body {
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
line-height: 1.6;
color: #333;
max-width: 800px;
margin: 0 auto;
padding: 20px;
}
.calculator-wrapper {
background: #f8f9fa;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0,0,0,0.1);
margin-bottom: 40px;
border: 1px solid #e9ecef;
}
.calc-title {
text-align: center;
margin-bottom: 25px;
color: #2c3e50;
font-size: 24px;
font-weight: 700;
}
.input-grid {
display: grid;
grid-template-columns: 1fr 1fr;
gap: 20px;
margin-bottom: 20px;
}
@media (max-width: 600px) {
.input-grid {
grid-template-columns: 1fr;
}
}
.input-group {
display: flex;
flex-direction: column;
}
.input-group label {
font-weight: 600;
margin-bottom: 8px;
color: #495057;
font-size: 14px;
}
.input-group input {
padding: 12px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 16px;
transition: border-color 0.15s ease-in-out;
}
.input-group input:focus {
border-color: #007bff;
outline: 0;
box-shadow: 0 0 0 0.2rem rgba(0,123,255,.25);
}
.helper-text {
font-size: 12px;
color: #6c757d;
margin-top: 4px;
}
.btn-calculate {
width: 100%;
padding: 15px;
background-color: #007bff;
color: white;
border: none;
border-radius: 4px;
font-size: 18px;
font-weight: 600;
cursor: pointer;
transition: background-color 0.2s;
margin-top: 10px;
}
.btn-calculate:hover {
background-color: #0056b3;
}
.result-box {
margin-top: 25px;
padding: 20px;
background-color: #ffffff;
border-radius: 6px;
border-left: 5px solid #28a745;
display: none;
}
.result-row {
display: flex;
justify-content: space-between;
margin-bottom: 10px;
padding-bottom: 10px;
border-bottom: 1px solid #eee;
}
.result-row:last-child {
border-bottom: none;
margin-bottom: 0;
padding-bottom: 0;
}
.result-label {
font-weight: 600;
color: #555;
}
.result-value {
font-weight: 700;
color: #2c3e50;
font-size: 18px;
}
.article-content {
background: #fff;
padding: 20px;
}
h2 {
color: #2c3e50;
margin-top: 30px;
border-bottom: 2px solid #eee;
padding-bottom: 10px;
}
h3 {
color: #495057;
margin-top: 25px;
}
p, li {
color: #444;
font-size: 16px;
}
.formula-box {
background: #f1f3f5;
padding: 15px;
border-radius: 4px;
font-family: "Courier New", Courier, monospace;
margin: 15px 0;
border: 1px solid #ddd;
}
function calculateRollOff() {
// Get input values
var f1 = parseFloat(document.getElementById('freq1').value);
var a1 = parseFloat(document.getElementById('amp1').value);
var f2 = parseFloat(document.getElementById('freq2').value);
var a2 = parseFloat(document.getElementById('amp2').value);
var resultBox = document.getElementById('result');
// Validation
if (isNaN(f1) || isNaN(a1) || isNaN(f2) || isNaN(a2)) {
alert("Please enter valid numbers for all fields.");
resultBox.style.display = "none";
return;
}
if (f1 <= 0 || f2 <= 0) {
alert("Frequency must be greater than 0 Hz.");
return;
}
if (f1 === f2) {
alert("Frequencies must be different to calculate a slope.");
return;
}
// Calculations
// 1. Calculate Amplitude Difference (Delta dB)
// We take the absolute difference to show the "steepness" magnitude
var deltaDB = Math.abs(a2 – a1);
// 2. Calculate Octaves
// Formula: log2(f2/f1)
// Ensure we handle f2 < f1 correctly by taking absolute of the log result
var ratio = f2 / f1;
var octaves = Math.abs(Math.log(ratio) / Math.log(2));
// 3. Calculate Decades
// Formula: log10(f2/f1)
var decades = Math.abs(Math.log10(ratio));
// 4. Calculate Slopes
var slopePerOctave = 0;
var slopePerDecade = 0;
if (octaves !== 0) {
slopePerOctave = deltaDB / octaves;
}
if (decades !== 0) {
slopePerDecade = deltaDB / decades;
}
// Update UI
resultBox.style.display = "block";
document.getElementById('resDeltaDb').innerHTML = deltaDB.toFixed(2) + " dB";
document.getElementById('resRatio').innerHTML = "1 : " + ratio.toFixed(2);
document.getElementById('resSlopeOct').innerHTML = slopePerOctave.toFixed(2) + " dB/octave";
document.getElementById('resSlopeDec').innerHTML = slopePerDecade.toFixed(2) + " dB/decade";
}
How to Calculate Roll-Off Rate
In audio engineering and electronics, the roll-off rate (or filter slope) defines how steeply a filter attenuates frequencies beyond its cutoff point. Whether you are designing a crossover for loudspeakers, analyzing an equalizer, or building an electronic circuit, understanding the roll-off rate is essential for predicting signal behavior.
The roll-off is typically measured in dB per octave (dB/oct) or dB per decade (dB/dec). A higher number indicates a steeper slope, meaning the filter removes unwanted frequencies more aggressively.
The Formula
To calculate the roll-off rate manually, you need two measurement points along the slope of the filter's frequency response curve. The formula calculates the change in amplitude divided by the change in frequency (on a logarithmic scale).
Slope (dB/octave) = ΔdB / log2(f2 / f1)
Slope (dB/decade) = ΔdB / log10(f2 / f1)
Where:
- ΔdB is the absolute difference in amplitude between the two points (|Amp2 – Amp1|).
- f1 and f2 are the two frequency points.
Understanding Filter Orders
In analog circuit design, the roll-off rate is directly related to the "order" of the filter. Each order adds a reactive component (capacitor or inductor) and increases the slope steepness by 6 dB/octave (or 20 dB/decade).
- 1st Order: 6 dB/octave (20 dB/decade)
- 2nd Order: 12 dB/octave (40 dB/decade)
- 3rd Order: 18 dB/octave (60 dB/decade)
- 4th Order: 24 dB/octave (80 dB/decade)
Calculation Example
Let's say you are analyzing a Low Pass Filter. You measure the signal at two points on the attenuation slope:
- Point 1: 1,000 Hz at -3 dB
- Point 2: 2,000 Hz at -15 dB
First, calculate the change in amplitude:
|-15 dB – (-3 dB)| = 12 dB
Next, determine the frequency interval. Since 2,000 Hz is double 1,000 Hz, this represents exactly one octave.
Result: Since the signal dropped 12 dB over the span of one octave, the roll-off rate is 12 dB/octave. This indicates it is likely a 2nd-order filter.
Why Decades vs. Octaves?
While audio engineers prefer octaves (a doubling of frequency) because it aligns with musical pitch perception, general electronics and control theory often use decades (a tenfold increase in frequency). The conversion factor is approximately 3.32. For example, 6 dB/octave is roughly equal to 20 dB/decade.