Mass Calculator

01

Mass represents the amount of matter in an object, calculated with the formula: Mass = Density × Volume. Density (ρ) is mass per unit volume, and volume (V) is the space occupied. For example, a 10cm × 10cm × 10cm iron cube (density 7.87 g/cm³) has mass: 7.87 × 1000 = 7,870g = 7.87kg. Aluminum (2.70 g/cm³) would be 2,700g = 2.7kg, about 3 times lighter. Mass is constant regardless of location or gravity, unlike weight which varies. Units: g (gram), kg (kilogram), ton. 1kg = 1000g, 1ton = 1000kg.

02

1. Cube/Cuboid: Volume = length × width × height. Example: 5m × 3m × 2m concrete block = 30m³. With concrete density 2.3 g/cm³, mass = 69,000kg = 69 tons. 2. Cylinder: Volume = π × radius² × height. Example: radius 10cm, height 20cm iron pipe = π × 10² × 20 = 6,283 cm³. With iron density 7.87 g/cm³, mass = 49.4kg. 3. Sphere: Volume = (4/3) × π × radius³. Example: radius 5cm gold sphere = 523.6 cm³. With gold density 19.32 g/cm³, mass = 10.1kg.

03

Construction Materials: Concrete 2.3~2.4 g/cm³ (1m³ = 2.3~2.4 tons), steel rebar 7.85 g/cm³, brick 1.8~2.0 g/cm³, wood (pine) 0.5~0.6 g/cm³. Metals: Iron 7.87 g/cm³, aluminum 2.70 g/cm³, copper 8.96 g/cm³, lead 11.34 g/cm³, titanium 4.51 g/cm³. Aircraft use lightweight aluminum alloys (2.7~2.8 g/cm³), cars use steel (7.85 g/cm³). Precious Metals: Gold 19.32 g/cm³, platinum 21.45 g/cm³, silver 10.49 g/cm³. 1L gold weighs 19.3kg.

04

Construction: Load calculation is essential for reinforced concrete structures. A 5-story building floor (100m², 20cm thick) concrete mass: 100 × 0.2 = 20m³ → 46 tons. Adding rebar (10%) gives ~50 tons per floor. Manufacturing: Aluminum window frame production requires accurate material calculation. Length 2m, cross-section 20cm² = 108g per frame. For 1000 frames: 108kg aluminum needed. Logistics: Container shipping requires weight limits (20ft container max 24 tons) calculation.

05

Floor Load: Living room floor (4m × 5m = 20m²) with 5cm concrete finishing: volume = 1m³ = 2.3 tons. Adding furniture and live load (200kg/m²) requires design for 4+ tons total. Crane Operations: Lifting steel beam (H-400×200×8×13, 10m length): cross-section ~84cm², volume 84,000 cm³ × 7.85 = 659kg. With safety factor 1.5, calculate as 1 ton. Bridge Design: 50m × 10m bridge deck (30cm concrete) self-weight: 345 tons.

06

1. Electronic Scales: From household (0.1g precision) to industrial (0.001g precision). Precious metal trading requires 0.01g precision - 1g error = significant loss. 2. Large Scales: Truck scales (max 100 tons), crane scales (max 50 tons) for cargo and steel weighing. 3. Indirect Measurement: Large structures measured by dimensions × density. Ships, aircraft, bridges use 3D modeling + material density. 4. Non-destructive Testing: Ultrasound, X-ray detect internal voids affecting actual density.