American Lutherie #111 featured an article I wrote about all of the properties of the geometry of the flattop guitar that combine to determine the total height of the bridge and saddle over the surface of the top of the instrument.1 That article included a number of diagrams and all the math needed to make bridge height calculations for most styles of flattop guitar. This page includes a calculator that will do all of those calculations for you - you just fill in the blanks and press the Calculate button. For the most part the descriptions of the parameters here are self explanatory, but for all practical purposes you'll need to reference the article for its diagrams and terminology before using this calculator.
For the most part if what you are doing is building a conventional guitar you already have a target bridge height in mind (0.5" for steel string guitars and 10mm for classical guitars for example). In that case the calculator can be used to determine what neck angle is needed to achieve that bridge height, and what top doming height is needed to achieve that bridge height, etc. The calculator is also useful to show just how much relief affects action. Nice thing about a calculator is you can quickly and easily answer "what if" questions just by plugging in trial values and seeing what happens.
Initial appearance: September 9, 2012
Last updated: February 08, 2020
Instrument designers should know that the calculator will work for all types of guitars including archtops and solid body electrics and for similar instruments as well. Since the equations solve for bridge height, and for most instrument types the designer will have a target bridge height in mind, a good approach to use is to begin by specifying values for those parameters which will not be variable in the design. For the most part this means everything other than neck angle and, assuming the instrument will have a raised fretboard, overstand. Even in that case the designer probably has some target value for overstand in mind. Once the constant values are plugged into the equations a trial calculation can be made and the results compared to the bridge height target. The variable parameters such as neck angle are then modified and the calculation is repeated until you home in on the target bridge height. This generally does not take too many iterations. Note again that neck angle should be specified in increments that can be accurately cut in wood. For practical purposes this means that increments of 0.5 degrees is about the best you can do. Also keep in mind that even though the radii of dished forms are usually specified in feet or meters, the equations require these to be entered in whatever units the rest of the parameters are specified in (usually inches or mm). For instruments that will have raised fretboards you can fine tune the results most easily with changes to fretboard elevation, because this is directly related to bridge height.
Note that the calculator outputs the total bridge height including the saddle. Subtract a reasonable amount of saddle exposure from the total and that will give you the height of the bridge itself, without the saddle.
Guitar builders usually will check for proper neck angle by flattening the fretboard and putting a straight edge on it and looking to see that the straight edge just clears the top of the bridge sans saddle. The calculator can be used to calculate this as well. Just enter values of zero for action (s) and relief (sr).
The formulae for calculating bridge height as a function of the construction geometry of a flattop guitar are:
If values for lne and ljt are specified, the calculator can check for collision between the top and the underside of the fretboard. Note that a collision or a lack thereof is not necessarily a good or bad thing, but must be accounted for in the construction of the instrument. Again, see the referenced article for more information about this.
Mottola, R.M. “Fretboard/Top Plate Geometry of the Flattop Guitar” American Lutherie, #111