Density to Weight Calculator — Mass, Force, and Shape Templates
Density multiplied by volume gives mass (kg). Mass multiplied by gravitational acceleration (9.81 m/s²) gives weight as force (N). In engineering, "weight" usually means force in newtons (N) or kilonewtons (kN), not mass in kilograms, so this calculator outputs both.
The calculator includes 8 common engineering shape templates — rectangular plate, cylinder, hollow tube, sphere, cone, hex bar, and custom volume — so you can enter geometry directly. It shares the same 232-material database as the material density calculator.
Select a material to preload density, or choose Enter custom density and type your own value.
Shape selector
Rectangular block dimensions
V = L × W × H
Gravity settings (advanced)
Mass vs Weight: An Important Distinction
In everyday language, "weight" and "mass" are used interchangeably. In physics and engineering, they are fundamentally different quantities. Mass (m) is the amount of matter in an object, measured in kilograms (kg). It does not change with location. Weight (W) is the gravitational force acting on that mass, measured in Newtons (N). Weight depends on the local gravitational field strength. For the base concept, see what is density.
Where:
- W = weight / gravitational force (N)
- m = mass (kg)
- g = gravitational acceleration (m/s²)
On Earth's surface, g varies from 9.780 m/s² at the equator to 9.832 m/s² at the poles, with a standard reference value of 9.80665 m/s². For most engineering calculations, 9.81 m/s² is used.
Structural engineers work in kilonewtons (kN) for forces and loads. A mass of 1,000 kg exerts a gravitational force of approximately 9.81 kN. The unit "kgf" (kilogram-force) is a legacy unit still used in some industries: 1 kgf = 9.80665 N, so a 100 kg object has a weight of 100 kgf ≈ 981 N. The calculator outputs both SI (N, kN) and legacy (kgf, lbf) units for compatibility with different engineering standards.
Shape Volume Formulas Reference
These are the 8 built-in shape volume formulas used by the calculator for manual checking or quick reference without the tool.
| Shape | Volume Formula | Variables |
|---|---|---|
| Rectangular block | V = L × W × H | L = length, W = width, H = height |
| Cylinder / Round bar | V = π/4 × D²L | D = diameter, L = length |
| Hollow tube / Pipe | V = π/4 × (Dₒ² − Dᵢ²)L | Dₒ = OD, Dᵢ = ID, L = length |
| Sphere | V = π/6 × D³ | D = diameter |
| Hollow sphere | V = π/6 × (Dₒ³ − Dᵢ³) | Dₒ = OD, Dᵢ = ID |
| Cone | V = π/12 × D²H | D = base diameter, H = height |
| Hexagonal bar | V = √3/2 × AF² × L | AF = across flats, L = length |
For hollow tube: ID = OD − 2t, where t is wall thickness. For hexagonal bar: the formula uses "across flats" (AF) dimension, which is the distance between two parallel flat faces (the wrench size). Across corners = AF / cos(30°) = AF × 1.1547.
Worked Examples
Example 1 — Steel plate dead load (structural engineering)
Material: Structural steel (density of steel: 7,850 kg/m³)
Shape: Rectangular block
Dimensions: 3,000 mm × 1,500 mm × 12 mm
Volume: 3.0 × 1.5 × 0.012 = 0.054 m³
Mass: 7,850 × 0.054 = 423.9 kg
Weight: 423.9 × 9.81 = 4,158 N = 4.16 kN
Application: Dead load contribution for structural slab design.
Example 2 — Aluminum round bar (manufacturing)
Material: Aluminum 6061 (density of aluminum: 2,700 kg/m³)
Shape: Cylinder
Dimensions: Diameter 50 mm, Length 2,000 mm
Volume: π/4 × 0.05² × 2.0 = 0.003927 m³
Mass: 2,700 × 0.003927 = 10.60 kg
Weight: 10.60 × 9.81 = 104.0 N
Application: Shipping weight estimate for a 2 m aluminium bar stock.
