What the wavelength calculator does
This page runs one equation in both directions: v = f x lambda. Here v is the speed of the wave, f is its frequency, and lambda is its wavelength. Type a frequency and you get a wavelength. Type a wavelength and you get a frequency. The calculator also names the spectrum band, and for visible light it names the color.
Light and sound need different speeds, so the tool has a medium selector. For light you can pick vacuum, air, water, crown glass, or diamond. For sound you can pick air, water, or steel. The speed of light in vacuum is 299,792,458 m/s. That exact value is what makes a 100 MHz FM signal land at 2.998 m, and not 3.000 m.
The formula and the medium
In vacuum, lambda = c / f. In a medium, lambda = (c / n) / f. The letter n is the refractive index, a number that tells you how much slower light moves in that material. Air at sea level has n = 1.000293. Water has n = 1.333. Crown glass has n = 1.52. Diamond has n = 2.417.
Frequency does not change when light enters a medium. Wavelength does. A 532 nm green laser beam in air keeps its 563.5 THz frequency in water, but its wavelength shrinks to about 399 nm. The color you see comes from the frequency, so the beam stays green.
Sound works the same way with v = f x lambda, but the speeds are much lower. Sound travels at 343 m/s in air at 20 C, 1480 m/s in water, and 5960 m/s in steel. A 440 Hz musical note in air has a wavelength of 343 / 440 = 0.78 m.
Worked example: FM radio at 100 MHz
Start with the frequency in Hz. 100 MHz is 100,000,000 Hz. Then lambda = 299,792,458 / 100,000,000 = 2.998 m. That is about 3 m. A half-wave dipole for this signal is half of that, near 1.5 m before the velocity factor is applied.
Worked example: green laser at 532 nm
Convert 532 nm to meters: 532 x 10^-9 m. Then f = c / lambda = 299,792,458 / (532 x 10^-9) = 563.5 THz. Photon energy is E = hc / lambda. With hc = 1239.84 eV nm, E = 1239.84 / 532 = 2.33 eV. That is a green photon.
Worked example: microwave oven at 2.45 GHz
2.45 GHz is 2,450,000,000 Hz. Lambda = 299,792,458 / 2,450,000,000 = 0.1224 m, or 12.24 cm. That is close to the size of the holes in the oven door mesh, which is why the mesh blocks the microwaves.
Spectrum bands and colors
The calculator labels the band from the vacuum wavelength. These boundaries are conventions, and different references draw them slightly differently.
| Band | Wavelength range |
|---|---|
| Radio | Longer than 1 m (below 300 MHz) |
| Microwaves | 1 mm to 1 m (300 MHz to 300 GHz) |
| Infrared | 750 nm to 1 mm |
| Visible | 380 nm to 750 nm |
| Ultraviolet | 10 nm to 380 nm |
| X-rays | 10 pm to 10 nm |
| Gamma rays | Shorter than 10 pm |
Inside the visible band, the calculator names the color. Violet is 380 to 450 nm, blue is 450 to 495 nm, green is 495 to 570 nm, yellow is 570 to 590 nm, orange is 590 to 620 nm, and red is 620 to 750 nm.
Common mistakes to avoid
- Mixing MHz and Hz. 100 MHz is 100,000,000 Hz, and not 100 Hz. The calculator handles the unit, but your own math needs the same care.
- Using the speed of light for sound. Sound in air is 343 m/s, about 874,000 times slower than light in vacuum.
- Forgetting the medium. A wavelength in water is shorter than the same wavelength in vacuum by a factor of n.
- Using the free-space speed for a wire antenna. The velocity factor, often 0.95 for thin wire, shortens the physical length.
- Using the non-relativistic de Broglie formula above about 0.1 c. The calculator warns and does not compute the relativistic value.
For a 146 MHz dipole, the free-space half wave is 1.027 m. Multiply by 0.95 to get 0.976 m total, or 3.20 ft. Each leg is 0.488 m. The textbook rule 468 / 146 gives 3.21 ft, which matches.
Every formula on this page is published at /how-we-calculate/. Related tools include the photon energy calculator, the antenna length calculator, and the de Broglie wavelength calculator. The full band chart is at /electromagnetic-spectrum/.