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Guitar String Diameter 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).

This calculator helps you select an appropriate string diameter. There is also a calculator to determine tension, when you know the string diameter.

 

Guitar String Diameter Calculator

Scale Length       inches        cm        
Desired Tension pounds       kg        
Desired Note      (a letter from A to G)
Desired Octave   (typically 0 to 5)

Results valid for any string material:
Unit Weight
Will resonate at desired pitch of
With the desired tension of
Results for plain steel strings:
Plain Steel String Diameter
Percent of plain string breaking tension
Some wound string diameter examples using D'Addario strings:
Phosphor Bronze - Round Wound
Phosphor Bronze - Flat Wound
80/20 Brass - Round Wound
85/15 Brass - Round Wound
Nickel Plated - Round Wound
Stainless - Round Wound
Stainless - Flat Wound
Bass - Nickel Plated- Round Wound

  Copyright 2010, 2018     Richard Shelquist


Using the String Diameter Calculator:

This String Diameter Calculator will determine the string diameter 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.

The Unit Weight is valid for any string construction and any string materials from any manufacturer. The Unit Weight of the desired string can be provided to your preferred string supplier (such as D'Addario or Kalium) to see if they offer a string with the required Unit Weight. In many cases, the resultant wound string will be around 1.1 to 1.2 times the diameter of the calculated plain string (but a plain string would be more difficult to bend, and would have greater inharmonicity).

The steel string calculations were originally created for guitar, but the calculations are valid for a variety of instruments which use steel or steel-core strings such as acoustic guitar, electric guitar, electric bass, mandolin and banjo.

If the calculator cannot provide appropriate data for the requested string size, it will simply display "na" (not available).

If the calculator results for wound strings do not include the type of string which you prefer, or you see the dreaded "na" indication, please use the Unit Weight value which the calculator provides.

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 30 pounds of string tension...

Scale length = 25.5 inches (65 cm)
Desired Tension = 30 pounds (14 kg)
Desired Note = G
Desired Octave = 3

The calculator predicts the following string diameters for various types of D'Addario strings: 
   Plain steel: 0.023 inches
   Phosphor Bronze - Round wound: 0.024 inches
   Phosphor Bronze - Flat wound: 0.022 inches
   80/20 Brass - Round wound: 0.024 inches
   85/15 Brass - Round wound: 0.024 inches
   Nickel-Plated Steel - Round wound: 0.025 inches
   Stainless Steel - Round wound: 0.024 inches
   Stainless Steel - Flat wound: 0.024 inches

 

Accuracy:

This calculator is only intended to provide a ballpark answer, perhaps within 5% or so of the actual tension of D'Addario strings... which in my experience is a lot closer than I often came by trial and error. Once I guessed wrong and ended up actually breaking pieces off of the bridge saddle, because I apparently had the tension of my lowest bass string accidentally cranked up to something over 100 pounds (45 kg)... it's a wonder the whole guitar didn't break! After that episode, I created the calculator as a way to verify that the string size is in the right ballpark, rather than risking damage to the instrument.

This calculator uses data from D'Addario for all of the wound strings, and therefore their strings should come close to matching the calculated values. Different string manufacturers have their own proprietary manner of making wound strings where the inner core diameter, winding material and diameter of the winding wire may be considerably different from any other manufacturer. Since few string manufacturers provide published string design details describing exactly how their wound strings are constructed, this calculator is designed around data provided by D'Addario for their strings, but should give results which are fairly close for similar products from other string manufacturers.

Please note that the Unit Weight calculation is valid for any string, made from any material, from any manufacturer, and may be your best bet for finding strings which are not shown in the calculator results.

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 a 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 (7 kg) for extra-light strings to around 40 pounds (18 kg) 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 on steel sting acoustic guitars, 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 instruments which were not specifically designed for such high tension.

For acoustic guitars, tensions around 20 to 30 pounds will be taut enough to have good tone, yet will still be fairly easy to play.

Note that the calculator will show a caution note when string tension is either lower or higher than customary for common instruments such as guitar, mandolin, banjo or electric bass.

