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Acoustic Guitar String Size Calculator

Creating Your Own Custom String Sets:

With custom string sizes, you can easily tune your guitar to non-standard tunings and/or alter the loudness of the sound coming from each string (to eliminate, or create, imbalance from string to string).

For a stringed instrument such as a guitar, each open string will vibrate at a natural frequency which is directly proportional to the string's tension and inversely proportional to the string's diameter. That is, more tension on the string produces a higher frequency, while a larger string diameter produces a lower frequency.

 

Guitar String Size Calculator

Scale Length       inches        cm        
Desired Tension pounds       newtons
Desired Note      (a letter from A to G)
Desired Octave   (an octave from 1 to 5)

Frequency Hz
String Type         
Diameter   inches   mm

  Copyright 2010 - 2012, Richard Shelquist


Using the String Size Calculator:

This String Size Calculator will determine the string size (plain steel or phosphor bronze wound) which will produce the desired note at the desired string tension. Then, you can simply use the closest available string size, based upon that idealized calculation.

This calculator was created primarily for use with steel stringed acoustic guitars, but should work reasonably well for a variety of other steel stringed instruments which use phosphor bronze strings.

This calculator is not designed to handle nylon, gut or silk strings... only plain steel and phosphor bronze wound.

For electric guitars, if you use nickel plated steel round wound strings rather than the intended phosphor bronze wound strings, the steel round wound strings will tune to pitch with about 10% less tension than is shown by this calculator.

CAUTION: Please carefully check the applicability (and sensibility) of each recommendation of this experimental calculator. In my own tests, these calculations have proven quite reliable, but your use of this calculator is completely at your own risk.


Standard Tuning on the Guitar:

The standard guitar tuning of E A D G B E uses these notes and octaves:

           E2  A2  D3  G3  B3  E4 

An Example:

As an example of using the calculator, let's find out what size of string to use on a typical full-size acoustic guitar to get the note G3 using 25 pounds of string tension...

Scale length = 25.5 inches
Desired Tension = 25 pounds
Desired Note = G
Desired Octave = 3

And the answer is:  wound, diameter 0.02177 inches, 0.553 mm

 

Calculator Variables:

Here's some further information about the variables which you enter into the calculator:

Scale length is the distance from nut to bridge. For full-size acoustic guitars this is typically around 25.5 inches (65 cm). A longer string will vibrate at at lower frequency, so the strings for the low notes on an electric bass or on a piano are longer than typical guitar strings.

Desired tension of each string on an acoustic guitar varies from about 16 pounds (70 newtons) for extra-light strings to around 40 pounds (180 newtons) for heavy-gauge strings.

As a starting point, you can simply copy the string tensions from a standard set of strings that you like the feel of. For example, if you like the feel of D'Addario medium gauge strings in standard tuning, simply copy the manufacturer's string tension data for each individual string of your new custom design. Sometimes the string tensions are given on the string package, other times it is necessary to hunt for the data on the manufacturer's web site. (A few typical examples of manufacturer's string data are given at the end of this article.)

Low tension produces less sound, but the strings are easier to play. At tensions somewhere below 12 or 14 pounds, the string may be too loose to have acceptable sound quality.

Higher string tension produces louder sound, but is harder to play and too much tension may damage guitars which were not specifically designed for heavy gauge strings.

For most people, tensions around 20 to 30 pounds will be taut enough to have good tone, yet still fairly easy to play. Note that the calculator will only accept string tensions between 8 and 50 pounds (35 to 220 newtons).

An additional consideration when choosing strings is the inharmonicity of a stiff heavy-gauge string. An ideal string would produce a variety of harmonics which are exactly integer multiples of the fundamental frequency. However, the stiffer a string actually is, the farther the harmonics will be from their ideal integer multiples. The stiffness causes the higher modes to become progressively sharper.

Up to a point, such inharmonicity can be used to deliberately impart a unique "character" to the instrument. Wound strings generally have less inharmonicity than an equivalent plain (solid) string. For both ease of playing and reduced inharmonicity, most pre-packaged string sets utilize wound strings for diameters greater than something around 0.020 inch (0.50 mm) to 0.023 inch (0.58 mm), depending upon the desired string tensions.

