Calculator
Formula used
The calculator is based on the wave relationship: v = f × λ. From this, we compute:
- f = v / λ (frequency from speed and wavelength)
- λ = v / f (wavelength from speed and frequency)
- T = 1 / f (period)
- ω = 2πf (angular frequency)
- k = 2π/λ and 1/λ (wavenumber and spatial frequency)
- E = hf (photon energy, when enabled)
All computations are performed in SI units internally, then formatted for display.
How to use this calculator
- Choose whether to solve for frequency, wavelength, or use auto mode.
- Select vacuum speed for light, or enter a custom medium speed.
- Type a known frequency or wavelength and choose its unit.
- Press Submit to see results above the form.
- Use the CSV or PDF buttons to export your result table.
Example data table
Sample conversions for common signals and waves.
| Scenario | Speed v (m/s) | Frequency f (Hz) | Wavelength λ (m) |
|---|---|---|---|
| 2.4 GHz Wi‑Fi (vacuum) | 2.99792458e8 | 2.4e9 | 0.1249135 |
| FM radio 100 MHz (vacuum) | 2.99792458e8 | 1.0e8 | 2.99792458 |
| Green light 532 nm (vacuum) | 2.99792458e8 | 5.635e14 | 5.32e-7 |
| Air sound 440 Hz (custom) | 343 | 440 | 0.7795455 |
FAQs
1) What is the relationship between frequency and wavelength?
They are inversely related when wave speed is fixed. Using v = fλ, higher frequency means shorter wavelength, and lower frequency means longer wavelength for the same medium.
2) When should I use a custom wave speed?
Use a custom speed for sound, water waves, cables, materials, or waveguides. Light in air is close to vacuum, but in glass or fiber it is slower, changing the wavelength.
3) Can I enter both frequency and wavelength?
Yes. Auto mode accepts both and also reports the implied speed from your inputs. This is helpful for checking measurement consistency or verifying a medium speed assumption.
4) Why do my results appear in scientific notation?
Very large or very small values are easier to read in scientific notation. The calculator automatically switches formatting for extreme magnitudes while keeping significant digits meaningful.
5) What is period and why is it shown?
The period is the time for one cycle. It is the reciprocal of frequency: T = 1/f. Period is often more intuitive for slow oscillations and timing analysis.
6) What does wavenumber mean here?
This tool shows spatial frequency 1/λ and wavenumber k = 2π/λ. They describe how rapidly the wave phase changes with distance.
7) Is photon energy valid for all waves?
Photon energy applies to electromagnetic radiation. When enabled, the calculator uses E = hf and converts joules to electronvolts. For mechanical waves, leave it off.
8) How do I export my results?
After submitting, use “Download CSV” for spreadsheet import or “Download PDF” for a printable report. The export uses the values shown in the results table.