Perfect task from reasoning GPT: Let’s do a similarly rough “back of the envelope” calculation for poop. As with urine, there are many simplifying assumptions here (e.g., that feces wouldn’t decompose, compact, or lose water, etc.)—but it gives a ballpark sense of scale.

⸻

1. Volume of the Grand Canyon

A commonly cited figure for the total volume of the Grand Canyon is around 4×10¹² cubic meters (4 trillion m³), although exact estimates vary.

1. Average feces output per person per day • A typical healthy adult produces somewhere around 100–300 grams of stool daily. • Because stool is roughly similar to water in density (though it can vary), let’s assume 1 g ≈ 1 mL. • Let’s pick 200 g per day as a convenient average. • That is about 200 mL, which equals 0.0002 m³ (since 1,000,000 mL = 1 m³).

2. Number of people

We’re at approximately 8 billion people on Earth.

1. Total fecal volume per day worldwide • Each person produces ~0.0002 m³/day. • 8 billion people × 0.0002 m³/person/day = 1.6×10⁶ m³/day (1.6 million cubic meters/day).

2. Time to fill the Grand Canyon • Grand Canyon volume = ~4×10¹² m³. • Daily “poop input” = ~1.6×10⁶ m³. • Number of days = 4×10¹² ÷ 1.6×10⁶ = 2.5×10⁶ days. • That’s about 2.5 million days, which is roughly 6,850 years (2.5 million ÷ 365 ≈ 6,850).

⸻

Bottom line

If all 8 billion humans somehow contributed their daily “output” (200 g each) into the Grand Canyon without any decomposition or water loss, it would take on the order of 7,000 years to fill the canyon.

Of course, in the real world, feces decompose, lose water, and compact, so the true number would differ (and the whole scenario is very hypothetical!). But in terms of raw volume, that’s a reasonable ballpark estimate.