Frequency (f) to Wavelength (λ)
Wavelength (λ) to Frequency (f)
Energy (E) to Wavelength (λ)
λ = hc / E
Electromagnetic Spectrum
This chart visualizes the full range of electromagnetic waves, from long radio waves to short gamma rays. Your calculated result is marked with a vertical line, providing immediate context.
The Wavelength Formula
The relationship between wavelength, frequency, and wave speed is fundamental in physics. The formula to calculate wavelength is:
Energy and Wavelength
The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This relationship is defined by the Planck–Einstein relation:
- Wavelength (λ): The distance over which the wave's shape repeats, measured in meters (m).
- Frequency (f): The number of wave crests that pass a point per second, measured in Hertz (Hz).
- Wave Speed (v): The speed at which the wave propagates. For electromagnetic waves, this is the speed of light (c), approximately 299,792,458 m/s.
- Energy (E): The energy of the wave, often measured in Joules (J) or electron-volts (eV).
Example 1: Wavelength of an FM Radio Station
Let's find the wavelength for an FM radio station broadcasting at 98.1 MHz.
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1Identify the knowns: Frequency (f) = 98.1 MHz, Wave Speed (v) = Speed of light (c).
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2Apply the formula:
λ = v / f -
3Result: 3.06 meters. This is a typical wavelength for radio waves.
Example 2: Frequency of a Microwave Oven
A typical microwave oven operates at a wavelength of 12.2 cm.
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1Identify the knowns: Wavelength (λ) = 12.2 cm, Wave Speed (v) = Speed of light (c).
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2Apply the formula:
f = v / λ -
3Result: 2.46 GHz.
What is the relationship between wavelength and energy?
Energy and wavelength are inversely related. Shorter wavelengths correspond to higher energy waves (like gamma rays), while longer wavelengths correspond to lower energy waves (like radio waves).
What is the wavelength of visible light?
Visible light for humans corresponds to a very narrow band of the electromagnetic spectrum, typically from about 380 nanometers (violet) to 750 nanometers (red).
Does the medium affect wavelength?
Yes. When a wave (like light) enters a different medium (like from air to water), its speed changes but its frequency remains constant. Since wavelength is dependent on speed (λ = v/f), a change in speed will cause a proportional change in wavelength.
Why is the speed of light the default wave speed?
This calculator is primarily designed for electromagnetic waves (light, radio, microwaves, etc.), which all travel at the speed of light in a vacuum. You can change this value to calculate the wavelength for other types of waves, such as sound in air (approx. 343 m/s).
Using Wavelength Results for PCB Interconnects
A PCB wavelength calculator needs both frequency and propagation medium. In free space, λ0 = c / f. On a PCB trace, the wave travels more slowly, so an initial guided estimate is λg ≈ λ0 / √εeff, where effective permittivity depends on stack-up and trace geometry rather than only the laminate's bulk dielectric constant. Frequency remains unchanged when a wave enters a dielectric; phase velocity and wavelength change. For timing or phase-critical routing, validate the calculator result with propagation delay and the fabricated stack-up, not the nominal material value alone.
- Enter frequency correctly: convert Hz, kHz, MHz, or GHz consistently; a factor-of-1000 unit error produces the same factor error in wavelength.
- Select the medium: use free-space velocity for air and an appropriate propagation velocity or
εefffor a transmission line. - Use effective permittivity: obtain it from a field solver or a geometry-appropriate microstrip or stripline model for the actual stack-up.
- Judge electrical length: compare routed length with the guided wavelength; fractions such as one-tenth or one-twentieth are engineering screening rules, not universal limits.
- Check model boundaries: connectors, vias, solder mask, dispersion, differential coupling, and dielectric tolerance can shift delay from the simple estimate.
