Wavelength calculator

What is a wavelength calculator?

A wavelength calculator is a free online tool that links the three quantities describing any travelling wave: its wavelength, its frequency, and the speed at which it moves. Wavelength is the distance over which a wave’s shape repeats — the gap between two neighbouring crests or two neighbouring troughs. Because these three quantities are tied together by a single relationship, knowing any two of them fixes the third. This calculator lets you solve for whichever one you need, fills in the speed of light automatically when you leave the wave speed blank, and handles all the unit conversions for you.

Wavelength, frequency, and wave speed

Every wave carries a repeating disturbance through space. The frequency counts how many full cycles pass a fixed point each second, measured in hertz (Hz). The wavelength is the spatial length of one of those cycles. The wave speed tells you how quickly the pattern advances. The three are not independent: a wave that oscillates quickly and travels fast must have short ripples, while a slow oscillation at the same speed stretches the ripples out. For light and other electromagnetic waves in a vacuum, the wave speed is the speed of light, $c = 299{,}792{,}458$ m/s, which is why this calculator uses it as the default.

How does the calculator work?

Pick which quantity you want to find from the dropdown, then enter the other two values and choose their units. If you are working with light, you can leave the wave speed field empty and the calculator assumes the speed of light. Internally every input is converted to SI base units — metres, hertz, and metres per second — before the formula is applied, so you can freely mix nanometres, megahertz, and kilometres per second.

Formula

The wavelength ($\lambda$) equals the wave speed ($v$) divided by the frequency ($f$):

$$\lambda = \frac{v}{f}$$

Where:

• $\lambda$ is the wavelength
• $v$ is the wave speed (the speed of light $c$ for electromagnetic waves in a vacuum)
• $f$ is the frequency

Rearranging the same relationship lets you solve for the other quantities:

$$f = \frac{v}{\lambda} \qquad v = \lambda \times f$$

The SI unit of wavelength is the metre (m), of frequency the hertz (Hz), and of wave speed the metre per second (m/s).

Examples

Example 1

Green light has a frequency of about $5.45 \times 10^{14}$ Hz and travels at the speed of light. What is its wavelength?

$$\lambda = \frac{v}{f} = \frac{299{,}792{,}458}{5.45 \times 10^{14}} \approx 5.50 \times 10^{-7} \, \text{m}$$

That is about 550 nanometres, in the green part of the visible spectrum.

Example 2

A wave travels at 500 m/s with a frequency of 100 Hz. What is its wavelength?

$$\lambda = \frac{v}{f} = \frac{500}{100} = 5 \, \text{m}$$

Example 3

A radio wave has a wavelength of 3 m and a frequency of 100 MHz. What is its speed?

$$v = \lambda \times f = 3 \times (100 \times 10^{6}) = 3 \times 10^{8} \, \text{m/s}$$

That is essentially the speed of light, as expected for a radio wave.

Notes

When working with wavelength, keep these points in mind:

• The simple relation $\lambda = v / f$ assumes the wave speed is constant in the medium it travels through.
• For light in a vacuum the wave speed is the speed of light; in glass, water, or other materials it is slower, which shortens the wavelength while the frequency stays the same.
• Wavelength and frequency are inversely proportional at a fixed speed, so doubling the frequency halves the wavelength.

FAQs

What is the default wave speed?

If you leave the wave speed field empty, the calculator uses the speed of light in a vacuum, $299{,}792{,}458$ m/s. This is the right choice for light, radio waves, and other electromagnetic radiation travelling through space. For sound or waves in other media, enter the appropriate speed yourself.

How are wavelength and frequency related?

They are inversely proportional when the wave speed is fixed: a higher frequency means a shorter wavelength, and a lower frequency means a longer one. Their product always equals the wave speed.

Does wavelength change between materials?

Yes. When a wave passes from one medium into another its frequency stays the same, but its speed changes, so its wavelength changes too. Light entering glass slows down and its wavelength shrinks, even though it still looks the same colour.

What units does the calculator support?

Wavelength can be entered in micrometres, millimetres, centimetres, metres, kilometres, inches, or feet; frequency in hertz up to terahertz as well as millihertz; and wave speed in several metric and imperial units. The calculator converts between them automatically.

Can I use this for sound waves?

Yes. Enter the speed of sound for your medium — about 343 m/s in air at room temperature — in the wave speed field, then provide either the frequency or the wavelength to find the other.