Example Data Table
| Case | Frequency | Wavelength | Speed |
|---|---|---|---|
| FM radio | 100 MHz | 2.9979 m | 299,792,458 m/s |
| Wi‑Fi | 2.4 GHz | 0.1249 m | 299,792,458 m/s |
| Microwave link | 14 GHz | 0.02141 m | 299,792,458 m/s |
| Green light | 545 THz | 550 nm | 299,792,458 m/s |
| Ultraviolet | 1.00 PHz | 299.8 nm | 299,792,458 m/s |
Formula Used
This calculator uses the basic wave relation:
- c = λ × f (speed equals wavelength times frequency)
- λ = c ÷ f (wavelength from speed and frequency)
- f = c ÷ λ (frequency from speed and wavelength)
Extra outputs include period T = 1/f, angular frequency ω = 2πf, and wavenumber k = 2π/λ.
How to Use This Calculator
- Select what you want to solve for: c, λ, or f.
- Enter the other two values and choose their units.
- Click Calculate to show results above the form.
- Use Download CSV or Download PDF for saving.
- Change units anytime; the math always uses SI internally.
Wave Speed, Wavelength, and Frequency Guide
What the Wave Relation Means
The relation c = λ × f connects wave speed, wavelength, and frequency. If one value increases while another stays fixed, the third must change to keep the product consistent. For electromagnetic waves in vacuum, c equals the speed of light, while in air, glass, or cables the effective speed is lower and can shift real‑world designs noticeably.
Speed of Light Versus Signal Velocity
Light in vacuum travels at 299,792,458 m/s, but most real systems are slower. Coaxial cables and fiber links have a velocity factor that reduces speed, and radio waves in air are slightly below the vacuum value. Using the correct c helps you estimate antenna lengths, propagation delay, and timing margins.
Wavelength may be shown in meters, centimeters, millimeters, micrometers, or nanometers. Frequency commonly uses Hz, kHz, MHz, GHz, or THz. This calculator converts your entries to SI units internally, then converts outputs back to your selected units for readable results, quick comparisons, fewer mistakes, and consistent engineering notation.
Frequency Bands You’ll See Often
Audio signals span roughly 20 Hz to 20 kHz. AM and FM broadcasting sit in kHz and MHz ranges. Wi‑Fi and Bluetooth are typically around 2.4 GHz and 5 GHz. Visible light is hundreds of terahertz, which corresponds to wavelengths near 400–700 nm, depending on color and the emitting source spectrum.
Example: Estimating an Antenna Length
A simple quarter‑wave antenna length is approximately λ/4. If a transmitter operates at 100 MHz, the wavelength is about 3 meters, so a quarter wave is near 0.75 m before practical shortening. Ground planes, wire thickness, and nearby objects also shift the tuned length.
Example: Converting Wavelength to Frequency
If you measure a laser wavelength of 532 nm, the corresponding frequency is in the hundreds of terahertz. Conversions like this appear in optics, spectroscopy, and photonics. Keeping units consistent is critical because nano‑scale wavelengths produce very large frequency values, and small wavelength errors can shift frequency significantly.
Why Period and Wavenumber Matter
The period T = 1/f tells you how long one cycle lasts, which is useful for timing and sampling. The wavenumber k = 2π/λ is common in wave equations and phase calculations. Reporting these alongside c, λ, and f helps with phase velocity checks and resonance estimates.
Rounding, Significant Figures, and Inputs
Real measurements have uncertainty. When inputs are approximate, avoid reporting too many digits in the output. Use the calculator’s results as a baseline, then round to meaningful precision for your application. For extreme values, scientific notation keeps numbers readable, improves copy‑paste, and reduces errors.
FAQs
When should I use the speed of light value?
Use 299,792,458 m/s for electromagnetic waves in vacuum. For air it is very close, but for cables, fiber, or materials you should use the medium’s effective wave speed or velocity factor.
Can I calculate wavelength from frequency only?
Yes, if you assume a wave speed. Choose “Solve for λ”, enter frequency, and set c to the correct speed for your medium. The calculator then returns λ and related outputs.
Why do my results change when I switch units?
The underlying physics does not change. Unit switching only changes how inputs and outputs are displayed. Internally, the calculator converts everything to SI units before computing.
What is the period output used for?
Period T is the time for one full cycle and equals 1/f. It helps with timing, sampling decisions, and understanding how fast a waveform repeats in time-domain systems.
What does the wavenumber k represent?
Wavenumber k = 2π/λ expresses spatial frequency in radians per meter. It is commonly used in phase calculations, wave equations, and analyzing propagation in guided structures.
How accurate are the numbers shown?
Accuracy depends on your input quality. If your measured values have limited precision, round the results to a sensible number of significant figures. Use scientific notation for very large or small values.
Can this be used for sound waves too?
Yes. Set c to the speed of sound in your conditions (temperature and medium), then solve for λ or f as needed. The same relation c = λ × f applies to sound waves.