Example 3 — Steel pipe batch order (procurement)
Material: Carbon steel (7,850 kg/m³)
Shape: Hollow tube
Dimensions: OD 114.3 mm, Wall thickness 6.02 mm, Length 6,000 mm
ID: 114.3 − 2×6.02 = 102.26 mm
Volume per pipe: π/4 × (0.1143² − 0.10226²) × 6.0 = 0.01232 m³
Mass per pipe: 7,850 × 0.01232 = 96.7 kg
Quantity: 50 pipes
Total mass: 4,835 kg | Total weight: 47.4 kN
Example 4 — Object weight on the Moon (physics / aerospace)
Material: Concrete (density of concrete: 2,400 kg/m³)
Shape: Rectangular block
Dimensions: 1.0 m × 1.0 m × 0.5 m
Volume: 0.5 m³
Mass: 2,400 × 0.5 = 1,200 kg (same on Moon and Earth)
Weight on Earth (g = 9.81): 1,200 × 9.81 = 11,772 N = 11.77 kN
Weight on Moon (g = 1.62): 1,200 × 1.62 = 1,944 N = 1.94 kN
The concrete block weighs 6× less on the Moon, but its mass is unchanged.
Common Material Weights per Unit Volume
These are common engineering material masses and gravitational forces per cubic metre for fast estimation without the calculator.
| Material | Density (kg/m³) | Mass per m³ | Weight per m³ | Weight per cm³ |
|---|---|---|---|---|
| Air | 1.225 | 1.225 kg | 12.0 N | 0.000012 N |
| Softwood (pine) | 500 | 500 kg | 4.91 kN | 0.00491 N |
| Hardwood (oak) | 750 | 750 kg | 7.36 kN | 0.00736 N |
| density of concrete | 2,400 | 2,400 kg | 23.5 kN | 0.0235 N |
| density of aluminum | 2,700 | 2,700 kg | 26.5 kN | 0.0265 N |
| Glass | 2,500 | 2,500 kg | 24.5 kN | 0.0245 N |
| density of steel | 7,850 | 7,850 kg | 77.0 kN | 0.0770 N |
| Copper | 8,960 | 8,960 kg | 87.9 kN | 0.0879 N |
| density of lead | 11,340 | 11,340 kg | 111.2 kN | 0.1112 N |
| density of gold | 19,320 | 19,320 kg | 189.5 kN | 0.1895 N |
Weight per m³ = density × 9.81 m/s². For structural engineering: 1 kN/m² (kPa) = 101.97 kgf/m². Steel floor plate at 10 mm thickness: 7,850 × 0.01 × 9.81 = 770 N/m² = 0.77 kPa dead load.
Related Calculators
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Frequently Asked Questions
What is the difference between weight and mass in engineering?
Mass (kg) is the amount of matter — it is constant regardless of location. Weight (N) is the gravitational force on that mass — it varies with gravitational acceleration. On Earth, a 100 kg object weighs 981 N (≈ 100 kgf). On the Moon, the same object still has a mass of 100 kg but weighs only 162 N. Structural engineers use weight (force in kN) for load calculations because structures must resist gravitational forces, not masses.
How do I calculate the weight of a steel plate?
Multiply the plate dimensions to get volume, multiply by steel density (7,850 kg/m³) to get mass, then multiply by 9.81 m/s² to get weight in Newtons. For a 2,000 × 1,000 × 10 mm plate:
V = 2.0 × 1.0 × 0.01 = 0.02 m³
Mass = 7,850 × 0.02 = 157 kg
Weight = 157 × 9.81 = 1,540 N = 1.54 kN.
How do I calculate the weight of a pipe?
Use the hollow tube formula. Volume = π/4 × (OD² − ID²) × Length, where ID = OD − 2 × wall thickness. Multiply by material density to get mass, then by 9.81 for weight. The calculator above handles this automatically when you select the "Hollow tube" shape template.
What is kgf (kilogram-force)?
Kilogram-force (kgf) is a legacy unit of force equal to the weight of 1 kg under standard gravity: 1 kgf = 9.80665 N. It is still used in some industries (hydraulics, pressure gauges, older engineering standards). Numerically, a mass of X kg has a weight of approximately X kgf on Earth's surface, which is why the two are often confused in everyday use.
Why does gravity vary across the Earth's surface?
Earth is not a perfect sphere — it is slightly flattened at the poles and bulges at the equator. Objects at the equator are further from Earth's centre (lower gravity) and also experience centrifugal force from Earth's rotation (further reducing effective gravity). The result is g = 9.780 m/s² at the equator vs 9.832 m/s² at the poles — a difference of about 0.5%. For most engineering purposes, the standard value of 9.80665 m/s² is used.
How many pieces can I calculate at once?
The calculator supports a quantity multiplier for batch calculations. Enter the number of pieces and the calculator will output the total mass and total weight for the entire batch. This is useful for procurement (total shipping weight of a steel order) or structural analysis (total dead load from multiple identical beams).