Surface-to-Volume Ratio Calculator

For a sphere of diameter d, surface area is πd² and volume is (π/6)d³, so S/V simplifies to 6/d. For a cube of side length d, surface area is 6d² and volume is d³, which also simplifies to 6/d — it's a coincidence of how these two particular shapes' surface and volume terms cancel, not a general rule that applies to other shapes like the cylinder, which instead uses the full surfaceArea/volume ratio.

It divides your particle's computed S/V ratio by the S/V ratio a 1 mm bulk particle of the same shape would have (6 per million nm, since 1 mm = 1,000,000 nm). Because S/V scales inversely with size, shrinking a particle from millimeter to nanometer scale — a factor of roughly a million in diameter — produces a proportionally enormous enhancement, which is the whole point of the comparison: it makes the nanoscale surface effect concrete rather than abstract.

No, it's a rough geometric approximation using the formula 4 × (atomic diameter / particle diameter) × 100, with atomic diameter fixed at a generic 0.3 nm regardless of what material you're modeling. It's useful for seeing the general trend — that surface atom fraction climbs sharply as particles shrink below roughly 10 nm — but it isn't calibrated to any specific crystal structure or element.

That calculation converts your particle's surface area and volume into mass using a hard-coded density of 19.3 g/cm³, which is gold's density, regardless of the shape or size you actually entered. If you're modeling a different material — silver, silica, polystyrene, or anything else — that one output will be off by exactly the ratio between gold's density and your material's real density, so treat it as illustrative unless gold is genuinely what you're calculating.