Mass Calculator
Free Mass Calculator for math. Enter values to solve step-by-step with verified formulas, worked examples, and detailed explanations. Free math tool.
Formula
Mass = Density × Volume
Mass equals density multiplied by volume. Rearrange to find density (m÷V) or volume (m÷ρ). Ensure consistent units.
Worked Examples
Example 1: Steel Beam Mass
Problem:Calculate the mass of a steel beam with volume 0.05 m³.
Solution:Density of steel = 7850 kg/m³ Volume = 0.05 m³ Mass = Density × Volume Mass = 7850 × 0.05 = 392.5 kg In pounds: 392.5 × 2.205 = 865.5 lb
Result:392.5 kg (865.5 lb)
Example 2: Water Tank Volume
Problem:How much volume does 500 kg of water occupy?
Solution:Density of water = 1000 kg/m³ Mass = 500 kg Volume = Mass ÷ Density Volume = 500 ÷ 1000 = 0.5 m³ In liters: 0.5 × 1000 = 500 L
Result:0.5 m³ (500 liters)
Example 3: Unknown Material Density
Problem:An object has mass 270 g and volume 100 cm³. What material might it be?
Solution:Mass = 270 g = 0.27 kg Volume = 100 cm³ = 0.0001 m³ Density = Mass ÷ Volume Density = 0.27 ÷ 0.0001 = 2700 kg/m³ This matches aluminum!
Result:2700 kg/m³ (Aluminum)
Frequently Asked Questions
How do I calculate mass from density and volume?
Use the formula: Mass = Density × Volume. For example, if water has density 1000 kg/m³ and volume is 0.5 m³, then mass = 1000 × 0.5 = 500 kg. Make sure units are consistent.
What is the difference between mass and weight?
Mass is the amount of matter in an object (measured in kg), while weight is the gravitational force on that mass (measured in Newtons). On Earth, weight = mass × 9.81 m/s². Mass is constant everywhere; weight varies with gravity.
How do I find the density of an object?
Measure the object's mass (using a scale) and volume (by displacement or geometric calculation). Then divide: Density = Mass ÷ Volume. Common units are kg/m³ or g/cm³.
What are common material densities?
Water: 1000 kg/m³, Aluminum: 2700, Steel: 7850, Copper: 8960, Gold: 19300, Wood: 500-900, Concrete: 2400, Air: 1.225 kg/m³. These are approximate values at room temperature.
How do I convert between density units?
To convert kg/m³ to g/cm³, divide by 1000. To convert g/cm³ to lb/ft³, multiply by 62.428. Water is 1 g/cm³ = 1000 kg/m³ = 62.4 lb/ft³.
Why does density matter in engineering?
Density determines buoyancy (whether objects float), structural weight calculations, material selection, shipping costs, and is crucial for designing aircraft, ships, buildings, and packaging.
How does temperature affect density?
Most materials expand when heated, decreasing density. Water is unusual: it's densest at 4°C (1000 kg/m³) and less dense as ice (917 kg/m³), which is why ice floats.
How do I calculate mass of irregular objects?
Use water displacement: submerge the object in water and measure the volume of water displaced. Then multiply by the material's density. This is Archimedes' method.
What's the densest common material?
Among common materials, gold (19,300 kg/m³) and lead (11,340 kg/m³) are very dense. Osmium is the densest element at 22,590 kg/m³. Platinum is 21,450 kg/m³.
Background & Theory
Mass, density, and volume are fundamental physical properties interconnected by a simple but powerful relationship: Density = Mass ÷ Volume.
Key Formulas:
Mass: m = ρ × V
Volume: V = m ÷ ρ
Density: ρ = m ÷ V
Where:
- m = mass (kg)
- V = volume (m³)
- ρ (rho) = density (kg/m³)
Common Density Units:
- kg/m³ (SI standard)
- g/cm³ (convenient for solids)
- lb/ft³ (US engineering)
- g/mL (liquids, same as g/cm³)
Density of Common Materials (kg/m³):
| Material | Density |
|---|---|
| Air | 1.225 |
| Water | 1,000 |
| Aluminum | 2,700 |
| Steel | 7,850 |
| Copper | 8,960 |
| Gold | 19,300 |
Buoyancy Principle:
Objects float if their density is less than the fluid they're in. Ships float because their average density (including air space) is less than water.
Applications:
- Material selection in engineering
- Shipping and logistics calculations
- Fluid mechanics and hydraulics
- Geology and mineralogy
- Food science and cooking