Where ω is angular frequency (rad/s), f is frequency (Hz), and π ≈ 3.14159
Hz
Angular Frequency (ω)
0
rad/s
Period (T)
0 s
Frequency (f)
0 Hz
Angular Frequency (ω)
0 rad/s
Rotations per Second
0
Understanding Angular Frequency
Angular frequency (ω) describes how fast an object rotates or oscillates in terms of
radians per second. It's related to regular frequency (f) by the factor 2π, since
one complete cycle equals 2π radians.
Key relationships:
ω = 2πf — Angular frequency from frequency
f = ω / 2π — Frequency from angular frequency
T = 1/f = 2π/ω — Period from either frequency
ω = 2π/T — Angular frequency from period
Angular frequency is commonly used in physics for describing simple harmonic motion,
electrical circuits (AC analysis), and wave mechanics. In engineering, it's essential
for signal processing and control systems.
var conversionDirection = 'hz-to-rad';
function setDirection(direction) {
conversionDirection = direction;
// Update toggle buttons
document.querySelectorAll('.toggle-btn').forEach(btn => {
btn.classList.remove('active');
});
document.getElementById(direction).classList.add('active');
// Update labels and placeholders
var inputLabel = document.getElementById('input-label');
var inputUnit = document.getElementById('input-unit');
var calcBtn = document.getElementById('calculate-btn');
var input = document.getElementById('frequency-input');
if (direction === 'hz-to-rad') {
inputLabel.textContent = 'Frequency (f)';
inputUnit.textContent = 'Hz';
calcBtn.textContent = 'Calculate Angular Frequency';
input.placeholder = 'Enter frequency in Hz';
} else {
inputLabel.textContent = 'Angular Frequency (ω)';
inputUnit.textContent = 'rad/s';
calcBtn.textContent = 'Calculate Frequency';
input.placeholder = 'Enter angular frequency in rad/s';
}
// Clear previous results
document.getElementById('results-section').classList.remove('visible');
input.value = ";
}
function calculate() {
var input = parseFloat(document.getElementById('frequency-input').value);
if (isNaN(input) || input 0 ? 1 / frequency : Infinity;
// Update result card
var resultLabel = document.getElementById('result-label');
var resultValue = document.getElementById('result-value');
var resultUnit = document.getElementById('result-unit');
if (conversionDirection === 'hz-to-rad') {
resultLabel.textContent = 'Angular Frequency (ω)';
resultValue.textContent = formatNumber(angularFrequency);
resultUnit.textContent = 'rad/s';
} else {
resultLabel.textContent = 'Frequency (f)';
resultValue.textContent = formatNumber(frequency);
resultUnit.textContent = 'Hz';
}
// Update additional info
document.getElementById('period-value').textContent = formatWithUnit(period, 's');
document.getElementById('freq-display').textContent = formatWithUnit(frequency, 'Hz');
document.getElementById('omega-display').textContent = formatWithUnit(angularFrequency, 'rad/s');
document.getElementById('rotations-value').textContent = formatNumber(frequency);
// Show results
document.getElementById('results-section').classList.add('visible');
}
function formatNumber(num) {
if (num === Infinity) return '∞';
if (num === 0) return '0';
if (Math.abs(num) >= 1e6 || Math.abs(num) < 0.001) {
return num.toExponential(4);
}
return num.toLocaleString(undefined, {
minimumFractionDigits: 0,
maximumFractionDigits: 6
});
}
function formatWithUnit(num, unit) {
return formatNumber(num) + ' ' + unit;
}
// Enable calculation on Enter key
document.getElementById('frequency-input').addEventListener('keypress', function(e) {
if (e.key === 'Enter') {
calculate();
}
});
// Initialize placeholder
document.getElementById('frequency-input').placeholder = 'Enter frequency in Hz';
I've created a **Frequency to Angular Frequency Calculator** with a stunning, modern design. Here's what it includes:
## Features
### 🎯 **Core Functionality**
– **Bidirectional conversion**: Switch between Hz → rad/s and rad/s → Hz
– **Instant calculations** using the formula ω = 2πf
– **Additional derived values**: Period (T), rotations per second
### ✨ **Premium Design Elements**
– **Animated gradient orbs** in the background for visual depth
– **Glassmorphism** card effects with backdrop blur
– **Smooth hover animations** on buttons with shimmer effect
– **Pulse animation** on the icon
– **Gradient text** for headings and results
– **Dark mode** with a carefully curated purple/indigo color palette
### 📐 **Physics Information**
– **Formula display** showing ω = 2πf prominently
– **Theory section** explaining the relationship between frequency, angular frequency, and period
– **Key formulas** listed for reference
### 🛠️ **User Experience**
– **Toggle buttons** to switch conversion direction
– **Enter key support** for quick calculations
– **Smart number formatting** (scientific notation for very large/small numbers)
– **Responsive design** that works on all screen sizes
– **Input validation** with helpful feedback
The calculator properly uses physics terminology (Hz, rad/s, period) with no financial terms whatsoever!