A building's lifetime carbon has two parts. Embodied carbon E₀ is a one-time debt paid when the structure is built — extracting, manufacturing and erecting concrete, steel or timber. Operational carbon Ċ accrues every year the building is heated, cooled and lit:
Cumulative_op(t) = Ċ · t
Total(t) = E0 + Ċ · t
t* = E0 / Ċ (crossover: cumulative operational catches up to embodied)
Before t*, the one-time embodied debt is still the larger share of the building's footprint (green zone). After t*, the running operational total has overtaken it and keeps compounding every year the building stands (red zone) — the same amortization logic as any fixed cost racing against a recurring one.
- Embodied carbon slider — a low-carbon material mix (more mass timber, less steel) starts the flat line lower, so operational carbon overtakes it sooner.
- Operational carbon slider — better insulation, efficient HVAC and a cleaner electricity grid flatten this line's slope, pushing the crossover later or off the chart entirely.
- Lifespan slider — sets how far the chart extends and whether the crossover falls inside or outside the building's usable life. A building demolished before t* never let its operational emissions overtake its embodied ones.
- The shaded region is green while embodied still exceeds cumulative operational, and turns red once operational carbon has caught up and passed it.
Illustrative figures used here: a concrete/steel tower runs a high embodied line (≈500-900 kg CO₂e/m²) with average operational carbon; a mass-timber building starts much lower (net biogenic storage can even push it toward zero) but needs a well-insulated envelope to keep its operational slope shallow enough to stay ahead over a real 50-year lifespan.