What is the formula for frequency?

Frequency equals 1 divided by period: f = 1/T, where f is in hertz (Hz) and T is period in seconds. From wavelength: f = v divided by lambda, where v is wave speed in m/s and lambda is wavelength in meters. For electromagnetic waves in a vacuum, v = 299,792,458 m/s (speed of light).

How do you calculate frequency from period?

Divide 1 by the period: f = 1/T. If a wave completes one cycle every 0.01 seconds, its frequency is f = 1/0.01 = 100 Hz. If the period is 0.002 seconds, the frequency is 1/0.002 = 500 Hz.

How do you calculate frequency from wavelength?

Use f = v / lambda, where v is the speed of the wave and lambda is the wavelength. For light in a vacuum, v = 3 x 10 to the power 8 m/s. For a wavelength of 500 nanometers (visible green light): f = 3e8 / 500e-9 = 6 x 10 to the power 14 Hz (600 THz).

What is the unit of frequency?

The SI unit of frequency is the hertz (Hz), equal to one cycle per second. Common multiples: kilohertz (kHz) = 1,000 Hz, megahertz (MHz) = 1,000,000 Hz, gigahertz (GHz) = 1,000,000,000 Hz, terahertz (THz) = 10 to the 12th Hz.

What is the relationship between frequency and period?

Frequency and period are reciprocals of each other: f = 1/T and T = 1/f. Doubling the frequency halves the period. A 100 Hz wave has a period of 0.01 seconds; a 1 kHz wave has a period of 0.001 seconds (1 millisecond).

What is the frequency of household electricity?

Household AC power runs at 60 Hz in the United States, Canada, and most of the Americas. Europe, Africa, Asia, and Australia use 50 Hz. This means the current completes 60 or 50 full cycles per second respectively, giving a period of 1/60 = 16.67 ms or 1/50 = 20 ms.

What is the frequency of visible light?

Visible light spans roughly 400 to 700 nanometers in wavelength, corresponding to frequencies of about 430 THz (red) to 750 THz (violet). Using f = c / lambda with c = 3 x 10 to the 8 m/s: red light at 700 nm gives f = 3e8 / 700e-9 = 4.29 x 10 to the 14 Hz.

How do you calculate the period from frequency?

Period is the reciprocal of frequency: T = 1/f. A 60 Hz wave has a period of T = 1/60 = 0.01667 seconds (16.67 milliseconds). A 2.4 GHz Wi-Fi signal has a period of T = 1/2,400,000,000 = 0.417 nanoseconds.

What is angular frequency and how does it relate to frequency?

Angular frequency (omega) measures how fast a wave oscillates in radians per second: omega = 2 x pi x f. For 60 Hz: omega = 2 x 3.14159 x 60 = 376.99 radians per second. Angular frequency is used in AC circuit analysis and wave equations.

How do you convert frequency to wavelength?

Wavelength = wave speed / frequency: lambda = v / f. For radio waves (speed of light): a 100 MHz FM station has wavelength = 3e8 / 100e6 = 3 meters. A 2.4 GHz Wi-Fi signal has wavelength = 3e8 / 2.4e9 = 0.125 meters (12.5 cm).

Frequency Calculator — CalculatorCove

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Sources & Methodology

✓Formulas verified against NIST CODATA 2022 physical constants and standard physics references.

📐

NIST CODATA — Speed of Light in Vacuum

c = 299,792,458 m/s (exact, by definition). Used for all electromagnetic wave frequency-wavelength calculations.

🌊

Engineering Toolbox — Speed of Sound

Sound at 20°C in air = 343 m/s; in water = 1,480 m/s; in steel = 5,120 m/s. Used for acoustic wavelength calculations.

From period: f = 1/T. Period converted to seconds before calculation.
From wavelength: f = v/λ. Wavelength converted to meters before calculation.
From frequency: T = 1/f; λ = v/f. Frequency converted to Hz. Angular frequency: ω = 2πf.

⏱ Last reviewed: April 2026

How to Calculate Frequency in 2026

Frequency describes how many complete cycles of a repeating event occur per second. It governs everything from the pitch of musical notes to the channel of a radio station, the speed of a computer processor, and the colour of visible light. The unit of frequency is the hertz (Hz), named after Heinrich Hertz who first demonstrated radio waves in 1887.

