Frequency Conversion
Frequency Conversion Formulas
Hertz ↔ BPM
BPM = Hz × 60
Hz = BPM ÷ 60
Convert between cycles per second and beats per minuteCommon Frequency Units
1 kHz = 1,000 Hz
1 MHz = 1,000,000 Hz
1 GHz = 1,000,000,000 Hz
SI prefixes for large frequenciesMusical Note Frequencies
A4 = 440 Hz (concert pitch)
f_n = f_0 × 2^(n/12)
Where: f_n = note frequency, f_0 = reference frequency, n = semitonesReference Frequency Values
| Reference Source | Hertz (Hz) | BPM | Period (s) | Application |
|---|---|---|---|---|
| Resting Heart Rate | 1.0 | 60 | 1.0 | Medical monitoring |
| Slow Waltz | 1.5 | 90 | 0.67 | Musical tempo |
| Moderate Walking | 2.0 | 120 | 0.5 | Exercise physiology |
| AC Power (US) | 60 | 3,600 | 0.0167 | Electrical systems |
| AC Power (Europe) | 50 | 3,000 | 0.02 | Electrical systems |
| Concert A | 440 | 26,400 | 0.00227 | Musical tuning |
| AM Radio | 1,000,000 | 60,000,000 | 1×10⁻⁶ | Broadcasting |
| FM Radio | 100,000,000 | 6×10⁹ | 1×10⁻⁸ | Broadcasting |
| Visible Light | 5×10¹⁴ | 3×10¹⁶ | 2×10⁻¹⁵ | Optics, photonics |
Frequency Unit Definitions
Hertz (Hz) - SI Base Unit
The SI unit of frequency, measuring the number of cycles per second.
Definition: One cycle per second (s⁻¹)
Named After: Heinrich Hertz (1857-1894), German physicist
Usage: Electronics, physics, engineering, audio systems
Range: From DC (0 Hz) to gamma rays (10²⁴ Hz or higher)
SI Status: Official SI derived unit
Beats Per Minute (BPM) - Musical/Medical Standard
Measures the number of beats or pulses occurring in one minute.
Definition: Number of beats in 60 seconds
Musical Use: Tempo marking for musical compositions
Medical Use: Heart rate, breathing rate measurements
Typical Ranges: Music 60-200 BPM, resting heart rate 60-100 BPM
Conversion: 1 Hz = 60 BPM
Frequency Spectrum Ranges
Extremely Low Frequency (ELF): 3-30 Hz
Audio Frequency: 20 Hz - 20 kHz (human hearing)
Radio Frequency (RF): 3 kHz - 300 GHz
Microwave: 300 MHz - 300 GHz
Visible Light: 400-790 THz (terahertz)
Biological Frequencies
Brain Waves: Alpha (8-12 Hz), Beta (13-30 Hz), Delta (0.5-4 Hz)
Heart Rate: 0.8-3.3 Hz (48-200 BPM)
Breathing Rate: 0.2-0.5 Hz (12-30 breaths/min)
Circadian Rhythm: ~1.16 × 10⁻⁵ Hz (24-hour cycle)
Scientific Applications
Audio & Acoustics
Sound Analysis: Frequency spectrum analysis, pitch detection
Audio Equipment: Sampling rates, filter design
Room Acoustics: Resonance frequencies, reverberation
Electronics & Communications
Radio Communications: Carrier frequencies, bandwidth
Digital Circuits: Clock frequencies, timing analysis
Signal Processing: Fourier transforms, filtering
Medicine & Biology
Vital Signs: Heart rate, respiratory rate monitoring
EEG/ECG: Brain wave and heart rhythm analysis
Ultrasound: Medical imaging frequencies (1-20 MHz)
Physics & Quantum Mechanics
Atomic Transitions: Spectroscopy, laser frequencies
Electromagnetic Radiation: Photon energy calculations
Particle Physics: Cyclotron frequencies, resonances
Mechanical Engineering
Vibration Analysis: Natural frequencies, resonance
Rotating Machinery: RPM to Hz conversion
Modal Analysis: Structural dynamics, fatigue
Music & Performance
Tempo Control: Metronome settings, rhythm programming
Pitch Standards: Tuning systems, equal temperament
Electronic Music: Oscillator frequencies, synthesis
Measurement Considerations
Sampling and Aliasing
Nyquist Theorem: Sampling frequency must be ≥2× highest frequency
Anti-Aliasing: Use low-pass filters before sampling
Digital Audio: CD quality = 44.1 kHz sampling rate
Measurement Accuracy
Time Base: Frequency accuracy depends on time reference
Gate Time: Longer measurement time improves resolution
Stability: Crystal oscillators for precise frequency standards
Practical Applications
Medical Monitoring: Consider patient movement and electrode placement
Audio Engineering: Account for room acoustics and equipment response
RF Systems: Temperature effects and regulatory compliance
Fundamental Frequency Equations
Basic Frequency Definition
f = 1/T
Where: f = frequency, T = period (time for one complete cycle)Wave Equation
c = fλ
Where: c = wave speed, f = frequency, λ = wavelengthAngular Frequency
ω = 2πf
Where: ω = angular frequency (rad/s), f = frequency (Hz)Energy-Frequency Relationship
E = hf
Where: E = photon energy, h = Planck's constant, f = frequency