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Wavelength, Frequency & Wave Velocity Calculator (v = λ·f)

Q: What is the formula for wavelength?

Wavelength is calculated with **λ = v / f**, where v is the wave's propagation speed (in m/s) and f is the frequency (in Hz). The result is the wavelength in meters. Example: a 440 Hz sound wave in air (343 m/s) → λ = 343 / 440 ≈ **0.78 m** (78 cm).

Q: What is the wavelength of WiFi?

WiFi 2.4 GHz: **λ ≈ 12.5 cm**. WiFi 5 GHz: **λ ≈ 6 cm**. WiFi 6 GHz: **λ ≈ 5 cm**. Longer wavelengths (2.4 GHz) penetrate walls better; shorter wavelengths offer higher bandwidth but less range.

Q: What is the wavelength of visible light?

Visible light ranges from **380 nm** (violet) to **700 nm** (red). Green light (~550 nm) oscillates at ≈ 545 THz. Ultraviolet is below 380 nm; infrared is above 700 nm.

Q: What is the frequency of the musical note A4?

The standard A4 (concert pitch) is **440 Hz**. In air at 20°C (343 m/s), its wavelength is λ = 343 / 440 ≈ **0.78 m** (78 cm). In water (1,480 m/s), λ ≈ 3.36 m.

Q: What is the electromagnetic spectrum?

The full range of EM radiation ordered by frequency: **Radio** ( 10 EHz). Only visible light is detected by human eyes.

Q: What happens to wavelength when a wave changes medium?

**Frequency stays constant** when a wave crosses a medium boundary, but the wave speed changes, so wavelength changes too. When light passes from vacuum into glass (speed ≈ 200,000 km/s), its frequency is unchanged but λ shrinks to about 67% of the vacuum value.

Calculate wavelength, frequency, or wave velocity using v = λf. Enter any two values and get the third instantly. Includes reference tables for sound, light, and radio waves.

Data verified · June 2026
Edited by Martín Rodríguez
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How to use this calculator

Follow this tool’s steps, then review its formula, assumptions, and limits below.

Step by step

Enter two known valuesFill in any two of the three fields: wave speed (m/s), wavelength (m), or frequency (Hz).

Leave the unknown field blankThe calculator solves for whichever field you leave empty using v = λ · f.

Click CalculateGet the missing value with appropriate unit scaling (nm, MHz, GHz, etc.).

The fundamental wave relationship is v = λ × f, where v is the speed of propagation, λ (lambda) is the wavelength, and f is the frequency. This applies to all wave types: sound, light, radio waves, microwaves, and more. Enter any two values and the calculator instantly solves for the third.

When to use this calculator

Solve wave problems in physics and acoustics
Calculate wavelengths of radio or WiFi signals
Determine light frequency by color
Understand the electromagnetic spectrum
Calculate musical instrument frequencies

Sound wavelength in air by frequency (v = 343 m/s at 20°C)

Wavelength of common sound frequencies, with real-world reference points.

Frequency	Wavelength λ	Real-world example
20 Hz	17.15 m	Lower limit of human hearing
100 Hz	3.43 m	Bass drum / subwoofer
440 Hz	0.78 m	Musical note A4 (concert pitch)
1,000 Hz	34.3 cm	Mid-range human voice
4,000 Hz	8.6 cm	Speech consonants
20,000 Hz	1.7 cm	Upper limit of human hearing

Calculated with λ = v / f, using v = 343 m/s (air at 20°C). Frequency stays constant across media, but speed and wavelength change (e.g. sound in water ≈ 1,480 m/s).

Radio, microwave and light wavelengths (v = c = 299,792,458 m/s)

Wave type	Frequency	Wavelength λ
AM radio	1 MHz	300 m
FM radio	100 MHz	3 m
WiFi 2.4 GHz	2.4 GHz	12.5 cm
WiFi 5 GHz	5 GHz	6.0 cm
Microwave oven	2.45 GHz	12.2 cm
Red light	428 THz	700 nm
Green light	545 THz	550 nm
Violet light	790 THz	380 nm

Calculated with λ = c / f (electromagnetic waves travel at the speed of light c in vacuum). Visible light spans roughly 380 nm (violet) to 700 nm (red).

