Each material starts at its embodied carbon — a one-time cost released while manufacturing and erecting the structure — then accumulates operational carbon every year the building is heated, cooled and lit.
cumulative(t) = embodied + operational_rate × t
crossover t* = (embodied_A − embodied_B) / (rate_B − rate_A)
- Embodied carbon — concrete and steel production is energy-intensive (cement calcination, blast-furnace steel), so it usually starts far higher than timber; well-sourced timber can even store more carbon than its processing releases.
- Operational rate — depends on how well-insulated and airtight the structure is, not just the material label; a badly detailed timber frame can leak more heat than a well-detailed concrete one, or vice versa — that's why both rates are independently adjustable here.
- Crossover — if the low-embodied material also has a higher operational rate, its cumulative total will eventually overtake the high-embodied material's; the crossover year is where that happens. It only exists within the plotted range if the rates differ and the sign works out.