Wavelength Calculator
Calculate wavelength from frequency and wave speed. Enter any two values — get wavelength, frequency, or speed for EM waves, sound, and antenna design.
Hz
m/s
Enter your values above to see the results.
Tips & Notes
- ✓Electromagnetic waves travel at c = 299,792,458 m/s in vacuum (speed of light). In other media, v = c/n where n is the refractive index. In glass (n≈1.5): v = c/1.5 = 200,000 km/s.
- ✓Antenna length for resonance: quarter-wave monopole = λ/4; half-wave dipole = λ/2. A 2.4 GHz WiFi antenna: λ = 0.3/2.4×10⁹ = 0.125 m = 12.5 cm → quarter wave = 3.125 cm (approx 3.1 cm for those small PCB antennas).
- ✓Sound speed in air: v ≈ 331 + 0.6 × T_celsius (m/s). At 20°C: v = 343 m/s. At 35°C: v = 352 m/s. Sound speed increases with temperature because warmer air molecules move faster. Speed in water: ~1,480 m/s (4× faster than air).
- ✓Human hearing range: 20 Hz to 20,000 Hz. At 20°C: wavelength range 17.15 m (20 Hz, bass rumble) to 1.715 cm (20 kHz, upper hearing limit). Musical middle A (440 Hz) has wavelength 0.780 m in air at 20°C.
- ✓For antenna calculations, actual antenna length is slightly shorter than the calculated electrical half-wavelength due to the velocity factor of the conductor material. Practical antennas use a factor of 0.92-0.97 × λ/2.
Common Mistakes
- ✗Using speed of light for sound calculations — electromagnetic waves travel at 3×10⁸ m/s; sound travels at ~343 m/s in air at 20°C. Using light speed for an audio frequency gives a wavelength millions of times too large.
- ✗Forgetting to convert frequency units — 2.4 GHz = 2,400,000,000 Hz = 2.4×10⁹ Hz. Entering "2.4" instead of "2,400,000,000" gives a wavelength in meters instead of centimeters.
- ✗Using free-space wavelength directly for antenna design without applying velocity factor — conductors slow wave propagation slightly. Physical antenna length = free-space λ × velocity factor (typically 0.93-0.97 for wire antennas).
- ✗Confusing wavelength with wave period — wavelength is a spatial measure (meters); period is a time measure (seconds). Period T = 1/f. Wavelength λ = v × T = v/f. Both decrease as frequency increases, but they measure different things.
- ✗Applying air sound speed for underwater acoustics — sound in water is ~1,480 m/s (4.3× faster than in air). A 100 Hz sound has wavelength 3.43 m in air but 14.8 m in water — critical for sonar design and underwater communication.
Wavelength Calculator Overview
Wavelength is the spatial period of a wave — the distance over which the wave pattern repeats. Every wave phenomenon from radio signals to sound to visible light follows the universal relationship λ = v/f, connecting spatial scale (wavelength) to temporal rate (frequency) through propagation speed.
Wavelength formula:
λ = v / f | f = v / λ | v = λ × f | For EM waves in vacuum: v = c = 299,792,458 m/s
EX: 5G mmWave at 28 GHz → λ = 3×10⁸ / 28×10⁹ = 0.01071 m = 10.71 mm. Antenna half-wave: 5.36 mm × 0.95 = 5.09 mm — extremely small, enabling tiny 5G antennas in smartphones.Sound wavelength in air:
v_sound = 331 + 0.6 × T(°C) m/s | At 20°C: v = 343 m/s | λ_sound = 343 / f
EX: Concert A at 440 Hz in air at 20°C → λ = 343/440 = 0.780 m. Same note in water (v=1480 m/s) → λ = 1480/440 = 3.36 m (4.3× longer in water).Electromagnetic spectrum wavelength reference:
| Band | Frequency | Wavelength | Examples |
|---|---|---|---|
| ELF/VLF | 3 Hz – 30 kHz | 10 km – 100,000 km | Submarine communication |
| AM Radio | 535–1,705 kHz | 176–561 m | AM broadcast stations |
| FM Radio | 88–108 MHz | 2.78–3.41 m | FM broadcast, VHF |
| WiFi 2.4 GHz | 2,400–2,484 MHz | 12.1–12.5 cm | 802.11 b/g/n, Bluetooth |
