Frequency Calculator – 555 Timer, LC, Wavelength & More | Free Online Tool

  • Adam
  • November 26, 2025

Calculate frequency instantly with our comprehensive calculator. Supports 555 timer, LC resonance, wavelength conversion, cutoff frequency, Nyquist frequency, and more. Free tool with step-by-step solutions and formulas.

Frequency Calculator - Calculate Frequency with Multiple Formulas

A frequency calculator is an essential tool for determining the number of oscillations, cycles, or waves per unit time in various applications including electronics, physics, signal processing, and audio engineering. This comprehensive calculator supports multiple calculation modes including basic frequency, 555 timer circuits, LC resonance, wavelength conversions, and more.

Basic Frequency
555 Timer
LC Resonance
Wavelength
Energy
Natural Frequency
Cutoff Frequency
Nyquist

Basic Frequency Calculator

Calculate frequency from time period, wavelength, or angular frequency

555 Timer Frequency Calculator

Calculate astable 555 timer oscillator frequency (NE555, LM555, IC555)

Common: µF = ×10⁻⁶, nF = ×10⁻⁹, pF = ×10⁻¹²

LC Resonant Frequency Calculator

Calculate resonant frequency for LC oscillator circuits

Common: mH = ×10⁻³, µH = ×10⁻⁶, nH = ×10⁻⁹
Common: µF = ×10⁻⁶, nF = ×10⁻⁹, pF = ×10⁻¹²

Wavelength to Frequency Calculator

Convert wavelength to frequency for electromagnetic waves

nm (×10⁻⁹), µm (×10⁻⁶), mm (×10⁻³)
Default: 299,792,458 m/s (speed of light)

Energy to Frequency Calculator

Calculate frequency from photon energy using Planck's equation

Planck's constant h = 6.62607015 × 10⁻³⁴ J·s

Natural Frequency Calculator

Calculate natural frequency for spring-mass systems

Cutoff Frequency Calculator

Calculate cutoff frequency for RC and RL filters

Nyquist Frequency Calculator

Calculate minimum sampling frequency to avoid aliasing

Result:

What is Frequency?

Frequency is the number of complete cycles, oscillations, or waves that occur per unit of time, typically measured in Hertz (Hz), where 1 Hz equals one cycle per second. Frequency is a fundamental concept in physics, electronics, telecommunications, and signal processing, describing everything from alternating current to electromagnetic radiation.

Key Characteristics of Frequency:

  • Unit of measurement: Hertz (Hz), kilohertz (kHz), megahertz (MHz), gigahertz (GHz)
  • Inverse relationship with period: Frequency = 1 / Period (f = 1/T)
  • Wavelength relationship: Higher frequency means shorter wavelength for electromagnetic waves
  • Energy relationship: Higher frequency photons carry more energy (E = hf)

Frequency Formulas

Different applications require different frequency calculation formulas based on the available parameters and system characteristics:

Basic Frequency Formulas

From Time Period:

f = 1 / T

Where T is the period in seconds

From Wavelength:

f = v / λ

Where v is wave velocity and λ is wavelength

From Angular Frequency:

f = ω / 2π

Where ω is angular frequency in rad/s

555 Timer Astable Frequency Formula

The 555 timer IC operates in astable mode to generate continuous square wave oscillations. The frequency formula accounts for the charging and discharging times through resistors R1 and R2:

f = 1.44 / [(R1 + 2R2) × C]

Where:

  • • f = output frequency in Hz
  • • R1 = resistance in ohms (Ω)
  • • R2 = resistance in ohms (Ω)
  • • C = capacitance in farads (F)

Duty Cycle:

D = (R1 + R2) / (R1 + 2R2) × 100%

Time High and Low:

Thigh = 0.693 × (R1 + R2) × C

Tlow = 0.693 × R2 × C

LC Resonant Frequency Formula

LC circuits resonate at a specific frequency determined by inductance and capacitance values, commonly used in oscillators, filters, and tuning circuits:

f = 1 / (2π√(LC))

Where:

  • • f = resonant frequency in Hz
  • • L = inductance in henries (H)
  • • C = capacitance in farads (F)
  • • π = 3.14159...

