Note Frequency Calculator

Calculate the frequency of any musical note, convert between notes and frequencies, and understand pitch relationships in music theory.

Convert musical notes to frequencies and vice versa using the 12-tone equal temperament system. Calculate pitch relationships, cents deviation, and wavelength for any note across all octaves.

Examples

Click on any example to load it into the calculator.

Standard A4 (440 Hz)

Standard

The standard reference note used by most orchestras and tuners worldwide.

Note: A

Octave: 4

Base Frequency: 440 Hz

Middle C (C4)

Middle C

Middle C, the central reference note on the piano keyboard.

Note: C

Octave: 4

Base Frequency: 440 Hz

High E (E6)

High Note

A high note commonly used in violin and flute music.

Note: E

Octave: 6

Base Frequency: 440 Hz

F# (F Sharp)

Sharp Note

A sharp note demonstrating accidentals in music notation.

Note: F#

Octave: 4

Base Frequency: 440 Hz

Other Titles
Understanding Note Frequency Calculator: A Comprehensive Guide
Master the relationship between musical notes and frequencies. Learn how pitch, frequency, and music theory work together to create the sounds we hear in music.

What is the Note Frequency Calculator?

  • Core Concepts and Definitions
  • Why Frequency Matters in Music
  • The 12-Tone Equal Temperament System
The Note Frequency Calculator is an essential tool for musicians, audio engineers, and music students that bridges the gap between musical notation and the physical properties of sound. It converts musical notes into their corresponding frequencies, enabling precise tuning, sound design, and understanding of pitch relationships. This calculator uses the 12-tone equal temperament system, which divides the octave into 12 equal semitones, making it the standard tuning system for most Western music.
The Physics of Musical Sound
Every musical note corresponds to a specific frequency measured in Hertz (Hz), which represents the number of vibrations per second. When a string vibrates or air moves through an instrument, it creates sound waves at particular frequencies. Our ears perceive these frequencies as different pitches—higher frequencies sound higher in pitch, while lower frequencies sound lower. The relationship between frequency and perceived pitch is logarithmic, which is why the 12-tone equal temperament system uses exponential frequency ratios.
The A4 = 440 Hz Standard
The international standard for musical pitch is A4 = 440 Hz, established in 1939. This means the A note in the fourth octave vibrates at exactly 440 cycles per second. This standard allows musicians worldwide to tune their instruments consistently. However, some orchestras use slightly different standards: many European orchestras tune to A4 = 442 Hz or 443 Hz for a brighter sound, while some Baroque ensembles use A4 = 415 Hz for historical authenticity.
Understanding Octaves and Note Names
Musical notes are organized in octaves, with each octave containing the same seven note names (A, B, C, D, E, F, G) plus their sharps and flats. Moving up one octave doubles the frequency, while moving down one octave halves it. For example, A4 = 440 Hz, A5 = 880 Hz, and A3 = 220 Hz. The octave numbering system places middle C (C4) at the center of the piano keyboard, with lower octaves having smaller numbers and higher octaves having larger numbers.

Key Frequency Relationships:

  • A4 = 440 Hz (international standard)
  • C4 (middle C) = 261.63 Hz
  • Each octave doubles the frequency
  • Each semitone increases frequency by a factor of 2^(1/12)

Step-by-Step Guide to Using the Note Frequency Calculator

  • Input Methodology
  • Understanding Results
  • Practical Applications
Using the Note Frequency Calculator effectively requires understanding musical notation and the relationship between notes and frequencies. Follow this comprehensive guide to get accurate results and meaningful insights from your calculations.
1. Selecting the Correct Note Name
Enter the note name using standard musical notation. Use the letters A, B, C, D, E, F, G for natural notes. For sharp notes, add a # symbol (e.g., A#, C#, F#). For flat notes, add a b symbol (e.g., Bb, Eb, Ab). Note that some notes have enharmonic equivalents: A# and Bb represent the same pitch, as do C# and Db, etc. The calculator will recognize both notations and give the same frequency result.
2. Determining the Correct Octave
The octave number is crucial for accurate frequency calculation. Middle C is C4, and A4 is the standard reference note (440 Hz). On a piano, the lowest note (A0) is in octave 0, and the highest note (C8) is in octave 8. Most music uses notes between octaves 2 and 6. If you're unsure about the octave, consider the context: bass notes are typically in octaves 1-3, middle range in octaves 3-5, and high notes in octaves 5-7.
3. Setting the Base Frequency
The base frequency determines the reference pitch for A4. The standard is 440 Hz, which is used by most modern instruments and tuners. However, you can adjust this value if you're working with instruments tuned to different standards. Many orchestras use 442 Hz or 443 Hz for a brighter sound, while some historical instruments use 415 Hz or 430 Hz. The calculator will automatically adjust all other note frequencies based on your chosen base frequency.
4. Interpreting the Results
The calculator provides four key results: frequency in Hz, cents deviation from A4, wavelength in meters, and period in milliseconds. The frequency is the primary result, showing the exact pitch in cycles per second. Cents show how far the note is from A4 in the logarithmic cent scale (100 cents = 1 semitone). Wavelength shows the physical length of the sound wave, useful for acoustic design. Period shows the time duration of one complete cycle.

