Dichterechner – Masse, Volumen und Dichte

ρ = m / V (Dichte = Masse ÷ Volumen). Wenn Sie Masse und Volumen kennen, teilen Sie die Masse durch das Volumen, um die Dichte zu erhalten. Wenn Sie zwei der drei Größen kennen, können Sie die dritte berechnen: m = ρ × V oder V = m / ρ.

Wasser hat eine Dichte von 1,000 g/cm³ (oder 1.000 kg/m³) bei 4°C, wo es am dichtesten ist. Bei Raumtemperatur (~20°C) beträgt die Dichte 0,998 g/cm³. Salzwasser ist dichter (~1,025 g/cm³), was erklärt, warum man im Meer leichter schwimmt.

Eis hat eine Dichte von 0,917 g/cm³, während flüssiges Wasser 1,000 g/cm³ hat. Da Eis weniger dicht ist, schwebt es oben. Das ist eine ungewöhnliche Eigenschaft – die meisten Substanzen werden beim Einfrieren dichter. Für das Leben auf der Erde ist dies entscheidend: Seen frieren von oben nach unten zu, nicht umgekehrt.

Ice has a density of about 0.917 g/cm³ — less than liquid water at 1.000 g/cm³. This anomalous behavior occurs because water molecules form a crystalline hexagonal lattice structure when freezing, with hydrogen bonds holding molecules in a more open arrangement than in the liquid state. This creates about 9% more volume, lowering the density. Almost all other substances are denser as solids than as liquids. This property is critical for aquatic life — ice forms on the surface of lakes and oceans, insulating the liquid water below from further freezing.

Specific gravity (SG) is the dimensionless ratio of a substance's density to the density of a reference substance (usually water at 4 °C for liquids/solids, or air at STP for gases). Since water's density is 1.000 g/cm³, specific gravity is numerically equal to density in g/cm³. A specific gravity greater than 1 means the substance sinks in water; less than 1 means it floats. SG is widely used in brewing (to measure sugar content), petroleum (API gravity), and medicine (urinalysis).

Use the water displacement method (Archimedes' principle): fill a graduated cylinder with water and record the initial level. Gently submerge the object completely and record the new level. The difference equals the object's volume in cm³ (since 1 mL = 1 cm³). Weigh the object on a balance to get mass in grams. Then ρ = mass / volume. For very small objects, use a pycnometer. For objects that absorb water, coat them in wax or use a non-reactive liquid.

Yes. Most substances expand when heated, decreasing density. The relationship is ρ(T) ≈ ρ₀ / (1 + β × ΔT), where β is the volumetric thermal expansion coefficient. Water is anomalous: it reaches maximum density at 3.98 °C, then expands as it cools further to 0 °C. Gases are most affected — their density is inversely proportional to absolute temperature at constant pressure (from the ideal gas law). Mercury thermometers and fuel dispensers must account for thermal expansion in their measurements.

Osmium (Os) holds the record at 22.59 g/cm³ at room temperature, slightly denser than iridium (22.56 g/cm³). Both are platinum-group metals and are extremely rare. Osmium is so dense that a 1-liter cube would weigh 22.59 kg (about 50 pounds). For comparison, lead — often considered "heavy" — is only 11.34 g/cm³, roughly half the density of osmium.

Density serves as a "fingerprint" for materials. By measuring an unknown sample's mass and volume, you calculate its density and compare it against tables of known materials. This method was famously used by Archimedes to determine whether King Hiero's crown was pure gold (19.32 g/cm³) or a gold-silver alloy (lower density). In geology, mineral density combined with crystal structure, hardness, and luster is used for identification. In forensics, glass fragment density can link evidence to crime scenes.

True (absolute) density is the density of the solid material itself, excluding any pores or voids. Bulk density includes the air spaces between particles in a granular or porous material. For example, solid quartz sand has a true density of 2.65 g/cm³, but loose sand has a bulk density of roughly 1.50 g/cm³ because of air gaps between grains. Bulk density is critical in civil engineering (soil compaction), agriculture (seed storage), and pharmaceuticals (powder filling).

Heating air causes it to expand, reducing its density relative to the surrounding cooler air. The less dense warm air is buoyed upward by the denser cool air around it — the same principle as a balloon floating in water. This convection process drives weather patterns, ocean currents, and the operation of hot-air balloons. The density difference is calculated from the ideal gas law: ρ = P × M / (R × T). At 20 °C, air density is about 1.204 kg/m³; at 100 °C, it drops to about 0.946 kg/m³ — a 21% decrease.

A hydrometer is a sealed glass tube with a weighted bulb at the bottom and a calibrated scale on the narrow stem. When placed in a liquid, it sinks until the weight of liquid displaced equals its own weight (Archimedes' principle). In denser liquids, it floats higher (less displacement needed); in less dense liquids, it sinks lower. The density is read directly from the scale at the liquid surface. Hydrometers are widely used in brewing (measuring wort sugar content), automotive (testing battery acid and antifreeze), and petroleum (measuring fuel density).

The average human body density is approximately 0.95–1.10 g/cm³, depending on body composition. Lean tissue (muscle, bone, organs) has a density of about 1.10 g/cm³, while fat tissue is about 0.90 g/cm³. A person with more body fat has a lower overall density and floats more easily. This principle underlies hydrostatic weighing for body fat measurement: the subject is weighed underwater, and their body density is calculated, then converted to body fat percentage using the Siri equation: %fat = (495/ρ) − 450.