Angular Resonant Frequency:

ω0 = 1 / √(LC)

Additional Frequency Formulas

Cutoff Frequency (RC Filter):

fc = 1 / (2πRC)

Cutoff Frequency (RL Filter):

fc = R / (2πL)

Natural Frequency (Spring-Mass):

fn = (1/2π) × √(k/m)

Energy-Frequency Relationship:

f = E / h

Where h = 6.626 × 10-34 J·s (Planck's constant)

Nyquist Sampling Frequency:

fs ≥ 2fmax

How to Calculate Frequency

The method for calculating frequency depends on which parameters are known and the specific application. Follow these systematic approaches:

Calculating Frequency from Time Period

  1. Measure or identify the period: Determine the time for one complete cycle in seconds
  2. Apply the formula: f = 1/T where T is the period
  3. Convert units if needed: Ensure the period is in seconds for frequency in Hz
  4. Express the result: State frequency with appropriate units (Hz, kHz, MHz, GHz)

Example: If a signal completes one cycle every 0.005 seconds:

f = 1 / 0.005 = 200 Hz

Calculating 555 Timer Frequency

  1. Identify component values: Note R1, R2 (in ohms), and C (in farads)
  2. Convert units to standard form: Convert kΩ to Ω, µF to F
  3. Apply the 555 formula: f = 1.44 / [(R1 + 2R2) × C]
  4. Calculate duty cycle (optional): D = (R1 + R2) / (R1 + 2R2) × 100%

Example: R1 = 1kΩ, R2 = 10kΩ, C = 10µF

f = 1.44 / [(1000 + 2×10000) × 10×10-6]

f = 1.44 / [21000 × 0.00001]

f = 1.44 / 0.21 = 6.86 Hz

Calculating LC Resonant Frequency

  1. Determine L and C values: Identify inductance (H) and capacitance (F)
  2. Calculate the product LC: Multiply inductance by capacitance
  3. Find the square root: Calculate √(LC)
  4. Apply the formula: f = 1 / (2π√(LC))

Example: L = 100µH = 100×10-6H, C = 100pF = 100×10-12F

LC = (100×10-6) × (100×10-12) = 10-14

√(LC) = √(10-14) = 10-7

f = 1 / (2π × 10-7) = 1.59 MHz

Types of Frequency Calculators

Different applications require specialized frequency calculators optimized for specific circuit types and measurement scenarios:

Timer IC Frequency Calculators

  • 555 Timer (NE555, LM555, IC555): Most common astable oscillator for generating square waves from less than 1 Hz to several hundred kHz
  • CD4047 CMOS Timer: Low-power oscillator with astable and monostable modes
  • TL494 PWM Controller: Switching power supply controller with programmable oscillator frequency
  • UC3842/UC3843/UC3845: Current-mode PWM controllers with internal oscillators
  • SG3524/SG3525: Voltage-mode PWM controllers for power supplies
  • IR2153: High-voltage half-bridge driver with integrated oscillator

Signal and Audio Frequency Calculators

  • Audio Frequency Calculator: Determines frequencies in the audible range (20 Hz - 20 kHz)
  • Musical Note Frequency: Calculates precise frequencies for musical notes and scales
  • Oscilloscope Frequency: Measures signal frequency from oscilloscope period measurements
  • Voice Frequency Calculator: Analyzes vocal formant frequencies (300 Hz - 3.4 kHz)

Electronics and Circuit Frequency Calculators

  • PWM Frequency Calculator: Determines pulse-width modulation frequencies for Arduino, AVR, and microcontrollers
  • LC Oscillator Calculator: Calculates resonant frequency for LC tank circuits
  • Cutoff Frequency Calculator: Determines -3dB point for low-pass, high-pass, band-pass filters
  • Center Frequency Calculator: Finds geometric mean frequency for band-pass and band-stop filters

Physics and Engineering Frequency Calculators

  • Natural Frequency Calculator: Determines resonant frequency for mechanical systems, beams, and structures
  • Fundamental Frequency Calculator: Calculates lowest resonant frequency of vibrating systems
  • Belt Frequency Calculator: Analyzes vibration frequencies in belt-driven machinery
  • Gear Mesh Frequency: Calculates tooth engagement frequency in gear systems

Frequency Units and Conversions

Frequency is expressed in various units depending on the magnitude and application domain:

Unit Symbol Equivalent Common Applications
Hertz Hz 1 cycle/second Audio frequencies, AC power
Kilohertz kHz 1,000 Hz Audio, AM radio, ultrasonic
Megahertz MHz 1,000,000 Hz FM radio, TV, microprocessors
Gigahertz GHz 1,000,000,000 Hz WiFi, cellular, microwave, CPUs
Terahertz THz 1,000,000,000,000 Hz Infrared light, molecular rotations

Applications of Frequency Calculators

Frequency calculators serve critical functions across numerous technical and scientific disciplines:

