Wavelength Calculator (λ = v/f)
Calculate wavelength from wave speed and frequency using λ = v/f, or solve for speed or frequency instead — with step-by-step working shown.
Wavelength formula
Wavelength relates how fast a wave travels to how often it repeats:
- λ (lambda) — wavelength, in metres (m) — always positive
- v — wave speed, in metres per second (m/s) — always positive
- f — frequency, in hertz (Hz) — always positive
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A sound wave travels at 340 m/s (typical for air) with a frequency of 170 Hz. What is its wavelength?
- Formula: λ = v/f
- Substitute: λ = 340 / 170
- Result: λ = 2 m
Solving in reverse
The same formula rearranges to find wave speed or frequency when wavelength is known:
- Speed: v = λf — enter λ and f, leave v blank. With λ = 2 m and f = 170 Hz, v = 2 × 170 = 340 m/s.
- Frequency: f = v/λ — enter v and λ, leave f blank. With v = 340 m/s and λ = 2 m, f = 340 / 2 = 170 Hz.
Common mix-ups
- Confusing frequency with wavelength. They're inversely related, not the same quantity — doubling one halves the other when speed is constant.
- Using the wrong wave speed. Sound in air (≈340 m/s) and light in a vacuum (≈3 × 10⁸ m/s) are very different — use the speed appropriate to the wave type in your problem.
- Mixed units for frequency. Hertz (Hz) means cycles per second; make sure a frequency given in kHz or MHz is converted to Hz first.
Where this shows up
Wavelength calculations explain how radio stations are tuned to specific frequencies, why different colors of light have different wavelengths, and how musical pitch relates to sound frequency. The same v = λf relationship connects to other wave and motion concepts, including the density of the medium a wave travels through and the ideal gas law governing the gas that carries a sound wave.
Frequently asked questions
- What is the formula for wavelength?
- Wavelength is λ = v/f, where λ (lambda) is wavelength in metres (m), v is wave speed in metres per second (m/s), and f is frequency in hertz (Hz, cycles per second).
- How do I find wave speed if I know wavelength and frequency?
- Rearrange the formula to v = λf. Enter the wavelength and frequency values and leave the speed field blank, and the calculator multiplies them for you automatically.
- How do I find frequency if I know wavelength and wave speed?
- Rearrange the formula to f = v/λ. Enter the speed and wavelength, leave frequency blank, and the calculator divides speed by wavelength to solve for it.
- Can wavelength, speed, or frequency be negative or zero?
- No — all three are physical measurements that must be strictly greater than zero. A wave with zero frequency isn't oscillating, and a zero or negative wavelength or speed has no physical meaning.
- Why are frequency and wavelength inversely related?
- For a fixed wave speed, a higher frequency means more wave cycles pass a point each second, which forces each individual wave to be shorter — that's why doubling frequency halves wavelength when speed stays the same.
- What wave speed should I use for sound versus light?
- Sound travels at about 340 m/s in air at room temperature, while light (and all electromagnetic waves) travels at about 3 × 10⁸ m/s in a vacuum — use the correct speed for the type of wave you're working with.