Common Note Frequencies:

  • C4 (middle C) = 261.63 Hz
  • E4 = 329.63 Hz
  • G4 = 392.00 Hz
  • A4 (standard) = 440.00 Hz
  • C5 = 523.25 Hz

Real-World Applications and Musical Context

  • Instrument Tuning and Maintenance
  • Audio Engineering and Production
  • Music Education and Theory
The Note Frequency Calculator serves as a fundamental tool across various musical disciplines, from instrument tuning to advanced audio production and music education.
Instrument Tuning and Maintenance
Musicians use frequency calculations for precise instrument tuning. Guitarists can tune their instruments by ear using the relationship between frets and frequency ratios. Piano tuners use frequency measurements to ensure each string produces the correct pitch. String players can verify their tuning against the calculated frequencies, especially when playing in different temperaments or with historical instruments. The calculator helps identify when instruments are out of tune and provides the exact frequencies needed for correction.
Audio Engineering and Sound Design
Audio engineers use frequency calculations for mixing, mastering, and sound design. Understanding note frequencies helps in EQ decisions—knowing that A4 is 440 Hz helps identify and treat problematic frequencies in recordings. Sound designers use frequency calculations to create musical effects, synthesize sounds, and design audio systems. The wavelength calculations are particularly useful for acoustic treatment and speaker placement, as they help determine room modes and standing waves.
Music Education and Theory
Music students use frequency calculations to understand the mathematical foundation of music theory. The relationship between frequency ratios and musical intervals helps students grasp concepts like consonance, dissonance, and harmonic relationships. Teachers can demonstrate how different tuning systems affect the same piece of music. The calculator helps students visualize the logarithmic nature of pitch perception and understand why equal temperament was developed as a compromise tuning system.

Professional Applications:

  • Piano tuning: Ensuring each string matches calculated frequency
  • Guitar setup: Calculating fret positions based on frequency ratios
  • Studio recording: Identifying and treating frequency conflicts
  • Concert hall design: Using wavelength data for acoustic optimization

Understanding Cents, Intervals, and Tuning Systems

  • The Cent Scale and Pitch Measurement
  • Musical Intervals and Frequency Ratios
  • Historical and Alternative Tuning Systems
Beyond simple frequency calculation, understanding cents, intervals, and different tuning systems provides deeper insight into the mathematical and historical aspects of music.
The Cent Scale and Logarithmic Pitch
Cents provide a logarithmic measure of pitch difference, with 1200 cents equal to one octave and 100 cents equal to one semitone. This logarithmic scale matches human pitch perception, which is also logarithmic. The cent scale allows precise measurement of pitch differences that would be difficult to express in frequency ratios. For example, a difference of 50 cents represents a pitch difference that's easily detectable by trained musicians but might be subtle to casual listeners.
Musical Intervals and Their Frequency Ratios
Musical intervals have specific frequency ratios that create different emotional and harmonic effects. The perfect octave has a 2:1 ratio, the perfect fifth has a 3:2 ratio, and the perfect fourth has a 4:3 ratio. These ratios create consonant, pleasing sounds. The equal temperament system approximates these ratios to allow music to be played in any key, but some intervals (like the major third) are slightly out of tune compared to their pure ratios.
Historical and Alternative Tuning Systems
Before equal temperament, musicians used various tuning systems like just intonation, Pythagorean tuning, and meantone temperament. These systems prioritized certain intervals over others, making some keys sound more in tune than others. The calculator can be adapted for these systems by adjusting the frequency ratios. Understanding these historical systems helps musicians interpret early music authentically and appreciate the evolution of musical tuning.

Interval Frequency Ratios:

  • Perfect Octave: 2:1 ratio (1200 cents)
  • Perfect Fifth: 3:2 ratio (702 cents in equal temperament)
  • Perfect Fourth: 4:3 ratio (498 cents in equal temperament)
  • Major Third: 5:4 ratio (386 cents in equal temperament)
  • Minor Third: 6:5 ratio (316 cents in equal temperament)

Mathematical Derivation and Advanced Concepts

  • The Equal Temperament Formula
  • Harmonic Series and Overtones
  • Digital Audio and Sample Rates
The mathematical foundation of the Note Frequency Calculator reveals the elegant relationship between mathematics and music, providing insights into both the physical and perceptual aspects of sound.
The Equal Temperament Formula
The fundamental formula for equal temperament is: f = f₀ × 2^(n/12), where f is the frequency of the desired note, f₀ is the frequency of the reference note (usually A4 = 440 Hz), and n is the number of semitones from the reference note. This formula ensures that each semitone represents an equal frequency ratio, allowing music to be transposed to any key while maintaining consistent interval relationships. The factor 2^(1/12) ≈ 1.05946 represents the frequency ratio between adjacent semitones.
Harmonic Series and Natural Overtones
Every musical note contains a series of overtones at frequencies that are whole number multiples of the fundamental frequency. The harmonic series for A4 (440 Hz) includes 440 Hz (fundamental), 880 Hz (octave), 1320 Hz (perfect fifth), 1760 Hz (perfect fourth), and so on. These overtones give each instrument its unique timbre and contribute to the richness of musical sound. Understanding the harmonic series helps in instrument design, audio processing, and music composition.
Digital Audio and Sample Rate Considerations
In digital audio, the sample rate determines the highest frequency that can be accurately represented. The Nyquist theorem states that the sample rate must be at least twice the highest frequency of interest. For music, this means a sample rate of at least 40 kHz is needed to accurately represent frequencies up to 20 kHz (the upper limit of human hearing). Most digital audio uses 44.1 kHz or 48 kHz sample rates, providing adequate headroom for accurate frequency representation.

Mathematical Relationships:

  • Semitone ratio: 2^(1/12) ≈ 1.05946
  • Cent formula: cents = 1200 × log₂(f/f₀)
  • Wavelength: λ = c/f (where c = speed of sound)
  • Period: T = 1/f (time for one complete cycle)