Question

I am working on an educational resource about the relative scales of resources compared to the earth. Attached is an example of the earth compared to various elements contained within, as well as a comparison of the sum of all water and the atmospheric gasses (at standard temperature and pressure). Such images are great for creating a sense of scale and displaying the fragility if earth's ecosystems.

I want to also include spheres of wet biomass, which I would imagine to be quite small. However, when I do math I am faced with spheres that seem too small. I did the math based on 3 methods and got answers of 6km to 14km diameter, based on Metric Ton estimates of 1.57E+12, 1.38E+11, 1.00E+12

Two folks on Quora estimate 10km diameter. My questions are these:

What is the appx wet biomass of all plant and animal life on earth?
What is the appx density of it such that it can be converted to volume?
Is it really so small? I am used to being humbled, but this seems excessive.

Answer 1

Estimates of the Earth's total biomass lead to a sphere ranging from 6 to 14 kilometers in diameter, which emphasizes the thinness of the biosphere relative to the planet. Calculations based on a biomass density similar to water's confirm that the sphere of wet biomass is quite minute compared to Earth's size.

Step-by-step explanation:

The question pertains to comparing the scale of the Earth's biomass to the size of the Earth itself. If we consider the total mass of living organisms on Earth to be about 2 trillion tons (2×10¹⁵ kg), and recognize that the density of biomass is similar to that of water, approximately 1000 kg/m³, then we can calculate the volume of this biomass.

The calculated diameter of the biomass sphere would indeed seem small relative to the size of Earth, which is consistent with the notion that life forms a very thin layer over the Earth's surface.

To estimate the volume of Earth's biomass, we use the formula V = mass/density, which leads us to convenient units for volume in cubic meters. Converting this volume to a sphere involves finding the radius that would fit this volume using the formula V = (4/3)πr³, and subsequently, calculating the diameter as 2 times the radius.

Your calculations yielding a biomass sphere with diameters ranging from 6 to 14 kilometers appear correct and indeed illustrate how physically small the totality of Earth's biomass is compared to the vastness of the planet itself.

Understanding the scale of Earth's biomass relative to the planet provides an insightful perspective on the fragility of Earth's ecosystems and the surprising scale of human impact.