Note Frequency Calculator
Free Note Frequency Calculator for creative & design. Free online tool with accurate results using verified formulas.
Formula
f = f_ref x 2^(n/12)
Where f is the target frequency, f_ref is the reference frequency (default 440 Hz for A4), and n is the number of semitones from the reference note. For cents adjustment: f = f_ref x 2^(cents/1200).
Worked Examples
Example 1: Finding Middle C Frequency
Problem: Calculate the frequency of Middle C (C4) given A4 = 440 Hz. C4 is 9 semitones below A4.
Solution: f = 440 x 2^(-9/12)\nf = 440 x 2^(-0.75)\nf = 440 x 0.5946\nf = 261.63 Hz\nWavelength = 343 / 261.63 = 1.311 m = 131.1 cm
Result: Middle C (C4) = 261.63 Hz | Wavelength: 131.1 cm
Example 2: Detuned A4 by +15 Cents
Problem: A musician tunes A4 to 440 Hz but their instrument drifts 15 cents sharp. What frequency are they playing?
Solution: f = 440 x 2^(15/1200)\nf = 440 x 2^(0.0125)\nf = 440 x 1.008686\nf = 443.82 Hz\nDifference = 443.82 - 440 = 3.82 Hz
Result: Detuned A4 (+15 cents) = 443.82 Hz (3.82 Hz sharp)
Frequently Asked Questions
How is the frequency of a musical note calculated mathematically?
Musical note frequencies follow an exponential relationship based on the equal temperament tuning system. The formula is f = refFreq times 2 raised to the power of (n divided by 12), where refFreq is the reference frequency (typically 440 Hz for A4) and n is the number of semitones from the reference note. Each octave doubles the frequency, and since there are 12 semitones per octave, each semitone represents a frequency ratio of the 12th root of 2, which is approximately 1.05946. For finer tuning adjustments, cents are used where 100 cents equal one semitone, giving the formula f = refFreq times 2 raised to the power of (cents divided by 1200).
What are harmonics and how do they relate to the fundamental frequency?
Harmonics are integer multiples of a fundamental frequency that naturally occur when a string, air column, or other resonator vibrates. The first harmonic is the fundamental itself. The second harmonic is twice the fundamental frequency, producing a note one octave higher. The third harmonic is three times the fundamental, approximately an octave plus a perfect fifth. The pattern continues with increasingly complex intervals. Harmonics determine the timbre or tone color of an instrument, which is why a violin and a flute playing the same note sound different despite having the same fundamental frequency. Each instrument produces a unique combination of harmonic amplitudes called its harmonic spectrum.
How does wavelength relate to frequency and why does it matter for acoustics?
Wavelength and frequency are inversely related through the speed of sound: wavelength equals speed of sound divided by frequency. At room temperature of 20 degrees Celsius, sound travels at approximately 343 meters per second. A low note like A2 at 110 Hz has a wavelength of about 3.12 meters, while a high note like A6 at 1760 Hz has a wavelength of only 19.5 centimeters. Wavelength matters enormously for acoustics because sound waves interact with obstacles relative to their wavelength. Low frequencies with long wavelengths diffract around obstacles easily, which is why bass sounds penetrate walls. Room dimensions should ideally not be exact multiples of common wavelengths to avoid standing wave resonance problems.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Can I use the results for professional or academic purposes?
You may use the results for reference and educational purposes. For professional reports, academic papers, or critical decisions, we recommend verifying outputs against peer-reviewed sources or consulting a qualified expert in the relevant field.
Does Note Frequency Calculator work offline?
Once the page is loaded, the calculation logic runs entirely in your browser. If you have already opened the page, most calculators will continue to work even if your internet connection is lost, since no server requests are needed for computation.