Wavelength & Frequency Calculator (c = fλ)
Calculate wavelength, frequency and photon energy of light using c = fλ. Enter wavelength in metres or frequency in Hz to find the other.
How to use this tool
- Enter wavelength (λ) and frequency (f) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your frequency and the full breakdown beneath it.
The speed of light is c = f × λ = 299,792,458 m/s. Given either wavelength λ (metres) or frequency f (Hz), the other follows directly. Photon energy is E = hf where h = 6.626 × 10⁻³⁴ J·s.
Formula
c = f × λ
Rearranged: f = c ÷ λ | λ = c ÷ f
Photon energy: E = h × f (h = 6.626 × 10−34 J·s)
Period: T = 1 ÷ f
Where c = 299 792 458 m/s (speed of light), f = frequency (Hz), λ = wavelength (m).
How it works
This calculator uses the wave equation for electromagnetic radiation in a vacuum, where the speed of light c is a fixed constant. Given wavelength or frequency, it derives the other, then computes the wave period and the energy of a single photon using Planck's constant. When both values are provided, frequency is recomputed from wavelength. Results apply to light in a vacuum; in other media the speed — and therefore the wavelength — changes.
Worked example
- Given: wavelength λ = 500 nm = 5 × 10−7 m. Frequency is unknown (entered as 0).
- Apply: f = c ÷ λ = 299 792 458 ÷ 5 × 10−7.
- Calculate: f = 5.99585 × 1014 Hz (approximately 599 584 916 000 000 Hz).
Frequency = 599,584,916,000,000 Hz (roughly 600 THz — visible green light)
Common mistakes to avoid
- Entering wavelength in nanometres (nm) instead of metres -- visible light at 500 nm must be entered as 5e-7 m, not 500.
- Assuming the formula c = f x lambda applies to sound -- the speed of sound is ~343 m/s, not 3e8 m/s, so this calculator only applies to electromagnetic radiation.
- Confusing period (T = 1/f) with wavelength -- they are different quantities measured in different units (seconds vs metres).
Key terms
- Wavelength (λ)
- The distance between successive wave crests, measured in metres. Visible light ranges from about 380 nm (violet) to 700 nm (red).
- Frequency (f)
- The number of wave cycles passing a point per second, measured in Hertz (Hz). Higher frequency means shorter wavelength and higher photon energy.
- Speed of light (c)
- The speed of electromagnetic waves in a vacuum: exactly 299 792 458 m/s. It is a universal physical constant.
- Photon energy (E)
- The energy carried by a single quantum (photon) of light, calculated as E = hf where h is Planck's constant (6.626 × 10−34 J·s).
- Period (T)
- The time for one complete wave cycle, equal to 1/f. For visible light, periods are on the order of femtoseconds (10−15 s).
Frequently asked questions
- What wavelength is visible light?
- Visible light spans roughly 380 nm (violet) to 700 nm (red). Green is around 550 nm with frequency ~545 THz.
- Why is the speed of light fixed?
- In vacuum, c is a fundamental constant (≈ 3 × 10⁸ m/s) by definition since 1983. In other media light slows down by a factor of the refractive index.