Formula 1 — Frequency from Period

f = 1 / T

f = frequency (Hz) T = period (seconds)

Example — 50 Hz AC mains: T = 1/50 = 0.02 s (20 ms)
Example — 440 Hz concert A: T = 1/440 = 0.00227 s (2.27 ms)

Formula 2 — Frequency from Wavelength

f = v / λ

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

Example — FM radio at 100 MHz: λ = 3×10⁸ / 100×10⁶ = 3 meters
Example — visible green light (550 nm): f = 3×10⁸ / 550×10⁻⁹ = 545 THz

Common Frequency Reference Values 2026

Signal	Frequency	Period	Wavelength
US AC power	60 Hz	16.67 ms	5,000 km
EU AC power	50 Hz	20 ms	6,000 km
A4 concert note	440 Hz	2.27 ms	78 cm (sound)
AM radio	535–1,605 kHz	0.62–1.87 μs	187–560 m
FM radio	87.5–108 MHz	9.3–11.4 ns	2.8–3.4 m
Wi-Fi 2.4 GHz	2.4 GHz	417 ps	12.5 cm
Wi-Fi 5 GHz	5 GHz	200 ps	6 cm
Visible light (red)	430 THz	2.3 fs	700 nm
Visible light (violet)	750 THz	1.3 fs	400 nm

Angular Frequency

Angular frequency (ω, omega) expresses oscillation rate in radians per second rather than cycles per second: ω = 2πf. For a 60 Hz AC circuit: ω = 2 × 3.14159 × 60 = 376.99 rad/s. Angular frequency is used extensively in AC circuit analysis, phasor diagrams, and wave equations where the 2π factor is already embedded.

Practical Applications

Electrical engineering — AC circuit design, resonance frequency of LC circuits (f = 1/2π√LC)
Telecommunications — antenna sizing (antenna length ≈ λ/4), channel allocation, interference analysis
Audio engineering — equalizer design, tuning instruments, room acoustics and standing wave frequencies
Medical imaging — ultrasound frequencies (1–20 MHz), MRI Larmor frequencies
Optics — converting between wavelength and frequency for laser specifications and LED color

💡 Resonance tip: An LC circuit resonates at f = 1 / (2π√(LC)), where L is inductance in henries and C is capacitance in farads. At resonance, impedance is purely resistive and current is maximised — the principle behind tuning a radio receiver to a specific station.

Frequently Asked Questions

Two main formulas: from period, f = 1/T (frequency in Hz, period in seconds). From wavelength, f = v/lambda (wave speed divided by wavelength in meters). For electromagnetic waves, use v = 299,792,458 m/s. For sound in air at 20°C, use v = 343 m/s.

Divide 1 by the period in seconds: f = 1/T. A wave with a period of 0.025 seconds has a frequency of 1/0.025 = 40 Hz. A period of 1 millisecond (0.001 s) gives 1/0.001 = 1,000 Hz = 1 kHz.

Use f = v / lambda. For radio waves (speed of light): a 3-meter wavelength gives f = 299,792,458 / 3 = approximately 100 MHz (FM band). For sound in air: a 1-meter wavelength gives f = 343 / 1 = 343 Hz.

The SI unit is the hertz (Hz) = one cycle per second. Multiples: kilohertz (kHz) = 1,000 Hz, megahertz (MHz) = 10 to the 6 Hz, gigahertz (GHz) = 10 to the 9 Hz, terahertz (THz) = 10 to the 12 Hz. Angular frequency uses radians per second (rad/s) where omega = 2 x pi x f.

60 Hz in the United States, Canada, and most of the Americas. 50 Hz in Europe, Africa, Asia, and Australia. These frequencies correspond to periods of 16.67 ms (60 Hz) and 20 ms (50 Hz) — meaning the current reverses direction 120 or 100 times per second.

They are exact reciprocals: f = 1/T and T = 1/f. Higher frequency means shorter period. A 1 Hz signal has a 1-second period; a 1 MHz signal has a 1-microsecond period. Multiplying frequency by period always equals 1.

Visible light spans roughly 400–700 nm in wavelength, giving frequencies of about 430 THz (red, 700 nm) to 750 THz (violet, 400 nm). Green light at 550 nm has a frequency of approximately 545 THz. These are calculated using f = c / lambda with c = 299,792,458 m/s.

Angular frequency (omega) = 2 x pi x f, measured in radians per second. It describes the rate of phase change rather than complete cycles. For 60 Hz AC: omega = 2 x 3.14159 x 60 = 376.99 rad/s. Angular frequency is used in differential equations and phasor analysis of AC circuits.

Use f = c / lambda with c = 299,792,458 m/s. For a 2-meter wavelength: f = 299,792,458 / 2 = 149.9 MHz. Practical shortcut: for radio waves, f (MHz) x lambda (m) approximately equals 300. So a 300 MHz signal has a 1-meter wavelength; a 3 GHz signal has a 10 cm wavelength.

2.4 GHz = 2,400,000,000 cycles per second. This gives a wavelength of c/f = 299,792,458 / 2,400,000,000 = 12.5 cm. The 2.4 GHz band penetrates walls better than 5 GHz (6 cm wavelength) but offers lower maximum speeds. It shares spectrum with Bluetooth, microwaves, and other devices.

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