CalcStack — free, instant, no signup. The interactive calculator loads automatically.
500 g in 200 cm³ is 2.5 g/cm³ — sinks. Oak at 0.6 floats. Gold is 19.3, which is why the fake-gold test is pure density.
Density is the identity card of materials — ice floats at 0.917, steel sinks at 7.85, and gold at 19.3 is so dense that fakes give themselves away on a scale. This calculator solves ρ = m/V in all three directions and gives the verdict everyone actually wants: does it float?
Science students and metal buyers use ρ = m/V: 500 g in 200 cm³ is 2.5 g/cm³ — sinks — with the float/sink verdict and the gold-fake test built in.
Because ice is less dense than liquid water — 0.917 g/cm³ versus 1.000 — and anything less dense than its surrounding fluid floats. Water is the weird exception: nearly every other substance is denser as a solid, but water's crystal lattice forces molecules into an open hexagonal arrangement that takes more space. The consequences run deep: ice floats, so lakes freeze top-down and fish survive winter under an insulating ice sheet; if ice sank, lakes would freeze solid from the bottom and temperate aquatic life would not exist. The same density logic runs your kitchen: oil floats on water (0.91–0.93), cream rises on milk, and a hydrometer tells a brewer the sugar content by how high the float sits.
Gold's density — 19.3 g/cm³ — is nearly impossible to fake cheaply. The test: weigh the piece, then measure volume by water displacement (submerge in a graduated cylinder, the rise in mL equals cm³), and divide. Real gold reads ~19.3; brass (8.5), copper (8.96), and gold-plated tungsten are the tells — only tungsten (19.25) is close enough to pass a density test, which is why high-value bars get ultrasonic or XRF testing too. Archimedes allegedly invented this method to catch a goldsmith who alloyed a crown with silver (density 10.5) — same weight, bigger volume, exposed by displacement. For jewelry: 24k is 19.3, but 18k (75% gold) reads ~15.5 and 14k ~13.5 depending on the alloy, so know your karat before judging.
Water 1.0 g/cm³ is the anchor — everything is judged against it. Below it (floats): ice 0.917, most woods 0.4–0.8, gasoline 0.74, olive oil 0.92. Above it (sinks): aluminum 2.7, titanium 4.5, steel 7.85, copper 8.96, lead 11.34, mercury 13.6 (a liquid denser than lead — cannonballs float on it), gold 19.3, tungsten 19.25, platinum 21.4, osmium 22.6 (densest element). The practical applications: concrete ships at ~2.4 g/cm³ which prices freight by the pallet; aluminum at one-third of steel's density is why aircraft exist; and lead's 11.34 makes it the cheap radiation shield and fishing sinker. One conversion to memorize: 1 g/cm³ = 1,000 kg/m³ = 62.4 lb/ft³.