| WiFi 5 GHz | 5,150–5,850 MHz | 5.1–5.8 cm | 802.11 a/n/ac |
| 5G mmWave | 24–100 GHz | 3–12.5 mm | 5G ultra-high-speed |
| Visible light | 430–770 THz | 380–700 nm | Human vision range |
| X-ray | 30 PHz – 30 EHz | 0.01–10 nm | Medical imaging |
| Frequency | λ (free space) | λ/4 antenna | λ/2 dipole | Application |
|---|---|---|---|---|
| 27 MHz (CB radio) | 11.1 m | 2.78 m | 5.56 m | CB whip antenna |
| 144 MHz (2m amateur) | 2.08 m | 52 cm | 1.04 m | VHF hand-held |
| 433 MHz (ISM) | 69.3 cm | 16.4 cm | 32.9 cm | 433 MHz sensors, LoRa |
| 915 MHz (ISM US) | 32.7 cm | 7.8 cm | 15.6 cm | LoRa, RFID |
| 2.4 GHz (WiFi) | 12.5 cm | 3.0 cm | 6.1 cm | WiFi, Bluetooth, Zigbee |
Frequently Asked Questions
Wavelength λ = c / f, where c = 299,792,458 m/s (speed of light in vacuum) and f is frequency in Hz. Examples: AM radio at 1 MHz → λ = 3×10⁸ / 10⁶ = 300 m. FM radio at 100 MHz → λ = 3 m. WiFi 2.4 GHz → λ = 0.125 m = 12.5 cm. Visible light red (700 nm) → f = 3×10⁸ / 700×10⁻⁹ = 4.29×10¹⁴ Hz = 429 THz. The relationship is exact: doubling frequency halves wavelength.
Sound wavelength λ = v_sound / f, where v_sound ≈ 343 m/s in air at 20°C. Sound speed varies with temperature: v = 331 + 0.6 × T(°C) m/s. Examples: middle C (261.6 Hz) → λ = 343/261.6 = 1.31 m. Concert A (440 Hz) → λ = 343/440 = 0.780 m. Human speech fundamental (85-300 Hz) → λ = 1.1-4.0 m. Ultrasound for medical imaging (1-15 MHz) in tissue (v≈1540 m/s) → λ = 0.1-1.54 mm — high frequency gives finer spatial resolution.
Quarter-wave monopole: L = λ/4 = c/(4f) × velocity_factor. Half-wave dipole: L = λ/2 = c/(2f) × velocity_factor. Velocity factor for copper wire antennas is typically 0.95. Examples: 2.4 GHz WiFi → λ = 12.5 cm → quarter-wave = 12.5/4 = 3.125 cm × 0.95 = 2.97 cm. 146 MHz VHF → λ = 2.05 m → half-wave dipole = 1.025 m × 0.95 = 0.974 m. 88-108 MHz FM broadcast → half-wave range: 1.4-1.7 m (FM antennas are roughly 1.5 m long).
Frequency and wavelength are inversely proportional: λ = v/f, so λ × f = v (constant for a given medium). Higher frequency always means shorter wavelength; lower frequency means longer wavelength. This inverse relationship applies to all wave phenomena — light, radio, sound, seismic waves, water waves. For electromagnetic waves in vacuum: a frequency doubled means wavelength halved. Practical implication: high-frequency radio systems (GHz) use short antennas (cm scale); low-frequency AM broadcast (MHz) requires long antennas (meters to hundreds of meters).
From longest wavelength (lowest frequency) to shortest (highest): Radio waves (>1 mm, <300 GHz): AM radio 300m, FM radio 3m, WiFi 12.5cm, 5G mmWave 1-10mm. Microwaves (1mm-1cm): radar, satellite communications, microwave ovens (12.2cm at 2.45GHz). Infrared (700nm-1mm): thermal cameras, TV remotes, fiber optic communications. Visible light (380-700nm): violet 380nm, green 550nm, red 700nm. Ultraviolet (10-380nm): germicidal UV-C (254nm). X-rays (0.01-10nm): medical imaging. Gamma rays (<0.01nm): nuclear medicine, cosmic radiation.
Antenna resonance occurs when the physical length matches a specific fraction of the operating wavelength — typically λ/4 (monopole over ground plane) or λ/2 (dipole in free space). At resonance, the antenna efficiently radiates/receives energy with minimal reflected power. Example design chain: Target frequency 433 MHz ISM band. λ = 3×10⁸ / 433×10⁶ = 0.693 m. Quarter-wave: 0.693/4 = 0.173 m × 0.95 (velocity factor) = 0.164 m = 16.4 cm. A 433 MHz antenna should be approximately 16.4 cm for quarter-wave resonance. Shortening below λ/4 reduces efficiency; lengthening beyond λ/2 changes the radiation pattern.