For best intonation, the calculator will recommend plain steel strings diameters up to 0.020, and all strings larger than 0.020 will be calculated as phosphor bronze wound.

String tension can also be used to balance (or unbalance) the sound of your specific guitar. Prepackaged string sets are at best a compromise, and you may be able to achieve a quite different sound by changing the sizes of some of your strings. If a specific string is too loud, then choose a new string with less tension. And conversely, if a specific string is not loud enough, then choose a string with greater tension. Differences of 2 or 3 pounds are often quite significant for the smaller diameter strings (such as diameters of 0.012 or less).

In order to avoid overstressing the guitar and causing serious physical damage to the guitar, it is also important to note the total tension of all the strings. For most 6-string guitars, total tension (the total tension of all six strings) around 160 pounds is generally structurally safe and works nicely. For most 12-string guitars, total tension (the total tension of all twelve strings) around 260 pounds is generally structurally safe and sounds good.

Desired Note must be an capital (upper-case) letter from A through G, and you may indicate sharp with #, or flat with b (small letter b). The desired note must be exactly one of the following:

A, A#, Bb, B, C, C#, Db, D, D#, Eb, E, F, F#, Gb, G, G#, Ab

For instruments such as a guitar which have an essentially constant scale length for all the strings (as opposed to a harp or a piano which have different lengths of strings) there will be a practical limit of the highest and lowest notes that the instrument will be able to play on an open string. At the upper frequency limit, any available string will require so much tension that it will always break. And at the lower frequency limit, the strings become either too large or too loose. For a guitar with a scale length of 25.5 inches, it is generally impractical to achieve an open string resonating above A4 or below G1.

Desired Octave is a number which describes which octave the note is in. This calculator uses a style of notation which is variously called Scientific Pitch Notation, Note-Octave Notation or American Standard Pitch Notation. For more details about this system of notation, see, for example:

                       http://en.wikipedia.org/wiki/Scientific_pitch_notation 

In this system of notation, each octave number begins on the C note, and middle C on the piano is C4. Note that B3 is one half-step below C4. And, as a reference point, A4 is defined as 440 Hz.

For example, in this system of notation, the white keys on a portion of a piano keyboard below middle C would be called:

C2 D2 E2 F2 G2 A2 B2 C3 D3 E3 F3 G3 A3 B3 C4

Standard tuning on a guitar uses strings tuned to:

 E2  A2  D3  G3  B3  E4

The frequency of E2 (low E on standard guitar tuning) is 82.407 Hz. An octave lower would be E1 at 41.203 Hz, and another octave lower would be E0 at 20.602 Hz.


Choosing Available Sizes:

Armed with the ideal answer, use the closest available string diameter. In general, for strings less than 0.012 it is best to try to find a string within 0.001 of the ideal size. For strings larger than 0.012, it may be acceptable to use strings within 0.002 of the ideal size.

 

Error Messages:

The calculator tries to alert you to any potential problems by displaying brief error messages in the windows immediately below the calculations.

For a standard sized acoustic guitar it is generally impractical to have an open string resonate above A4 or below G1.

If a string is close to the calculated breaking point, it may be prone to breaking and may have a shorter life than other strings.

If a string is beyond its calculated breaking point, it is unlikely that you will be able to tune it up to pitch without breakage.

If a string is too small, see if a higher tension is acceptable.

If a string is too large, see if a lower tension is acceptable.

Note: This calculator cannot calculate the breaking point of wound strings, since there is no industry standard for the core diameter of wound strings. Therefore, only plain strings will show error messages related to string breakage. In general, the characteristics of the wound strings are based on data from D'Addario, and your results may differ if you use strings which have a markedly different core diameter.

 

Windows PC Tuner:

There is a handy piece of Windows software called AP Tuner which is freely available via the internet. The AP Tuner software provides an easy to use general purpose instrument tuner and/or pitch indicator for use on Windows PCs.

One of the nice features of the AP Tuner is that it shows the notes in the same pitch notation as has been used in this article, so that it's easy to see if you're at F2, F3 or F4 rather than simply F as is shown on most tuners.

