Ground Temperature Calculator

Damping depth is √(365·α/π), derived from your soil's thermal diffusivity, and it represents how far the seasonal temperature signal has to travel before it's largely smoothed out. Every other depth-dependent result — the damping factor and the phase shift — is expressed relative to this one number, so it's the first thing the Kasuda equation needs before it can find the temperature at any specific depth.

It traces to Tamami Kusuda and P.R. Achenbach's 1965 paper "Earth Temperature and Thermal Diffusivity at Selected Stations in the United States," published in ASHRAE Transactions — the original spelling is "Kusuda," though "Kasuda" is widely used as an alternate spelling in geothermal and HVAC industry materials. The same cosine model — mean annual temperature, seasonal amplitude, damping depth, and phase shift — is still implemented today in building-energy simulation tools like EnergyPlus under the name "Kusuda-Achenbach undisturbed ground temperature model."

Day 35 (roughly early February) is a fixed northern-hemisphere assumption baked into the Kasuda phase term, representing when surface temperatures typically bottom out. If you're modeling a southern-hemisphere location, the seasonal cycle is inverted, so the result will be roughly six months out of phase unless you manually offset the day-of-year input by about 182 days.

Stable depth estimates how far down you'd need to go before the seasonal temperature swing shrinks below roughly 1°F, at which point the ground is essentially at your site's mean annual air temperature year-round. Loops buried well past this depth see a fairly constant source temperature regardless of season, which is why vertical bores (which go far deeper) are less exposed to seasonal swings than shallow horizontal trenches.

Diffusivity directly sets the damping depth, so higher-diffusivity ground like rock lets the seasonal signal travel deeper and faster than dense, wet clay with lower diffusivity — that shifts both the damping factor and the phase shift meaningfully at any given depth. Because diffusivity feeds into nearly every other output, choosing a value that doesn't match your actual soil type is the single biggest source of error in this calculator.