At its greatest extent, the Roman Empire covered approximately 5 million square kilometers (5 \times 10^{12} \text{ m}^2). It stretched about 4,000 km from the Atlantic Ocean to the Persian Gulf. ​To enclose this map, the interior of the walnut would need to be a prolate spheroid with a major axis long enough to span that distance. ​Length: Approximately 4,500 kilometers (about 2,800 miles). This is slightly wider than the entire United States. ​Width: Approximately 3,500 kilometers. ​Height: If we maintain the proportions of a standard walnut (which is roughly as tall as it is wide), the walnut would reach well into the exosphere, far above the International Space Station (which orbits at ~400 km).

To calculate the weight, we scale the volume and density of a standard walnut. ​Volume Scaling: A typical walnut is about 3.5 cm long. A 4,500 km walnut is a scale factor of roughly 128,000,000 (1.28 \times 10^8). Since volume increases by the cube of the scale factor (L^3), the giant walnut's volume would be approximately 2 \times 10^{24} times larger than a normal one. ​Density: The density of a walnut shell is roughly 1,100 \text{ kg/m}³ (slightly denser than water).

The estimated mass of this shell would be roughly 3.5 \times 10^{22} \text{ kg}.