How it works

The Fundamental Wave Equation

The relationship v = λ · f connects speed, wavelength, and frequency for any wave — mechanical or electromagnetic. Rearranged for each unknown:

v = λ · f — speed (m/s) = wavelength (m) × frequency (Hz)

λ = v / f — wavelength (m) = speed (m/s) ÷ frequency (Hz)

f = v / λ — frequency (Hz) = speed (m/s) ÷ wavelength (m)

This equation holds for all wave types: sound, light, radio, seismic, water waves. What changes between them is the propagation speed, which depends on the medium — not on frequency.

How to Calculate: Step-by-Step

Example 1 — Find the wavelength of a 440 Hz sound in air:
λ = 343 m/s ÷ 440 Hz = 0.78 m

Example 2 — Find the frequency of a 12.5 cm WiFi signal (speed = c):
f = 299,792,458 m/s ÷ 0.125 m = ≈ 2.4 GHz

Example 3 — Find wave speed given λ = 2 m and f = 50 Hz:
v = 2 m × 50 Hz = 100 m/s

Always confirm units before calculating. Mixing cm with Hz and expecting m/s is the most common error.

Sound Wavelengths in Air (343 m/s at 20°C)

Why does speed change with temperature? In air, v ≈ 331 + 0.6·T (°C). At 0°C: 331 m/s; at 35°C: 352 m/s. A 3% variation matters in precision acoustics and musical instrument tuning outdoors.

Why does sound travel faster in solids? Speed depends on the medium's elasticity and density. Steel is far more rigid than air, so disturbances propagate much faster — this is why you can hear a train on the tracks before hearing it through the air.

Radio & Light Wavelengths

The microwave oven frequency (2,450 MHz) is deliberately close to — but not exactly at — the water absorption peak, which is actually near 22 GHz. Energy transfer occurs through dielectric heating, not resonance absorption, which is a common misconception.

AM radio's long wavelengths (hundreds of meters) allow signals to diffract around hills and buildings, explaining its longer transmission range compared to FM.

Wave Propagation Speeds

Medium	Speed
Sound in air (20°C)	343 m/s
Sound in water (25°C)	1,480 m/s
Sound in steel	5,960 m/s
Light in vacuum	299,792,458 m/s (exact, by definition)
Light in glass (typical)	~200,000,000 m/s
Light in fiber optic cable	~200,000,000 m/s

The speed of light in vacuum is fixed by definition since 1983 (SI system). The meter is defined from it, not the other way around.

Key Tips & Common Mistakes

Unit consistency is critical: if speed is in m/s, wavelength must be in meters and frequency in Hz. Convert MHz → Hz (×10⁶), GHz → Hz (×10⁹), nm → m (×10⁻⁹) before calculating.

Frequency does not change when a wave crosses media. Speed and wavelength change; frequency stays constant. This is why light bends (refracts) when entering water — same frequency, shorter wavelength, lower speed.

Wavelength ≠ amplitude. Wavelength is the spatial period of the wave; amplitude relates to energy/loudness/brightness. This equation says nothing about amplitude.

For electromagnetic waves in vacuum, always use c = 299,792,458 m/s. In any other medium, use the actual propagation speed (c divided by the refractive index for light).

Doppler effect is not covered here. This calculator assumes a stationary source and observer. If source or observer moves, the observed frequency shifts and this equation applies to the perceived values, not the emitted ones.

What This Calculator Does Not Cover

Doppler shift (moving sources or observers)

Wave attenuation (how amplitude decreases with distance)

Dispersion (when wave speed varies with frequency, as in optical fiber or ocean waves)

Standing waves and resonance frequencies

Quantum energy of photons (E = h·f — requires Planck's constant)

For electromagnetic radiation, if you need photon energy rather than wavelength, use a dedicated Planck equation calculator.

Example: Wavelength of WiFi 2.4 GHz

Given: frequency f = 2.4 GHz = 2,400,000,000 Hz; speed of light c = 299,792,458 m/s.

Formula: λ = v / f = 299,792,458 / 2,400,000,000.

Result: λ ≈ 0.1249 m ≈ 12.5 cm.