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 instrument structure and causing serious physical damage to the instrument, it is important to note the total tension of all the strings. For safety, it is best to look up the total tension of the string set which is recommended by the manufacturer of your instrument, and use that tension as a target value. For many 6-string acoustic guitars, total tension (the total tension of all six strings) around 160 pounds (72 kg) is generally structurally safe and works nicely. For many 12-string acoustic guitars, total tension (the total tension of all twelve strings) around 260 pounds (118 kg) is generally structurally safe and sounds good.

Inharmonicity

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.

 

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:

    Wikipedia article about 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.


Interpreting the Calculator Results:

Unit Weight:

Unfortunately, there are so many different types of stringed instruments, and so many different types of string construction from so many different manufacturers, it is not practical for the calculator to show every possible string type for every possible stringed instrument. So, as an alternative, the calculator shows the "Unit Weight" of the desired string, with which you can happily go to your favorite string manufacturer's literature (and/or technical support) to find a string which has the desired unit weight.

The unit weight value is valid for any string material, from any manufacturer.

 

Choosing Applicable String 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.

If a calculated string diameter is too small for your application, see if a higher tension is acceptable.

If a calculated string diameter is too large for your application, see if a lower tension is acceptable.

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

 

Potential String Breakage:

With small diameter strings, the tension required to tune the string to the desired pitch may stress the string so much that it breaks easily. The calculator tries to help warn you about string breakage by displaying the percent of breaking tension which will be required to tune the string to the desired pitch.

Whenever the percentage is greater than about 60 to 70 percent, there is a significant likelihood that the string will be prone to breakage. As the percentage increases above 60 to 70 percent, any sort of defects in the string (such as scratches, nicks, kinks, or metal impurities) or bends in the string (such as bends at the bridge saddle, nut, or tuning machines) may lead to failure either while the instrument is being tuned to pitch or shortly thereafter. The sharper the bend, the greater the likelihood of breakage at a relatively low percentage.

As the percentage approaches 100 percent, string breakage becomes extremely likely. Only in the rarest of occasions will it be possible to exceed 100 percent without immediate breakage.

The exact breaking percentage will vary from string to string and will also vary somewhat depending upon the manufacturer of the string and the exact steel alloy which has been used. For this calculator, the minimum values for ASTM A228 music wire have been used, although some manufacturers claim to be able to provide strings which may exceed those values.

 

Error Messages:

There are three types of messages provided by the calculator to help alert you to potential problems:

 1) The percentage of string breaking tension is intended to help determine the likelihood of a string failure due to excessive stress in the string.

2) A "high tension" message appears when the string tension is higher than normally used in common instruments such as guitar, mandolin, banjo or electric bass. This message is intended to help avoid structural damage to the instrument, and may be too conservative for some instruments.

3) A "low tension" message appears when the string tension is much lower than normally used in common instruments such as guitar, mandolin, banjo or electric bass. This message is intended to help avoid excessively loose and unresponsive strings.

Note: This calculator cannot calculate the breaking point of wound strings, because 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.

 

Examples of Wound Strings:

All of the examples of wound strings use data from D'Addario, and therefore only apply to D'Addario wound strings.

This is not an advertisement for that particular manufacturer, but they are the only manufacturer which I've found who fully specifies the technical details such as Unit Weight and typical string tensions for all of their individual strings. Without those technical details, the desired calculations cannot be performed. Consequently, I've used the published data for their strings, and these results may be noticeably different than wound strings from other manufacturers.

 

Tuner Apps:

A very useful feature of some Tuner Apps is that they show the note using 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 many tuners.

Android:

My favorite Tuner for Android devices:

    Da Tuner

Windows:

There is a handy piece of Windows software called AP Tuner which is freely available via the internet. With the AP Tuner software, any Windows PC with a microphone can be used to measure the pitch of any sound:

    AP Tuner for Windows

 

Equations used in this Calculator:

This calculator is based on the equations and data provided by string manufacturer D'Addario in their PDF document located at:

D'Addario String Information Booklet

 

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!

 

Last updated: 6 Jul 2018

 

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----- Shelquist Engineering -- Richard Shelquist -- Colorado, USA -----