Frequency to Wavelength Converter
Quick Conversions
Formula and Calculation Method
The relationship between frequency and wavelength is expressed as:
Where:
• λ (lambda) = Wavelength (meters)
• c = Speed of light or wave propagation (meters/second)
• f = Frequency (Hertz)
This inverse relationship means higher frequencies correspond to shorter wavelengths, and vice versa.
Step-by-Step Conversion Examples
Example 1: Radio Wave Frequency
Convert 100 MHz to wavelength
Step 1: Convert frequency to Hz: 100 MHz = 100 × 10⁶ = 100,000,000 Hz
Step 2: Apply formula: λ = c / f = 299,792,458 / 100,000,000
Step 3: Calculate: λ = 2.998 meters
Result: 100 MHz corresponds to a wavelength of approximately 3 meters
Example 2: WiFi Frequency
Convert 2.4 GHz to wavelength
Step 1: Convert frequency to Hz: 2.4 GHz = 2.4 × 10⁹ = 2,400,000,000 Hz
Step 2: Apply formula: λ = 299,792,458 / 2,400,000,000
Step 3: Calculate: λ = 0.1249 meters = 12.49 cm
Result: 2.4 GHz corresponds to a wavelength of approximately 12.5 cm
Example 3: Visible Light
Convert 500 THz to wavelength
Step 1: Convert frequency to Hz: 500 THz = 500 × 10¹² = 500,000,000,000,000 Hz
Step 2: Apply formula: λ = 299,792,458 / 500,000,000,000,000
Step 3: Calculate: λ = 5.996 × 10⁻⁷ meters = 600 nm
Result: 500 THz corresponds to orange-yellow light at 600 nanometers
Electromagnetic Spectrum Reference
| Wave Type | Frequency Range | Wavelength Range | Applications |
|---|---|---|---|
| Radio Waves | 3 kHz – 300 GHz | 1 mm – 100 km | Broadcasting, Communication |
| Microwaves | 300 MHz – 300 GHz | 1 mm – 1 m | Radar, Satellite, WiFi |
| Infrared | 300 GHz – 430 THz | 700 nm – 1 mm | Thermal Imaging, Remote Controls |
| Visible Light | 430 THz – 750 THz | 400 nm – 700 nm | Human Vision, Photography |
| Ultraviolet | 750 THz – 30 PHz | 10 nm – 400 nm | Sterilization, Fluorescence |
| X-Rays | 30 PHz – 30 EHz | 0.01 nm – 10 nm | Medical Imaging, Security |
| Gamma Rays | > 30 EHz | < 0.01 nm | Cancer Treatment, Astronomy |
Common Frequency Conversions
| Frequency | Wavelength (Vacuum) | Common Use |
|---|---|---|
| 50 Hz | 6,000 km | AC Power (Europe) |
| 60 Hz | 5,000 km | AC Power (USA) |
| 20 kHz | 15 km | Upper Hearing Limit |
| 88-108 MHz | 2.78-3.41 m | FM Radio |
| 433 MHz | 69.3 cm | Remote Controls |
| 915 MHz | 32.8 cm | RFID, ISM Band |
| 1.575 GHz | 19 cm | GPS L1 Band |
| 2.4 GHz | 12.5 cm | WiFi, Bluetooth |
| 5 GHz | 6 cm | WiFi 5/6 |
| 10 GHz | 3 cm | Satellite Communication |
Visible Light Wavelengths
Violet: 380-450 nm
Frequency: 668-789 THz | Shortest visible wavelength
Blue: 450-495 nm
Frequency: 606-668 THz | High energy visible light
Green: 495-570 nm
Frequency: 526-606 THz | Peak sensitivity of human eye
Yellow: 570-590 nm
Frequency: 508-526 THz | Sodium vapor lamp emission
Orange: 590-620 nm
Frequency: 484-508 THz | Sunset colors
Red: 620-750 nm
Frequency: 400-484 THz | Longest visible wavelength
Wavelength in Different Media
| Medium | Speed (m/s) | Refractive Index | 100 MHz Wavelength |
|---|---|---|---|
| Vacuum | 299,792,458 | 1.000 | 2.998 m |
| Air (sea level) | 299,702,547 | 1.0003 | 2.997 m |
| Water | 224,901,000 | 1.333 | 2.249 m |
| Glass | 199,861,638 | 1.5 | 1.999 m |
| Diamond | 124,034,173 | 2.417 | 1.240 m |
Related Conversions
Frequency to Period
Period (T) = 1 / Frequency (f)
Example: 100 Hz = 0.01 seconds
Wavelength to Energy
Energy (E) = hc / λ
Where h = Planck’s constant
Frequency to Energy
Energy (E) = h × f
Direct proportionality
Wavenumber Conversion
Wavenumber = 1 / Wavelength
Measured in cm⁻¹
Frequently Asked Questions
What is the relationship between frequency and wavelength?
Frequency and wavelength have an inverse relationship. As frequency increases, wavelength decreases, and vice versa. This relationship is governed by the equation λ = c / f, where c is the speed of light (or wave propagation velocity). When a wave oscillates more times per second (higher frequency), each individual wave cycle covers less distance (shorter wavelength).
Why does wavelength change in different media?
When waves travel from one medium to another, their frequency remains constant, but their speed changes. Since wavelength depends on both speed and frequency (λ = v / f), a change in speed causes a proportional change in wavelength. For example, light slows down in water compared to air, resulting in shorter wavelengths while maintaining the same frequency.
How do you convert MHz to wavelength in meters?
First, convert MHz to Hz by multiplying by 1,000,000. Then divide the speed of light (299,792,458 m/s) by the frequency in Hz. For example: 100 MHz = 100,000,000 Hz, so λ = 299,792,458 / 100,000,000 = 2.998 meters. This gives you the wavelength in a vacuum or air.
What is the wavelength of common WiFi frequencies?
WiFi operates mainly on two frequency bands. The 2.4 GHz band has a wavelength of approximately 12.5 centimeters, while the 5 GHz band has a wavelength of about 6 centimeters. These shorter wavelengths at 5 GHz provide higher data rates but have less ability to penetrate obstacles compared to 2.4 GHz signals.
Can two waves have the same frequency but different wavelengths?
Yes, when waves travel through different media. For instance, a 100 MHz radio wave has a wavelength of 3 meters in air but only 2.25 meters in water. The frequency remains 100 MHz in both cases, but the reduced propagation speed in water results in a shorter wavelength. This is why the medium selection is important in wavelength calculations.
What wavelength range can humans see?
The human eye can detect electromagnetic radiation with wavelengths approximately between 380 nanometers (violet) and 750 nanometers (red). This corresponds to frequencies from about 400 THz to 790 THz. This narrow band is called the visible spectrum, representing a tiny fraction of the entire electromagnetic spectrum.
How are frequency and wavelength used in antenna design?
Antenna dimensions are typically designed as fractions or multiples of the operating wavelength. Common designs include half-wave dipoles (λ/2) and quarter-wave monopoles (λ/4). For example, an antenna for 100 MHz (wavelength ≈ 3 meters) would be approximately 1.5 meters long for a half-wave dipole. This relationship between physical size and wavelength makes lower frequencies require larger antennas.
Why do different colors have different wavelengths?
Color is our perception of different wavelengths of visible light. Red light has longer wavelengths (around 620-750 nm) and lower frequencies, while violet light has shorter wavelengths (around 380-450 nm) and higher frequencies. The wavelength determines how the light interacts with the cone cells in our eyes, producing the sensation of different colors.