Resistance wire length  
Wrap count Number of wraps  
— rounded to "full wraps"  
— rounded to "half wraps"  
Coil Ω Resistance per coil  Ω  
Heat flux
@
W

^{mW}/_{mm²} ^{mW}/_{in²}  
Heat capacity (each coil)  mJ K^{1}  
Leg loss Leg power loss  % 
Wire length (l_{r}  l_{l})  
Outer ⌀ Outer diameter (⌀_{c}+2⌀_{r})  
Neutral axis ⌀ Neutral axis diameter  
Circumference Loop circumference  
Helix angle Helix angle  °  
Loop length Length of each loop  
Width  
Surface area  mm² in² 
Volume  mm³ in³  
Density  ^{g}/_{cm³} ^{oz}/_{in³}  
Mass  mg gr  
Surface area  mm² in²  
Cross section area  mm² in² 
All calculations are done in JavaScript, which uses 64 bit floating point. This yields a precision of 15–17 significant decimal digits, which is more than sufficient for the purpose of modeling a coil build.
Internally, all variables are stored and calculated in metric units. Unneccessary unit conversions are avoided in order to prevent accumulation of rounding errors when using imperial units.
Three values are written to the input fields during use (advanced mode): Wire diameter, wire resistance per mm, and resistance wire length. These numbers are rounded in the input fields, but still preserved with full precision in memory. If you manually override a value, you can enter your own number with any precision you want. When you save, and subsequently load the settings, rounded values will be displayed, but the number will still exist with the full precision in memory.
AWG is converted to diameter by using the formula that defines AWG. This should make the AWG conversion more precise than the numbers stated by many resistance wire vendors.
Wire resistance per length is determined by the specific resistivity of the wire material, and the cross section area of the wire. The specific resistivity for each material is looked up in a small table of constants.
The resistance wire length is your set target resistance divided by the wire resistivity per mm. Leg length is subtracted before calculating the number of wraps.
Material  Specific resistivity (^{Ω mm²}/_{m}) 

Kanthal A1/APM  1.45 
Kanthal A/AE/AF  1.39 
Kanthal D  1.35 
Nichrome N20  0.95 
Nichrome N40  1.04 
Nichrome N60  1.11 
Nichrome N70  1.18 
Nichrome N80  1.09 
When you input the inner diameter of the coil, the outer diameter is simply the inner diameter plus twice the wire thickness. The circumference of your coil is then by multiplying the outer diameter with π, and we have length of a single wrap. The wrap does not go in a straight circle around the mandrel, but rather in a helix, making it slightly longer than the coil circumference. For twisted coils, the 2–4 strands are combined into one diameter using the diameter of an outer circle encompassing the 2 4 tangent circles of each strand.
The heat flux is more or less evenly distributed over the resistance wire. Hot legs are undesirable, so the power used to heat the legs can be regarded as "lost".
The density of the coil material is used to calculate the wire mass and heat capacity. Because of lacking data on the density of different Nichrome alloys (except N80), the density of the Nichrome qualities are interpolated from the densities of the main alloy elements.
The heat capacity of the wire materials do not vary much between the alloys used. Therefore 0.46 kJ kg^{1} K^{1} is used for all kanthal, and 0.447 kJ kg^{1} K^{1} is used for all nichrome.
This coil calculator is a pretty simple and straightforward digital model of the geometry and electrical properties of an atomizer coil, and can be expected to be concistent with at least itself. Real life, on the other hand, involves a myriad of ways to introduce error to your numbers:
These are some of the factors that can impact real life accuracy. Another possible error source is the inner diameter of the coil. If the mandrel is off spec by only 0.1 mm, the length of a single wrap will be off by roughly 0.314 mm. Multiplied by ten wraps, this small error has grown more than thirtyfold. The output from a calculator can never be better than the input.
All these error sources can cancel each other out to some degree, but they can also add up. This is one of the reasons why you should always have a decent multimeter handy, and measure your coil after you build it. A model is great for getting you into the ballpark, but getting the final build right still requires your skills, and some measuring equipment. The Steam Engine is not intended to replace a multimeter.