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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)

Frequency
Unit Weight
Plain Steel String
Some wound string examples:
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 calculator was 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 does not have appropriate data for the requested string size, it will simply display "na" (not available).

For unusual applications, such as extremely low frequency bass strings, the calculator provides the desired Unit Weight of the required string, which can then be provided to specialty string suppliers (such as Kalium) to see if they offer a string with the required Unit Weight. In many cases, the resultant specialty 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).

This calculator is not designed to handle nylon, gut or silk strings... only steel core strings.

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 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 phosphor bronze guitar 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 guitar damage.

It is a difficult challenge to create an extremely accurate string size calculator, since various manufacturers have their own proprietary manner of making wound strings where the inner core diameter and diameter of the winding wire may be considerably different from any other manufacturer. Without detailed published string design details describing exactly how the wound string is constructed, it is essentially impossible to create a string calculator which does any better than giving a ballpark answer. This calculator uses data from D'Addario, and therefore their strings should come close to matching the calculated values.

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 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 guitars which were not specifically designed for heavy gauge strings.

For acoustic guitars, 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 5 and 50 pounds (2.3 to 23 kg).

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 structure and causing serious physical damage to the guitar, 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 guitar, 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.


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.

 

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!

 

 

 

https://wahiduddin.net/calc
----- Shelquist Engineering -- Richard Shelquist -- Colorado, USA -----