Interpretation: WiFi 2.4 GHz antennas are typically ~6 cm long — half the wavelength (λ/2 dipole antenna is the standard design for maximum efficiency).

WiFi at 2.4 GHz has a wavelength of approximately 12.5 cm.

Frequently asked questions

What is the formula for wavelength?

Wavelength is calculated with λ = v / f, where v is the wave's propagation speed (in m/s) and f is the frequency (in Hz). The result is the wavelength in meters. Example: a 440 Hz sound wave in air (343 m/s) → λ = 343 / 440 ≈ 0.78 m (78 cm).

What is the wavelength of WiFi?

WiFi 2.4 GHz: λ ≈ 12.5 cm. WiFi 5 GHz: λ ≈ 6 cm. WiFi 6 GHz: λ ≈ 5 cm. Longer wavelengths (2.4 GHz) penetrate walls better; shorter wavelengths offer higher bandwidth but less range.

What is the wavelength of visible light?

Visible light ranges from 380 nm (violet) to 700 nm (red). Green light (~550 nm) oscillates at ≈ 545 THz. Ultraviolet is below 380 nm; infrared is above 700 nm.

What is the frequency of the musical note A4?

The standard A4 (concert pitch) is 440 Hz. In air at 20°C (343 m/s), its wavelength is λ = 343 / 440 ≈ 0.78 m (78 cm). In water (1,480 m/s), λ ≈ 3.36 m.

What's the difference between Hz, kHz, MHz, and GHz?

1 kHz = 1,000 Hz; 1 MHz = 1,000,000 Hz; 1 GHz = 1,000,000,000 Hz; 1 THz = 10¹² Hz. FM radio: ~88–108 MHz (λ ≈ 3 m). Microwave oven: 2.45 GHz (λ ≈ 12.2 cm). Visible light: 400–790 THz.

Is the speed of sound always 343 m/s?

No. 343 m/s is the speed in air at 20°C. It changes with medium: water ≈ 1,480 m/s, steel ≈ 5,960 m/s. In air, speed increases by roughly 0.6 m/s per degree Celsius. Speed changes affect wavelength but not frequency.

What is the electromagnetic spectrum?

The full range of EM radiation ordered by frequency: Radio (< 3 GHz) → Microwave (3–300 GHz) → Infrared (300 GHz–430 THz) → Visible light (430–790 THz) → Ultraviolet → X-rays → Gamma rays (> 10 EHz). Only visible light is detected by human eyes.

Why are subwoofers so large?

Low frequencies have very long wavelengths: at 20 Hz in air, λ ≈ 17 m; at 100 Hz, λ ≈ 3.4 m. A speaker cone must be large enough to displace sufficient air to reproduce these long wavelengths efficiently. High-frequency tweeters can be tiny because their wavelengths are just centimeters.

What happens to wavelength when a wave changes medium?

Frequency stays constant when a wave crosses a medium boundary, but the wave speed changes, so wavelength changes too. When light passes from vacuum into glass (speed ≈ 200,000 km/s), its frequency is unchanged but λ shrinks to about 67% of the vacuum value.

Sources & references

Methodology & trust

Editorial

ciencia calculator with its formula verified automatically against NIST — Speed of Light (CODATA 2018), per our editorial policy and methodology.

Updates

Updated: June 2026. Parameters are verified periodically against the cited sources.

Privacy

Calculations run 100% in your browser. We do not store or transmit your data.

Limitations

Indicative results. For critical decisions, consult a professional.

📌 How to cite this calculator

APA format

Rodríguez, M. (2026). Wavelength, Frequency & Wave Velocity Calculator (v = λ·f). Hacé Cuentas. https://hacecuentas.com/en/wave-frequency-wavelength-velocity

BibTeX

@misc{hacecuentas_wave_frequency_wavelength_velocity_2026,
  author       = {Rodríguez, Martín},
  title        = {{Wavelength, Frequency & Wave Velocity Calculator (v = λ·f)}},
  year         = {2026},
  howpublished = {\url{https://hacecuentas.com/en/wave-frequency-wavelength-velocity}},
  note         = {Hacé Cuentas}
}

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