequently Asked Questions
Does the order of discounts matter?
Mathematically, no. Because multiplication is commutative ($A \times B = B \times A$), a discount series of 20/10 results in the same net price as 10/20. However, in standard business notation, the larger discount is usually listed first.
What is the Net Price Equivalent Rate?
The Net Price Equivalent Rate (NPER) is the percentage of the original list price that you actually pay. If the Single Equivalent Discount Rate is 28%, the NPER is 72%.
How many discounts can be in a chain?
While most businesses use two or three (e.g., 20/10/5), there is no theoretical limit. However, the returns diminish rapidly with each additional discount applied to the shrinking balance.