  • Electronics Design: Designing oscillators, clock generators, timing circuits, and signal generators for precise frequency control
  • Communications: Setting carrier frequencies, modulation rates, channel spacing, and bandwidth allocations in radio and telecommunications
  • Audio Engineering: Tuning musical instruments, equalizer design, crossover frequency selection, and acoustic analysis
  • Power Electronics: Determining switching frequencies for DC-DC converters, inverters, motor drives, and power supplies
  • Signal Processing: Setting sampling rates, designing digital filters, analyzing frequency spectra, and preventing aliasing
  • Mechanical Engineering: Analyzing vibration frequencies, modal analysis, resonance avoidance, and structural dynamics
  • Medical Devices: Ultrasound frequency selection, bioelectric signal analysis, and therapeutic frequency applications
  • Scientific Research: Spectroscopy, particle acceleration, laser frequency stabilization, and quantum computing

Frequently Asked Questions

How do you calculate frequency from period?
Frequency is the inverse of period. Use the formula f = 1/T where f is frequency in Hz and T is period in seconds. For example, if the period is 0.02 seconds, the frequency is 1/0.02 = 50 Hz. This fundamental relationship means that longer periods correspond to lower frequencies and shorter periods to higher frequencies.
What is the formula for 555 timer frequency?
The 555 timer astable frequency formula is f = 1.44 / [(R1 + 2R2) × C], where R1 and R2 are resistances in ohms and C is capacitance in farads. This applies to standard astable configurations of NE555, LM555, and IC555 timers. The duty cycle is (R1 + R2) / (R1 + 2R2) × 100%, with minimum duty cycle around 50% due to circuit topology.
How do you calculate LC resonant frequency?
LC resonant frequency is calculated using f = 1 / (2π√(LC)) where L is inductance in henries and C is capacitance in farads. At resonance, the inductive reactance equals capacitive reactance, causing the circuit to oscillate naturally at this frequency. This formula is fundamental for designing LC oscillators, tank circuits, and RF filters.
What is cutoff frequency and how is it calculated?
Cutoff frequency is the -3dB point where filter output power drops to half (voltage to 70.7%) of the passband level. For RC filters, fc = 1/(2πRC). For RL filters, fc = R/(2πL). This frequency marks the boundary between passband and stopband, critical for designing low-pass, high-pass, band-pass, and band-stop filters in signal processing applications.
What is Nyquist frequency in signal processing?
Nyquist frequency is half the sampling rate (fN = fs/2) and represents the maximum frequency that can be accurately represented in a digital signal. The Nyquist theorem states that the sampling frequency must be at least twice the highest frequency component in the signal (fs ≥ 2fmax) to prevent aliasing. For audio CD quality, 44.1 kHz sampling captures frequencies up to 22.05 kHz.
How do you convert wavelength to frequency?
Use the formula f = v/λ where v is wave velocity and λ is wavelength. For electromagnetic waves in vacuum, v = c = 299,792,458 m/s (speed of light), so f = c/λ. For example, red light with wavelength 700 nm has frequency f = (3×10⁸)/(700×10⁻⁹) = 4.29×10¹⁴ Hz or 429 THz. Higher frequencies correspond to shorter wavelengths.
What is the relationship between frequency and energy?
For photons and electromagnetic radiation, energy and frequency are directly proportional according to Planck's equation: E = hf, where h = 6.626×10⁻³⁴ J·s is Planck's constant. Higher frequency photons carry more energy. For example, X-rays have higher frequency and more energy than visible light, which is why X-rays can penetrate matter more effectively.
How do you calculate PWM frequency for Arduino?
Arduino PWM frequency depends on the timer prescaler and resolution. For most pins, default PWM frequency is approximately 490 Hz or 980 Hz. Calculate using f = Clock_Speed / (Prescaler × (1 + TOP)), where Clock_Speed is typically 16 MHz. Frequency can be adjusted by changing timer prescaler values (1, 8, 64, 256, 1024) or modifying timer TOP value for specific applications.
What is natural frequency in mechanical systems?
Natural frequency is the rate at which a system naturally oscillates when disturbed without external forcing. For a simple spring-mass system, fn = (1/2π)√(k/m) where k is spring constant (N/m) and m is mass (kg). Structures vibrate at natural frequencies, and resonance occurs when external forcing frequency matches natural frequency, potentially causing dangerous amplification.
How do you calculate center frequency for band-pass filters?
Center frequency is the geometric mean of the upper and lower cutoff frequencies: fc = √(fL × fH) where fL is lower cutoff and fH is upper cutoff frequency. For narrow bandwidth filters, it approximates the arithmetic mean (fL + fH)/2. Center frequency is critical for radio receiver tuning, audio equalizers, and spectrum analyzers to define the passband center.

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