With the AP Tuner software, any Windows PC with a microphone can be used to measure the pitch of any sound, which makes this both a very useful tool for instrument tuning, and also a fun tool for learning to accurately control one's vocal pitch.

    http://www.aptuner.com/cgi-bin/aptuner/apmain.html

 

Using Manufacturer's Data:

One way to gain insight into string sizes and string tensions is to study the data which major string companies provide in their literature.

Note that the different strings of a typical string-set generally have different tensions which have been selected to balance the sound of the various notes on a typical guitar. However, your guitar may respond nicely to some string tension changes based on how you want your specific instrument to sound. More tension (larger string) will make the string louder, and less tension (smaller string) will produce a softer sound.

Many string manufacturers provide detailed data about string tension, such as the following pre-packaged string sets for acoustic guitars, which can help to demonstrate typical examples of appropriate string tension for both structural integrity of the guitar and playability:

 
Extra-Light Gauge 6-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.010 0.25 16.2 7.35
  B3 0.014 0.36 17.8 8.07
  G3 0.023 0.58 27.9 12.65
  D3 0.030 0.76 27.1 12.29
  A2 0.039 0.99 25.4 11.52
  E2 0.047 1.19 20.7 9.39

 

Light Gauge 6-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.012 0.30 23.3 10.57
  B3 0.016 0.41 23.3 10.57
  G3 0.024 0.61 30.2 13.70
  D3 0.032 0.81 30.5 13.83
  A2 0.042 1.07 29.9 13.56
  E2 0.053 1.35 26.0 13.15



Medium Gauge 6-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.013 0.33 27.4 12.43
  B3 0.017 0.43 26.3 11.93
  G3 0.026 0.66 35.3 16.01
  D3 0.035 0.89 36.8 16.69
  A2 0.045 1.14 34.0 15.42
  E2 0.056 1.42 29.0 13.15

 


Heavy Gauge 6-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.014 0.36 31.8 14.42
  B3 0.018 0.46 29.5 13.38
  G3 0.027 0.69 38.4 17.41
  D3 0.039 0.99 45.2 20.50
  A2 0.049 1.24 40.0 18.14
  E2 0.059 1.50 32.2 14.60

 

Light Top/Medium Bottom 6-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.012 0.3 23.3 10.57
  B3 0.016 0.41 23.3 10.57
  G3 0.025 0.64 32.8 14.88
  D3 0.035 0.89 36.8 16.69
  A2 0.045 1.14 34.0 15.42
  E2 0.056 1.42 29.0 13.15

 

Extra-Light Gauge 12-string (data from D'Addario):

Diameter Tension
Note inches mm lbs kg
E4 0.009 0.23 13.1 5.94
E4 0.009 0.23 13.1 5.94
B3 0.013 0.33 15.4 6.98
B3 0.013 0.33 15.4 6.98
G3 0.021 0.53 23.1 10.48
G4 0.008 0.20 14.7 6.67
D3 0.029 0.74 25.2 11.43
D4 0.011 0.28 15.6 7.07
A2 0.036 0.91 21.9 9.93
A3 0.016 0.41 18.5 8.39
E2 0.045 1.14 19.1 8.66
E3 0.026 0.66 24.9 11.29

 

Light Gauge 12-string (data from D'Addario):

Diameter Tension
  Note inches mm lbs kg
  E4 0.010 0.25 16.2 7.35
  E4 0.010 0.25 16.2 7.35
  B3 0.014 0.36 17.8 8.07
  B3 0.014 0.36 17.8 8.07
  G3 0.023 0.58 27.2 12.65
  G4 0.008 0.20 14.7 6.67
  D3 0.030 0.76 27.1 12.29
  D4 0.012 0.30 18.5 8.39
  A2 0.039 0.99 25.4 11.52
  A3 0.018 0.46 23.4 10.61
  E2 0.047 1.19 20.7 9.39
  E3 0.027 0.69 27.1 12.29

 

Enjoy!

 

 

 

http://wahiduddin.net/calc
----- Shelquist Engineering -- Richard Shelquist -- Longmont, Colorado -----