Step 1: Earth absorbs S(1−α)/4 = 1361×(1−0.30)/4 = 238 W/m². Find the no-atmosphere temperature and the greenhouse warming. Step 2: σT⁴ = 238 → T⁴ = 238/5.67×10⁻⁸ = 4.198×10⁹. Step 3: T = (4.198×10⁹)^{1/4}. √ = 64790, √ again = 254.5 K ≈ 255 K (−18 °C). Step 4: Actual surface average ≈ 288 K (15 °C). Greenhouse warming = 288 − 255 = 33 K. Step 5: CO₂ doubling forcing: ΔF = 5.35·ln2 = 3.7 W/m² → ΔT ≈ 0.8 × 3.7 ≈ 3 K (with feedbacks). Result: The atmosphere's 33 K blanket makes Earth habitable; thickening it with CO₂ adds ~3 K per doubling — the physics of global warming in one calculation.